Multi-objective optimization framework for sustainable olive oil supply chains: integrating environmental compliance with economic performance

Introduction: Mediterranean olive oil production faces a critical sustainability challenge: managing olive mill wastewater (OMW), a highly polluting byproduct (0.8–1.2 m³/ton) threatening environmental compliance and supply chain viability.

Methods: This study develops an integrated multi-objective Mixed-Integer Linear Programming framework that jointly optimizes harvest scheduling, processing allocation, and OMW management. The ε-constraint method generates Pareto frontiers revealing trade–offs between environmental performance, oil quality, and economic profit. Implementation used Python 3.9+ with Gurobi optimizer, validated through a Tunisian case study (18 groves, 4 teams, 3 mills, 14-day horizon).

Results: Operational optimization achieved 14.6% CO₂ emission reduction and maintained regulatory compliance. However, OMW valorization remained at 12.8%-far below 80% policy targets-revealing fundamental infrastructure-regulation disconnect. Multi-objective analysis shows balanced solutions achieve 80–85% of maximum performance across all dimensions, while single-objective approaches sacrifice 35–65% in non-prioritized objectives. Sensitivity analysis quantifies that doubling valorization capacity increases recovery to 23.6% with 30.8% profit improvement.

Discussion: The framework demonstrates that environmental constraints, when architecturally embedded, define opportunity spaces for competitive advantage rather than performance limitations. Infrastructure analysis provides actionable guidance for phased regulatory implementation with 3–4 season payback periods.

1 Introduction

Modern agricultural supply chains face unprecedented pressure to balance economic competitiveness with environmental sustainability, particularly in Mediterranean agri-food systems where traditional practices must adapt to stringent environmental regulations and circular economy imperatives. The olive oil industry exemplifies this challenge, where production scaling to meet global demand generates significant environmental externalities that threaten the long-term viability of supply chain operations.

In Mediterranean olive oil supply chains, the management of olive mill wastewater (OMW) represents a critical bottleneck that directly impacts operational efficiency, regulatory compliance, and environmental performance. OMW, a toxic liquid byproduct rich in organic matter and phenolic compounds, generates approximately 0.8–1.2 m³ per ton of processed olives and ranks among the most polluting effluents in agro-industrial systems. Improper management leads to soil degradation, groundwater contamination, and biodiversity loss, creating supply chain disruptions through regulatory penalties and operational shutdowns while threatening the sustainability credentials essential for premium market positioning.

The complexity of OMW management within olive oil supply chains stems from the interconnected nature of upstream harvesting decisions, processing allocation strategies, and downstream waste treatment options. Traditional supply chain optimization approaches address these elements sequentially, leading to suboptimal solutions that fail to capture the synergies between operational efficiency and environmental compliance. This fragmented approach becomes particularly problematic under increasingly strict environmental regulations that impose hard constraints on lagooning capacities and land spreading limits while promoting circular economy principles through waste valorization mandates.

Contemporary supply chain management theory emphasizes the integration of environmental constraints as core design elements rather than peripheral considerations. The circular economy paradigm, aligned with United Nations Sustainable Development Goals—SDG 6 (Clean Water and Sanitation), SDG 12 (Responsible Consumption and Production), and SDG 15 (Life on Land)—requires supply chain architectures that transform waste streams into value-creating resources. However, existing decision support systems for agricultural supply chains typically optimize economic objectives subject to basic capacity constraints, failing to embed environmental compliance and circular economy principles into the fundamental optimization framework.

The olive oil sector in Tunisia, contributing over e1.5 billion annually while supporting thousands of rural jobs, provides a compelling case study for sustainable supply chain optimization. Tunisia's regulatory framework strictly limits OMW disposal through controlled lagooning and land spreading, with emerging policy frameworks establishing progressive valorization targets culminating in 80% through composting, anaerobic digestion, or other circular economy pathways. These regulations create a complex multi-objective optimization environment where supply chain efficiency, product quality, environmental compliance, and economic viability must be simultaneously optimized.

Addressing these interconnected challenges requires advanced decision support systems that can navigate trade-offs between conflicting objectives while ensuring robust operational performance. Multi-objective optimization techniques, particularly Mixed-Integer Linear Programming (MILP) approaches, offer the mathematical rigor necessary to handle discrete operational decisions (harvest timing, facility allocation) alongside continuous variables (quantities, quality metrics, environmental flows). When combined with multi-criteria decision-making frameworks, these approaches enable supply chain managers to visualize and navigate the complex solution space defined by competing objectives.

This study contributes to the sustainable supply chain management literature by developing an integrated multi-objective optimization framework that embeds environmental compliance and circular economy principles as hard mathematical constraints directly into operational decision-making. The ε-constraint approach generates comprehensive Pareto frontiers that enable systematic exploration of trade-offs between environmental performance, product quality, and economic profitability, revealing infrastructure bottlenecks invisible to single-objective or sequential optimization approaches. Unlike previous approaches that treat environmental management as a separate planning phase, our framework jointly optimizes harvest scheduling, processing allocation, and waste management within a unified mathematical model. The approach recognizes that sustainable supply chain performance emerges from the systematic integration of environmental, economic, and operational considerations rather than their sequential optimization. Figure 1 provides a conceptual overview of this integrated framework, illustrating the interconnections between operational decisions, multi-objective optimization, and circular economy pathways.

Figure 1

Figure 1. Representative conceptual flowchart of the problem definition of the model, illustrating the operational logic of the Olive Mill Waste (OMW) management system. The figure highlights decision pathways for valorization, lagooning, and land spreading under regulatory constraints, clarifying the key components and relationships within the supply chain.

Our integrated framework addresses three critical research gaps in sustainable agricultural supply chain management. First, existing optimization models typically focus on either operational efficiency or environmental compliance, failing to capture the synergies and trade-offs between these objectives. Second, current decision support systems inadequately address the spatial and temporal complexity of waste management in distributed agricultural systems. Third, literature lacks frameworks that effectively translate circular economy principles into actionable operational decisions for agricultural supply chain managers.

The proposed MILP model simultaneously optimizes three objectives: minimization of non-valorized waste volume (environmental performance), maximization of product quality indicators (market competitiveness), and maximization of economic profit (financial sustainability). By embedding environmental capacity constraints as hard limits rather than soft penalties, the framework ensures compliance with current infrastructure capacities while identifying operational strategies that maximize circularity and economic performance within feasible solution spaces and revealing the infrastructure investments necessary to achieve long-term regulatory targets.

Application to Tunisia's Henchir Chaal region demonstrates both the framework's analytical power and the sector's infrastructure challenges. While operational optimization achieves 14.6% reduction in transport emissions and maintains compliance with lagooning and land-spreading capacity limits, OMW valorization remains limited to 12.8% due to insufficient processing infrastructure—highlighting that sustainable supply chain transformation requires coordinated infrastructure investment alongside operational excellence. Sensitivity analysis reveals that strategic capacity expansion could achieve 60%–70% valorization rates while improving profits by 30.8%, providing actionable roadmaps for phased progression toward regulatory targets and demonstrating the economic viability of circular economy transitions.

The remainder of this paper is organized as follows. Section 2 reviews relevant literature on sustainable agricultural supply chains, circular economy implementation, and multi-objective optimization methodologies. Section 3 develops the integrated MILP model, detailing objectives, constraints, and decision variables. Section 4 presents the ε-constraint resolution framework. Section 5 applies the framework to Tunisia's Henchir Chaal region, comparing multi-objective vs. single-objective performance and analyzing infrastructure investment scenarios. Section 6 discusses managerial implications for three key stakeholder groups, study limitations, and future research directions. Section 7 concludes with broader lessons for agricultural supply chain sustainability transformation.

2 Literature review

2.1 Sustainable supply chain management in agricultural systems

Contemporary agricultural supply chain management integrates environmental and social sustainability with economic performance, addressing unique challenges of perishability, seasonality, and resource dependence that distinguish agricultural systems from manufacturing contexts (Kumar et al., 2020; Behzadi et al., 2018). These characteristics require specialized frameworks that account for biological uncertainties and quality deterioration, with complexity increasing significantly when waste streams generate environmental externalities affecting supply chain continuity and regulatory compliance.

Multi-objective optimization approaches have emerged as essential tools for navigating sustainability trade-offs in supply chain design. Seuring and Müller (2008) established the theoretical foundation for sustainable supply chain management, emphasizing integrated approaches across value networks—a framework extended to agricultural contexts where seasonal production and quality deterioration create complex interdependencies between upstream and downstream operations. Brandenburg et al. (2014) demonstrated that environmental considerations significantly alter optimal supply chain configurations when embedded as hard constraints rather than soft objectives, a principle increasingly relevant as regulatory frameworks impose binding environmental limits on agricultural operations.

Recent advances have refined sustainable agricultural supply chain frameworks, particularly regarding economic-environmental integration. Jayarathna et al. (2021) provide a comprehensive review of multi-objective optimization methodologies, demonstrating that successful implementations require simultaneous consideration of multiple performance dimensions rather than sequential optimization. Belamkar et al. (2023) extended these principles to agro-food supply chain network design, developing a multi-objective fuzzy optimization framework that integrates economic viability with environmental sustainability under uncertainty. While these approaches have advanced the field significantly, they typically address waste management as an end-of-pipe solution rather than integrating waste minimization into upstream operational decisions—a gap that becomes critical when regulatory constraints impose hard limits on waste disposal capacity.

2.2 Circular economy integration in agricultural supply chains

The circular economy paradigm shifts supply chain design from linear “take-make-dispose” models to closed-loop systems that eliminate waste through resource cycling and valorization (Velenturf and Purnell, 2021; Mirabella et al., 2014). Geissdoerfer et al. (2017) provide the conceptual foundation for circular implementation in supply chains, emphasizing system-wide design approaches that connect waste outputs to valuable inputs. However, translating these conceptual frameworks into operational reality requires addressing significant barriers related to infrastructure capacity, spatial coordination, and economic viability at practical scales.

Empirical studies reveal persistent implementation challenges in agricultural supply chains. Donner et al. (2022) examined olive oil production systems and identified infrastructure limitations as the primary constraint to waste valorization, with insufficient processing capacity preventing achievement of regulatory circularity targets even when technologies are technically mature. Moglie et al. (2024) demonstrated that while valorization technologies achieve technical feasibility at pilot scales, their economic viability depends critically on achieving minimum processing volumes and establishing regional coordination mechanisms. Recent comprehensive reviews confirm that technological maturity alone does not guarantee successful circular economy adoption, with infrastructure capacity constraints and spatial coordination remaining primary barriers (Spina et al., 2025)—findings directly validated by our Tunisian case study where limited capacity (20 m³/day at single mill) restricts valorization to 12.8% despite 80% regulatory targets. These studies reveal a critical gap between circular economy theory and practical implementation in distributed agricultural systems, where most research focuses on centralized facilities rather than addressing the spatial and logistical complexity of coordinating waste streams across multiple production sites.

Recent technological advances have expanded valorization pathways while demonstrating persistent infrastructure constraints. Ruggeri et al. (2024) document high-value compound extraction technologies (antioxidants, phenolic derivatives, biopolymers) commanding premium prices ($100–2,000/kg across pharmaceutical, cosmetic, and functional food markets), though economic viability requires minimum processing scales (50–100 m³/day) often exceeding individual mill capacities (10–30 m³/day). Vaz et al. (2024) show that integrated treatment systems (ozonation, anaerobic digestion, and advanced oxidation) achieve 85%–95% pollutant reduction while recovering biogas (150–250 m³ CH/ton OMW) and biofertilizers, but require substantial capital investment ($2–5M for 100 m³/day capacity). These advances demonstrate technical maturity but highlight that valorization economic viability depends fundamentally on operational coordination: harvest timing determines temporal waste concentration, mill allocation determines spatial distribution, and processing schedules affect waste characteristics influencing valorization yields—integration requirements that existing optimization frameworks inadequately address.

Keskes et al. (2024) applied multi-criteria decision-making frameworks to prioritize circular olive oil production strategies in Tunisia, demonstrating strong regulatory and market pressure for circularity while revealing critical gaps in operational implementation frameworks. Their analysis shows that while stakeholders recognize circularity as essential for long-term sustainability, existing decision support systems lack mechanisms to translate circular economy principles into actionable operational decisions regarding harvest scheduling, processing allocation, and waste flow coordination. This implementation gap is particularly acute in distributed agricultural systems where waste generation occurs across spatially dispersed sites while valorization infrastructure remains centralized, creating logistical coordination challenges that current frameworks inadequately address.

2.3 Environmental compliance and regulatory constraints in supply chain optimization

Environmental regulations increasingly impose hard constraints on supply chain operations, particularly in waste-intensive industries. The transition from voluntary environmental initiatives to mandatory compliance requirements has transformed optimization paradigms, creating decision contexts where feasible solution spaces are defined by environmental capacity limits rather than traditional resource constraints. This shift requires embedding environmental compliance as core design elements rather than peripheral considerations.

The Mediterranean olive oil sector exemplifies this regulatory evolution. Jarboui et al. (2010) documented severe environmental impacts from traditional OMW disposal methods—soil contamination, groundwater pollution, and ecosystem degradation—which catalyzed increasingly strict regulatory frameworks. Contemporary regulations impose binding capacity constraints on conventional disposal methods (limiting lagooning volumes and land spreading rates) while simultaneously mandating minimum valorization rates to promote circular economy transitions. These dual regulatory mechanisms transform waste management from a cost-minimization problem to a multi-constraint coordination challenge where environmental limits define operational feasibility.

Traditional sequential optimization approaches—where production and processing decisions are optimized first based on economic objectives and waste management strategies developed subsequently—frequently generate infeasible solutions when environmental constraints are binding. This failure occurs because upstream operational decisions (harvest timing, facility allocation, and production volumes) directly determine waste generation patterns without considering downstream environmental capacity constraints. Fernandez-Lobato et al. (2022) applied life cycle assessment principles to olive oil supply chains, demonstrating that upstream production decisions significantly influence downstream environmental impacts across multiple categories. Spatial optimization approaches using Local Indicators of Spatial Association (LISA) demonstrate that mill-grove proximity based on road network travel time differs substantially from Euclidean distance assumptions (Modica et al., 2024), validating our framework's explicit incorporation of routing costs which achieved 14.6% CO₂ emission reduction through optimized mill allocation. However, LCA studies remain primarily diagnostic tools that quantify impacts rather than prescriptive frameworks that can simultaneously optimize operational efficiency and environmental compliance within binding regulatory constraints.

Recent regulatory intensification since 2020 reflects growing policy emphasis on circular economy transitions. Mediterranean countries have progressively tightened disposal regulations while establishing ambitious valorization targets that require fundamental restructuring of waste management systems. Tunisia's mandatory 80% valorization target—among the most stringent in the Mediterranean region—creates unprecedented operational challenges (Keskes et al., 2024). While stakeholders acknowledge regulatory necessity, existing decision support systems treat regulatory constraints as external requirements to be verified post-optimization rather than as embedded design elements that fundamentally shape feasible solution spaces. This architectural limitation prevents identification of operational configurations that achieve environmental compliance efficiently, forcing supply chains into reactive compliance modes characterized by high costs and operational disruptions.

2.4 Multi-objective optimization in agricultural supply chains

Multi-objective optimization has emerged as the dominant mathematical framework for addressing sustainability trade-offs in supply chain management, providing rigorous methods to navigate conflicts between competing performance dimensions. The agricultural sector has been particularly active in adopting these approaches due to fundamental tensions between productivity maximization, quality preservation, economic performance, and environmental impact mitigation—objectives that rarely align and require explicit trade-off analysis.

The ε-constraint method has proven particularly effective for agricultural applications where certain objectives must be treated as hard constraints rather than soft optimization targets. Mavrotas and Florios (2013) demonstrated that the augmented ε-constraint approach (AUGMECON2) provides superior computational performance for mixed-integer programming problems, generating complete Pareto frontiers efficiently while avoiding weakly efficient solutions. This methodological advantage becomes critical in agricultural contexts where environmental compliance requirements and quality standards define mandatory performance thresholds that cannot be violated regardless of economic trade-offs.

Despite these methodological advances, agricultural applications have typically focused on single-stage problems rather than integrated multi-echelon frameworks. Masri and Hamza (2011) developed stochastic programming models for olive oil production planning under yield uncertainty, but omitted environmental constraints related to waste generation and quality deterioration effects. Lahyani et al. (2015) optimized transportation logistics for olive collection, minimizing costs and delays, but treated processing decisions as exogenous parameters, failing to capture how collection routing affects processing schedules and downstream waste management. These single-stage approaches miss critical interdependencies where upstream decisions constrain downstream performance across economic, quality, and environmental dimensions.

Recent advances have enhanced practical applicability, though integration gaps persist. Contemporary solution methods—including improved ε-constraint implementations, evolutionary algorithms, and hybrid meta-heuristics—enable efficient computation of Pareto frontiers for large-scale problems (Jayarathna et al., 2021). However, even recent applications typically optimize network configuration or single operational stages rather than integrating multiple decision layers—such as harvest scheduling, processing allocation, and waste management coordination—within unified frameworks that capture cross-stage interdependencies and cumulative environmental impacts (Belamkar et al., 2023).

This methodological landscape reveals a critical gap: while multi-objective optimization theory and solution algorithms have matured substantially, their application to agricultural supply chains remains predominantly single-stage or sequential. The literature lacks integrated frameworks that simultaneously optimize operational decisions across harvest, processing, and waste management stages while explicitly embedding environmental constraints as hard limits and generating Pareto-efficient frontiers that enable transparent trade-off navigation between economic, quality, and environmental objectives.

2.5 Research gaps and theoretical contributions

This literature review reveals five critical interconnected gaps in sustainable agricultural supply chain management that our work addresses. Table 1 synthesizes key contributions from prior research and positions our study within this landscape, demonstrating how our integrated framework advances beyond existing approaches.

Table 1

Table 1. Literature positioning and research contributions.

Five critical research gaps:

(1) Integration gap: Existing research treats operational optimization and environmental management as separate domains requiring sequential solution, preventing identification of synergies where operational efficiency improvements simultaneously enhance environmental performance (Belamkar et al., 2023; Ruggeri et al., 2024).

(2) Spatial-temporal complexity gap: Current optimization approaches inadequately address spatial distribution of waste generation across dispersed production sites and temporal coordination required to match episodic waste flows with continuous treatment capacity (Vaz et al., 2024; Keskes et al., 2024). Models lack capability to simultaneously determine optimal harvest schedules, mill allocations, and waste routing strategies.

(3) Regulatory implementation gap: Existing frameworks treat regulatory constraints as external requirements subject to post-optimization verification rather than embedded design elements defining feasible solution spaces (Keskes et al., 2024). This creates implementation failures when regulatory limits are binding, forcing costly adjustments or non-compliance.

(4) Operational-strategic integration gap: While technological assessments document valorization feasibility and investment requirements (Ruggeri et al., 2024; Vaz et al., 2024), the literature lacks frameworks connecting strategic infrastructure investments to operational harvest and processing strategies. Supply chain managers cannot evaluate how valorization capacity investments alter optimal operational configurations.

(5) Decision support gap: Existing agricultural DSS implementations achieve efficiency gains in single-objective contexts (Bei et al., 2025) but provide limited support for navigating multi-objective trade-offs transparently. Most systems present single solutions based on pre-specified weights, obscuring trade-off structures and preventing stakeholders from exploring how alternative preferences affect optimal decisions.

Positioning of present study: Our research addresses these five interconnected gaps through an integrated multi-objective optimization framework that embeds circular economy principles and environmental constraints directly into operational decision-making. Unlike recent studies focusing either on technological assessments or single-stage optimization, our contribution provides simultaneous optimization of harvest scheduling, processing allocation, and OMW flow management, with regulatory limits imposed as hard mathematical constraints. This joint integration enables systematic evaluation of how valorization infrastructure investments alter optimal operational configurations and quantitative assessment of infrastructure capacity's impact on achievable economic and environmental performance.

Our research contributes to sustainable supply chain management theory through four distinct innovations:

• Methodological innovation: Joint optimization of harvest scheduling, processing allocation, and waste management within a unified multi-objective MILP model treating environmental constraints as hard limits, ensuring a priori regulatory compliance while optimizing economic and quality performance.

• Spatial-temporal coordination: Explicit modeling of distributed waste generation and temporal coordination mechanisms matching episodic waste flows with continuous treatment capacity requirements through integrated decision-making.

• Circular economy operationalization: Translation of circular economy principles into actionable optimization variables, constraints, and objectives enabling quantitative evaluation of valorization pathways and sensitivity to infrastructure investments.

• Decision support advancement: Development of a Pareto frontier framework using the ε-constraint method generating multiple Pareto-efficient solutions representing optimal trade-offs between conflicting objectives, enabling transparent multi-criteria decision-making.

Table 1 includes the present study as its final entry, enabling direct comparison of methodological approaches, problem scope, and environmental integration mechanisms. This comparative positioning demonstrates clear advancement beyond state-of-the-art in integrated sustainable supply chain optimization for agricultural systems, particularly in embedding circular economy principles and regulatory compliance as core operational decision elements.

3 Environmentally conscious harvesting and processing model

This section introduces an Environmentally Conscious Harvesting and Processing Model formulated as a multi-objective Mixed-Integer Linear Programming (MILP) framework. The model is designed to optimize the operational planning of olive harvesting, transportation, and processing in public olive estates, with a central focus on reducing environmental impact—particularly through the effective management of OMW. It simultaneously integrates oil quality preservation and economic performance into a unified decision-support tool.

The environmental component is pivotal, addressing the significant ecological risks posed by OMW—a highly polluting liquid effluent rich in organic matter and phenolic compounds. Improper management can result in soil degradation, groundwater contamination, and biodiversity loss, driving strict environmental regulations that cap lagooning and land spreading capacities. The model explicitly embeds these environmental constraints to ensure full compliance with national and international sustainability standards (e.g., SDGs 6, 12, and 15).

We adopt a discretized planning horizon where each day is subdivided into decision intervals—typically 12 2-h slots. For each day d ∈ D, the set of time intervals is defined as

$I_d=\left\{1,2,\dots ,k_d\right\},$

where k_d is the number of available slots on day d. Each time slot i ∈ I_d is associated with a harvesting cost $C{C}_{di}^{cf}$ for every team-parcel pair (c, f), ensuring accurate interval-based aggregation.

The model optimizes the following three core objectives:

1. Minimization of environmental costs, accounting for OMW generation and management, including penalties for exceeding lagoon and land spreading limits and incentives for valorization (e.g., composting, biogas production);

2. Preservation of oil quality, measured through key indicators (acidity, peroxide index, etc.) that deteriorate with processing delays;

3. Maximization of economic performance, reflecting net profit from olive oil production after operational and environmental costs.

This environmentally conscious optimization framework addresses a fundamental challenge in sustainable supply chain management: the integration of environmental constraints as core design elements rather than peripheral considerations. Traditional supply chain optimization approaches, as identified by Seuring and Müller (2008), typically treat environmental factors as external impositions that constrain otherwise optimal solutions. In contrast, our approach aligns with Brandenburg et al. (2014)'s demonstration that environmental considerations fundamentally alter optimal supply chain configurations when embedded as hard constraints within the optimization framework.

The model operationalizes circular economy principles within agricultural supply chains by transforming waste streams into decision variables that directly influence operational efficiency and economic performance. This integrated approach recognizes that sustainable agricultural supply chains require simultaneous optimization across operational, environmental, and quality dimensions, as the interdependencies between harvest timing, processing allocation, and waste management create synergies invisible to sequential optimization approaches. By embedding OMW valorization pathways directly into the harvest scheduling and mill allocation decisions, the framework transcends traditional end-of-pipe waste management to achieve integrated optimization of environmental and operational objectives.

3.1 Input data, parameters, and decision variables

The model integrates multiple data sources and variables to represent the operational, environmental, and logistical facets of the olive harvesting and processing system.

Sets:

• D: Set of planning days,

• P: Set of oil extraction units (mills),

• C: Set of harvesting teams,

• F: Set of olive groves (parcels),

• F^c ⊆ F: Set of parcels accessible by team c,

• I: Set of time slots per day (default: 12 two-hour slots),

• I_d = {1, …, k_d}: Ordered time slots for day d,

• $I_c^0\subseteq I$: First decision instants for team c (typically start of each day),

• p_c ∈ P: Assigned base mill for team c,

• C^p ⊆ C: Teams associated with mill p ($C^p=\left\{c\in C:p_c=p\right\}$).

Parameters:

• $V_d^p$: Selling price (TND/ton) of oil at mill p on day d,

• $AT{R}_d^f$: Oil yield (ton of oil per ton of olives) for parcel f on day d,

• $O_d^f,A_d^f,P_d^f,H_d^f$: Quality attributes of olives from parcel f on day d (oil content, acidity, peroxide index, moisture/impurities),

• $C{C}_{di}^{cf}$: Harvesting cost (TND) for team c on parcel f at time i,

• $C{T}_{di}^{(c{f}_1{f}_2)}$: Travel cost (TND) for team c moving from f₁ to f₂ at time i,

• $C{P}_d^{fp}$: Transport and processing cost (TND/ton) from parcel f to mill p on day d,

• R_f: Estimated productivity (tons/day) of parcel f,

• M_f: Max harvestable quantity (tons) of parcel f,

• $Q_c^{(d,min)},Q_c^{(d,max)}$: Min/max daily harvest (tons) for team c,

• $Q{P}_d^{(p,min)},Q{P}_d^{(p,max)}$: Min/max daily capacity (tons) at mill p,

• $O_d^p,A_d^p,P_d^p,H_d^p$: Quality thresholds at mill p,

• S_p: Temporary storage capacity (tons) at mill p,

• α: OMW production coefficient (m³/ton of olives),

• B_p: Lagooning capacity (m³/day) at mill p,

• E_f: Max spreading capacity (m³/day) on parcel f,

• $V_{(d,fp)}^{max}$: Maximum daily valorization capacity (m³) for parcel f at mill p on day d,

• CL_p: Lagooning cost (TND/m³),

• CE_f: Spreading cost (TND/m³),

• CR_f: Return cost (TND/ton) for rejected olives from parcel f,

• l_c ∈ F ∪ P: Initial location (plot or mill) of team c.

The quality parameters $O_d^f,A_d^f,P_d^f,H_d^f$ are pre-adjusted to reflect expected post-harvest degradation under typical harvest-to-processing delays. These values are derived from empirical observations collected on semi-intensive estates and account for decay dynamics specific to each day d.

Decision variables:

• $z_d^{fp}\in {ℝ}_{+}$: Quantity (tons) of olives harvested from parcel f and processed at mill p on day d,

• $x_f^p\in \left\{0,1\right\}$: Binary, 1 if parcel f is assigned to mill p,

• $r_d^f\in {ℝ}_{+}$: Quantity (tons) of olives harvested but not processed (returned) on day d,

• $y_{(i_1{i}_2)}^{cf}\in \left\{0,1\right\}$: 1 if team c harvests parcel f from slot i₁ to i₂,

• $o_{(i_1{i}_2)}^{(c{f}_1{f}_2)}\in \left\{0,1\right\}$: 1 if team c moves from f₁ to f₂ between i₁ and i₂,

• $n_i^{cf}\in \left\{0,1\right\}$: 1 if team c idles on parcel f at time i,

• $h_{di}^{cf}\in \left\{0,1\right\}$: 1 if team c reallocates to parcel f at decision instant i on day d,

• k_(cfpc) ∈ {0, 1}: 1 if team c starts its first activity by departing from base mill p_c.

Auxiliary variables for OMW management:

• $w_d^{fp}\in {ℝ}_{+}$: Volume (m³) of OMW lagooned from parcel f at mill p on day d,

• $e_d^{fp}\in {ℝ}_{+}$: Volume (m³) of OMW spread on parcel f on day d,

• $v_d^{fp}\in {ℝ}_{+}$: Volume (m³) of OMW valorized (composting, anaerobic digestion) from parcel f at mill p on day d.

3.2 Objective functions and constraints

The proposed problem is modeled as a multi-objective Mixed-Integer Linear Program (MILP), jointly optimizing three key dimensions: environmental sustainability, product quality, and economic performance. Each objective targets a specific facet of the harvest scheduling and olive processing system.

(1) Environmental objective—minimization of non-valorized olive mill wastewater:

The first objective focuses on minimizing the total volume of OMW that is not valorized through advanced treatment pathways (e.g., composting, anaerobic digestion). Rather than penalizing the entire OMW volume, this formulation promotes circular economy principles by distinguishing between valorized and non-valorized fractions:

$Z_1={\displaystyle \sum _{d\in D}}{\displaystyle \sum _{f\in F}}{\displaystyle \sum _{p\in P}}\left(\alpha ·z_d^{fp}-v_d^{fp}\right)$

where $\alpha ·z_d^{fp}$ represents the total volume (m³) of OMW produced by processing olives from parcel f at mill p on day d, and $v_d^{fp}$ is the volume (m³) of OMW that is successfully valorized (e.g., via composting or biogas production), typically handled by third-party firms.

It is by reducing the volume of OMW it must manage through lagooning or land spreading. Thus, this objective encourages both reducing total OMW production and maximizing external valorization to minimize environmental burdens borne by the mill.

(2) Quality objective—maximization of delivered olive quality:

The second objective Z₂ captures the overall quality of olives delivered to mills by combining key physicochemical indicators into a single weighted score:

$Z_2={\displaystyle \sum _{d\in D}}{\displaystyle \sum _{p\in P}}{\displaystyle \sum _{f\in F}}\left({\omega }_1·O_d^f-{\omega }_2·A_d^f-{\omega }_3·P_d^f-{\omega }_4·H_d^f\right)·z_d^{fp}$

where ω₁, ω₂, ω₃, ω₄ ∈ ℝ₊ reflect the relative importance of oil content, acidity, peroxide index, and impurity levels.

(3) Economic objective—maximization of gross profit:

The third objective Z₃ maximizes the net operational profit, defined as the balance between oil sales revenues and all operational/environmental costs:

$\begin{array}{l}{Z}_3={\displaystyle \sum _{d\in D}}{\displaystyle \sum _{f\in F}}{\displaystyle \sum _{p\in P}}{V}_d^p·AT{R}_d^f·z_d^{fp}\\ -{\displaystyle \sum _{d\in D}}{\displaystyle \sum _{c\in C}}{\displaystyle \sum _{f\in F}}{\displaystyle \sum _{i_1,i_2\in I_d}}\left({\displaystyle \sum _{i=i_1}^{i_2}}C{C}_{di}^{cf}\right)·y_{\left(i_1{i}_2\right)}^{cf}\\ -{\displaystyle \sum _{d\in D}}{\displaystyle \sum _{c\in C}}{\displaystyle \sum _{f_1,f_2\in F}}{\displaystyle \sum _{i\in I_d}}C{T}_{di}^{\left(c{f}_1{f}_2\right)}·o_i^{\left(c{f}_1{f}_2\right)}\\ -{\displaystyle \sum _{d\in D}}{\displaystyle \sum _{f\in F}}{\displaystyle \sum _{p\in P}}C{P}_d^{fp}·z_d^{fp}\\ -{\displaystyle \sum _{d\in D}}{\displaystyle \sum _{f\in F}}C{R}_f·r_d^f\\ -{\displaystyle \sum _{d\in D}}{\displaystyle \sum _{f\in F}}{\displaystyle \sum _{p\in P}}\left(C{L}_p·\left(w_d^{fp}-v_d^{fp}\right)+C{E}_f·e_d^{fp}\right)\end{array}$

Here, $(w_d^{fp}-v_d^{fp})$ represents the non-valorized portion of OMW, which still incurs a disposal cost (e.g., lagooning fees). The valorized portion $v_d^{fp}$, handled by third parties, is excluded from this cost calculation because the mill transfers this waste without additional expense or profit.

These objectives are optimized simultaneously through a multi-objective resolution framework, enabling decision-makers to explore trade-offs between environmental compliance, oil quality, and economic performance. Special attention is paid to prioritizing valorization pathways, reducing the environmental burden of olive oil production, and aligning operations with circular economy principles and sustainable development goals.

3.2.1 Environmental constraints: olive mill wastewater management

The extraction of olive oil inevitably generates OMW—a toxic effluent rich in organic matter and phenolic compounds—recognized as one of the most polluting agro-industrial wastes. OMW threatens both ecosystems and public health: phenolic compounds, known carcinogens and persistent pollutants, can contaminate drinking water sources, especially in rural areas reliant on groundwater, increasing the risk of waterborne diseases and chronic exposure to toxic substances (Enaime et al., 2020; Meftah et al., 2019). Mismanagement severely impacts soil health, groundwater resources, and biodiversity, directly linking OMW management to SDG3 (Good Health and Well-being), SDG6 (Clean Water and Sanitation), and SDG15 (Life on Land). Empirical studies show that uncontrolled land spreading can increase soil organic carbon (SOC) content by up to 150% within three months, creating anaerobic soil conditions that reduce microbial biodiversity by more than 40% (Karaouzas et al., 2011; Mekki et al., 2006).

To address these challenges, the proposed model integrates OMW management through a structured three-tiered system:

1. Valorization (if available) is prioritized to promote circular economy principles,

2. Lagooning serves as the primary containment method, and

3. Land spreading acts as a fallback when other options are saturated.

Each route is subject to operational and regulatory capacity constraints to ensure full environmental and public health compliance. Figure 2 provides a schematic overview of this system, illustrating the prioritization logic and material flow between the three treatment pathways.

Figure 2

Figure 2. Flowchart of the OMW management system: valorization, lagooning, and land spreading fallback, all governed by regulatory limits.

OMW allocation balance:

For each plot f, mill p, and day d, the total volume of OMW generated by processing olives must be fully allocated between valorization, lagooning, and land spreading:

$\alpha ·z_d^{fp}=v_d^{fp}+w_d^{fp}+e_d^{fp},\forall d\in D,\forall f\in F,\forall p\in P$

where:

• α is the OMW production coefficient (m³/ton of olives), calibrated from Tunisian benchmarks,

• $v_d^{fp}$ is the volume valorized (e.g., composting, anaerobic digestion),

• $w_d^{fp}$ is the volume directed to lagooning,

• $e_d^{fp}$ is the volume allocated for land spreading.

This balance ensures a full accounting of OMW flows, aligned with national waste traceability standards.

Non-negativity constraints:

All OMW-related variables must be non-negative:

$v_d^{fp}\ge 0,w_d^{fp}\ge 0,e_d^{fp}\ge 0,\forall d,f,p$

Valorization capacity constraints:

Valorization is limited by two factors:

• Production constraint: valorized volume cannot exceed what is produced:

$v_d^{fp}\le \alpha ·z_d^{fp},\forall d,f,p$

• External demand constraint: valorization depends on external company demand, bounded by an exogenous parameter $V_{d,fp}^{max}$:

$v_d^{fp}\le V_{d,fp}^{max},\forall d,f,p$

$V_{d,fp}^{max}$ represents the maximum valorization capacity negotiated with third-party facilities, reflecting real-world limits in market demand and logistics.

Lagooning capacity constraint:

Each mill has a daily lagooning capacity B_p (m³):

${\displaystyle \sum _{f\in F}}{w}_d^{fp}\le B_p,\forall d,p$

B_p is set by environmental permits and reflects basin sizes approved by the Tunisian ANPE. This constraint is crucial to prevent overflow and contamination of nearby water sources (SDG6).

Land spreading capacity constraint:

Each agricultural plot f has a maximum absorption capacity E_f (m³):

$e_d^{fp}\le E_f,\forall d,f,p$

E_f is calibrated based on agronomic standards and environmental guidelines (e.g., minimum distances from water bodies per the Tunisian Water Code), safeguarding soil health and biodiversity (SDG15).

Environmental compliance mechanismt:

When valorization and lagooning capacities are saturated, surplus OMW is redirected to land spreading if soil absorption allows. If all pathways are saturated, olives from parcel f on day d cannot be processed at mill p to prevent environmental breaches. This tight linkage between operational feasibility and environmental thresholds ensures strict compliance.

Regulatory contextualization:

• α: derived from empirical measurements in Tunisian mills (0.9–1.2 m³/ton), reflects typical effluent yield,

• B_p: lagooning capacity based on mill infrastructure, as specified in environmental permits,

• E_f: soil absorption limits, respecting national agronomic and hydrological safety thresholds, and

• $V_{d,fp}^{max}$: valorization potential updated periodically based on third-party demand and valorization plant availability.

By embedding these constraints, the model enforces regulatory compliance and promotes circular economy principles, balancing operational needs with environmental stewardship—key priorities for sustainable olive oil production systems.

3.2.2 Quality compliance constraints

This set of constraints ensures that only high-quality olive batches—meeting stringent industrial standards for oil content, acidity, peroxide index, and moisture/impurities—are processed in the oil mills. Maintaining these quality attributes is essential not only for securing high-grade product classification (e.g., extra virgin) but also for protecting consumer health and preserving processing infrastructure, thereby aligning with SDG3 (Good Health and Wellbeing) and SDG12 (Responsible Consumption and Production).

Minimum oil content threshold: To guarantee satisfactory oil yields and processing efficiency, the average oil content of olives delivered to each mill must meet or exceed a prescribed minimum. To preserve linearity in the optimization model, this requirement is reformulated as:

$\begin{array}{ll}{\displaystyle \sum _{f\in F}}(O_d^f-O_d^p)·z_d^{fp}\ge 0,\forall d\in D,\forall p\in P& (1)\end{array}$

where $O_d^f$ is the oil content of olives from plot f on day d, and $O_d^p$ is the minimum threshold required by mill p. This ensures that the weighted average oil content across all deliveries satisfies minimum economic and technical acceptability criteria.

Maximum acidity threshold: To preserve oxidative stability and desirable sensory properties, the average acidity of processed olives must not exceed a maximum allowable limit:

$\begin{array}{ll}{\displaystyle \sum _{f\in F}}{A}_d^f·z_d^{fp}\le A_d^p·{\displaystyle \sum _{f\in F}}{z}_d^{fp},\forall d\in D,\forall p\in P& (2)\end{array}$

Here, $A_d^f$ denotes the acidity level of olives from plot f. Lower acidity is critical to preventing rancidity and ensuring product classification as extra virgin olive oil, typically requiring thresholds below 0.8%.

Maximum peroxide index threshold: To prevent oxidative spoilage and maintain product freshness, the average peroxide index of olives delivered must not surpass a critical limit:

$\begin{array}{ll}{\displaystyle \sum _{f\in F}}{P}_d^f·z_d^{fp}\le P_d^p·{\displaystyle \sum _{f\in F}}{z}_d^{fp},\forall d\in D,\forall p\in P& (3)\end{array}$

The peroxide index serves as an early indicator of oxidation. Its control is crucial to meet both legal standards and consumer expectations regarding oil stability and shelf life.

Maximum moisture and impurities threshold: The average moisture and impurity content of delivered olives must remain below critical thresholds to optimize extraction efficiency and protect processing equipment:

$\begin{array}{ll}{\displaystyle \sum _{f\in F}}{H}_d^f·z_d^{fp}\le H_d^p·{\displaystyle \sum _{f\in F}}{z}_d^{fp},\forall d\in D,\forall p\in P& (4)\end{array}$

Excess moisture or foreign matter can clog machinery, increase energy consumption, and degrade oil quality. Tight control mitigates environmental and operational risks.

Together, the four quality constraints above ensure rigorous compliance with industry benchmarks. By enforcing these thresholds, the model not only guarantees the economic and sensory value of olive oil but also protects consumers from substandard products and reduces environmental burdens associated with reprocessing or disposal of low-quality batches—directly contributing to SDG3 and SDG12. Table 2 summarizes the typical operational thresholds adopted in this study.

Table 2

Table 2. Typical quality thresholds for olive oil processing.

3.2.3 Industrial and resource constraints

This set of constraints ensures the operational feasibility of the harvest and processing system by enforcing realistic production, transportation, and storage conditions. It guarantees that resource utilization remains aligned with logistical capacities while maintaining continuity and traceability throughout operations.

Single harvest per plot: Each plot must be harvested at most once during the planning horizon:

$\begin{array}{ll}{\displaystyle \sum _{d\in D}}{\displaystyle \sum _{c\in C}}{\displaystyle \sum _{i_1,i_2\in I_d}}{y}_{(i_1{i}_2)}^{cf}\le 1,\forall f\in F& (5)\end{array}$

This constraint ensures that each plot is harvested within a single continuous window, preventing overlapping assignments across teams or time slots and maintaining operational consistency.

Daily processing capacities of extraction units: The daily intake at each processing unit must fall within its authorized minimum and maximum processing capacities:

$\begin{array}{ll}Q{P}_d^{(p,min)}\le {\displaystyle \sum _{f\in F}}{z}_d^{fp}\le Q{P}_d^{(p,max)},\forall d\in D,\forall p\in P& (6)\end{array}$

This constraint prevents both under-utilization and overload of milling facilities, ensuring smooth extraction activities without bottlenecks.

Compliance with daily harvesting capacities for teams: Each harvesting team's daily output must respect operational feasibility limits:

$\begin{array}{lll}{Q}_c^{(d,min)}& \le & {\displaystyle \sum _{f\in F}}{\displaystyle \sum _{i_1,i_2\in I_d}}{R}_f·(i_2-i_1+1)·y_{(i_1{i}_2)}^{cf}\le Q_c^{(d,max)},\end{array}$

$\begin{array}{ll}\forall d\in D,\forall c\in C& (7)\end{array}$

Here, (i₂ − i₁ + 1) counts the number of two-hour time slots during which team c is harvesting parcel f. The parameter R_f denotes the estimated daily productivity of parcel f (in tons/day) and is scaled in this constraint according to the actual harvesting duration. This formulation ensures that team workload remains within realistic limits while adapting to parcel-specific yield capacities.

Unique assignment of plots to processing units: Each harvested plot must be allocated to exactly one oil extraction mill:

$\begin{array}{ll}{\displaystyle \sum _{p\in P}}{x}_f^p=1,\forall f\in F& (8)\end{array}$

This ensures traceability and simplifies logistics throughout the harvesting and processing chain.

Immediate delivery or return of harvested olives: All olives harvested on a given day must either be immediately delivered for processing or returned to the producer if processing is not feasible:

$\begin{array}{ll}{\displaystyle \sum _{p\in P}}{z}_d^{fp}+r_d^f={\displaystyle \sum _{c\in C}}{\displaystyle \sum _{i_1,i_2\in I_d}}{R}_f·(i_2-i_1+1)·y_{(i_1{i}_2)}^{cf},\forall d\in D,\forall f\in F& (9)\end{array}$

with $r_d^f\ge 0$ representing the quantity of harvested olives that are not processed. This constraint ensures full routing of harvested batches, maintaining product freshness and avoiding logistical backlog. Returned quantities may result from non-compliance with quality standards or from environmental/capacity limitations.

Processing conditioned on plot assignment: A mill can only process olives from plots formally assigned to it:

$\begin{array}{ll}{z}_d^{fp}\le M_f·x_f^p,\forall d\in D,\forall f\in F,\forall p\in P& (10)\end{array}$

This enforces logical consistency between plot assignments and processing operations, safeguarding traceability and compliance. (Note: We now include d in the constraint for strict daily consistency.)

Respect of temporary storage capacities: The cumulative quantity of olives delivered to each processing unit on any given day must not exceed its temporary storage capacity:

$\begin{array}{ll}{\displaystyle \sum _{f\in F}}{z}_d^{fp}\le S_p,\forall d\in D,\forall p\in P& (11)\end{array}$

This ensures that storage limits S_p are respected, preventing facility overloads regardless of internal throughput rates.

3.3 Sustainable harvesting logistics: flow-based team coordination

The harvesting, movement, and idling activities of each team are modeled via binary flows on a time-expanded graph specific to each team. Each day is discretized into decision instants (e.g., 2-h slots), during which an activity can terminate and a new one can commence.

Each team c ∈ C operates independently within its own temporal transition graph. Arcs in this graph represent three core types of operational transitions:

• Harvesting arcs: uninterrupted work on a specific plot over a given time window;

• Idling arcs: waiting periods between consecutive instants without active harvesting;

• Travel arcs: movements between distinct plots f₁ → f₂ across different instants.

The duration of each arc is activity-dependent, reflecting harvesting rates, travel times, and the temporal structure of the working day. From an environmental standpoint, these transitions are critical. Studies report that olive harvesting machinery emits approximately 2.3–3.1 kg CO₂-eq per liter of diesel consumed, with transport between plots representing up to 30% of total emissions for smallholder operations (Food and Agriculture Organization, 2020; Anvari et al., 2024). Similarly, extended idling not only wastes fuel but also accelerates engine wear and contributes to localized air pollution (PM2.5, NO_x) (U.S. Environmental Protection Agency, 2018).

3.3.1 Flow initialization: initial team positions

Let l_c ∈ F ∪ P denote the initial location of team c, either at a plot or at a processing mill. If starting from a mill, p_c ∈ P specifies the base mill; if from a plot, p_c is undefined, and terms involving k_cfpc are null by convention.

At the start of the planning horizon, each team must inject exactly one unit of operational flow into the network:

$\begin{array}{ll}{\displaystyle \sum _{f\in F^c}}\left({\displaystyle \sum _{i_2\ge i_0^c}}{y}_{i_0^c{i}_2}^{cf}+n_{i_0^c}^{cf}+{\displaystyle \sum _{f^{\prime }\in F^c}}{\displaystyle \sum _{i_2\ge i_0^c}}{o}_{i_0^c{i}_2}^{cf{f}^{\prime }}\right)+{\displaystyle \sum _{f\in F^c}}{k}_{cf{p}_c}=1,\forall c\in C& (12)\end{array}$

Each team must begin its daily schedule via exactly one operational activity—harvesting, idling, traveling toward a plot, or departing from a base mill. Note that the reallocation flow $h_{di}^{cf}$ is only activated from the second planning day onward (d ≥ 2), as flow initialization for the first day d = 1 is handled separately through this constraint.

3.3.2 Flow conservation at activity nodes

After initialization, operational flow must be conserved at each temporal node. For every node (f, i), representing the team being at plot f at instant i on day d, the total incoming flow must equal the total outgoing flow, ensuring seamless continuity of operations:

$\begin{array}{l}{\displaystyle \sum _{i_1\le i\le i_2}}{y}_{i_1{i}_2}^{cf}+n_{i-1}^{cf}+{\displaystyle \sum _{f^{\prime }\in F^c}}{\displaystyle \sum _{i_1<i}}{\displaystyle \sum _{i_2=i}}{o}_{i_1{i}_2}^{c{f}^{\prime }f}={\displaystyle \sum _{i_2\ge i}}{y}_{i{i}_2}^{cf}+n_i^{cf}\end{array}$

$\begin{array}{ll}+{\displaystyle \sum _{f^{\prime }\in F^c}}{\displaystyle \sum _{i_2>i}}{o}_{i{i}_2}^{cf{f}^{\prime }},\forall c\in C,\forall f\in F^c,\forall d\in D,\forall i\in I_d& (13)\end{array}$

This ensures continuous logical progression—whether the team stays on the same plot, idles, or transitions to another plot—avoiding temporal discontinuities. In environmental terms, this tight scheduling prevents unnecessary back-and-forth trips, contributing to a reduction of up to 15% in fuel consumption per team per day (estimated at 0.5–0.8 liters saved), which represents 1.5–2.5 kg CO₂-eq daily per team.

3.3.3 Daily relocation for manual teams

Manual harvesting teams (non-automated) typically return to their lodging facilities each evening. At the start of each new day, the first available instants must include their relocation from lodging to work plots. Let $I_c^0\subset I$ denote the set of first decision instants for each team each day (excluding the initial instant on Day 1).

At these instants, incoming flows come not from standard activity arcs but from reallocation arcs $h_{di}^{cf}$:

$\begin{array}{ll}{\displaystyle \sum _{f\in F^c}}& \left({\displaystyle \sum _{i_1<i}}{y}_{i_{1}i}^{cf}+n_{i-1}^{cf}+{\displaystyle \sum _{f^{\prime }\in F^c}}{\displaystyle \sum _{i_1<i}}{\displaystyle \sum _{i_2=i}}{o}_{i_1{i}_2}^{c{f}^{\prime }f}\right)={\displaystyle \sum _{f\in F^c}}{h}_{di}^{cf},\end{array}$

$\begin{array}{llll}\forall c& \in & C,\forall i\in I_c^0& (14)\end{array}$

These reallocation arcs simulate the team's arrival at their first plot of the day. The corresponding flow distribution after relocation is:

$\begin{array}{ll}{h}_{di}^{cf}={\displaystyle \sum _{i_2\ge i}}{y}_{i{i}_2}^{cf}+n_i^{cf}+{\displaystyle \sum _{f^{\prime }\in F^c}}{\displaystyle \sum _{i_2>i}}{o}_{i{i}_2}^{cf{f}^{\prime }},\forall c\in C,\forall i\in I_c^0,\forall f\in F^c& (15)\end{array}$

This ensures that manual teams properly reset each morning, reflecting both labor law compliance and energy management (linked to SDG8 and SDG12). By optimizing these daily transitions, the model contributes to lowering noise pollution and reducing fuel consumption peaks typically observed at the start of operations, in line with Tunisia's Low Carbon Strategy (Food and Agriculture Organization, 2020).

This detailed network flow formulation offers flexibility and rigor, accurately modeling complex operational patterns while keeping environmental and sustainability challenges at the core of the optimization—helping minimize unnecessary movements, idling, and associated emissions (Anvari et al., 2024; U.S. Environmental Protection Agency, 2018; Agence Nationale pour la Maǐtrise de l'Energie, 2022; Food and Agriculture Organization, 2020).

4 Environmentally-conscious resolution framework

This study adopts the ε-constraint method as the exact resolution technique for the proposed multi-objective MILP. This approach is particularly suited to the context of environmentally sensitive agricultural planning, where certain objectives (e.g., environmental impact) must meet strict thresholds, while others (e.g., economic performance) remain secondary optimization targets.

4.1 Theoretical foundation and environmental relevance

The ε-constraint method, initially formalized by Haimes et al. (1971) and further developed by Mavrotas (2009), transforms a multi-objective problem into a series of single-objective problems by retaining one objective function for optimization while converting others into parameterized constraints. This aligns with SDG principles, where environmental thresholds are treated as strict limits rather than tradeable objectives (Rockström et al., 2009; Steffen et al., 2015).

In the context of OMW management, this methodological choice embodies the precautionary principle advocated by environmental policy scholars (Harremöes et al., 2002) and circular economy frameworks (Kirchherr et al., 2017) by ensuring that economic optimization never comes at the expense of exceeding critical environmental thresholds. As Geissdoerfer et al. (2017) note, setting hard constraints on environmental objectives operationalizes the strong sustainability concept, which maintains that natural capital cannot be infinitely substituted by manufactured capital.

Given our three objectives—minimizing non-valorized wastewater (Z₁), maximizing olive quality (Z₂), and maximizing economic profit (Z₃)—we formulate the ε-constraint model as:

$\begin{array}{c}\begin{array}{cc}\hfill \min & Z_1(x)\hfill \\ \hfill \text{s}\text{.t}\text{.}& Z_2(x)\ge {\epsilon }_2,\end{array}\\ \begin{array}{c}{Z}_3(x)\ge {\epsilon }_3,\\ x\in X\hfill \end{array}\end{array}$

where X represents the feasible region defined by the harvesting, logistical, and environmental constraints detailed in previous sections. The values ε₂ and ε₃ are progressively tightened to generate the efficient frontier of solutions, revealing the trade-offs between environmental protection and economic performance.

The implementation follows the augmented ε-constraint method (AUGMECON2) developed by Mavrotas and Florios (2013), which incorporates lexicographic optimization and early exit techniques to address computational efficiency challenges when applying the method to large-scale agricultural planning problems.

Our parametrization strategy uses a two-phase approach:

• Range determination phase: We first compute the individual optima for each objective to establish the range of values $\left[Z_j^{min},Z_j^{max}\right]$ for each objective j. This step ensures that the full extent of each objective's feasible space is captured before proceeding to multi-objective exploration.

• Grid exploration phase: The range of each objective is divided into p_j equal intervals, creating p_j+1 grid points. Following best practices in environmental multi-criteria analysis (Cinelli et al., 2014), we set p₂ = 5 and p₃ = 10, ensuring a denser sampling of the economic dimension to better capture potential win–win solutions. This structured discretization allows decision-makers to visualize trade-offs with precision across environmental and economic axes.

This implementation generates a representative subset of the Pareto frontier, allowing decision-makers to visualize explicit trade-offs between environmental and economic objectives. The approach is consistent with the ecological economics perspective articulated by Costanza et al. (2014), who argue that making environmental–economic trade-offs explicit is essential for sustainable resource management.

4.2 Environmental prioritization

A key methodological innovation in our approach is the explicit prioritization of environmental objectives, reflecting Tunisia's regulatory emphasis on wastewater management compliance. Following Cairns et al. (2009) and their framework for environmentally sustainable decision-making, we incorporate:

• Lexicographic ordering: Environmental objectives take precedence, with economic objectives optimized only within the solution space that satisfies environmental constraints. This hierarchical approach ensures that sustainability goals are never compromised in favor of short-term economic gains.

• Sensitivity analysis: Multiple runs with varying ε values for the environmental objective help identify critical thresholds where marginal economic costs of environmental compliance increase sharply. This process allows policymakers to assess the robustness of operational plans under stricter environmental standards and anticipate tipping points.

This methodology enables policymakers to identify what (Liu et al., 2007) term “just manageable” environmental windows—operational regimes that maintain ecological function while allowing for economic activity. The approach has proven effective in other agricultural contexts facing environmental constraints, such as wine production (Yengue et al., 2008) and irrigated crops (Yang et al., 2024).

5 Case study and experimental results

5.1 Study area: Henchir Chaal, Tunisia

This section presents the results of applying a multi-objective optimization model to a real-world case study in a selected area of the olive-growing region of Henchir Chaal, Tunisia, using data from the 2020–2021 harvest season. Henchir Chaal is one of the largest olive-growing regions in Tunisia, and our study focuses on a representative portion of this area, characterized by:

• 18 olive groves (parcels) covering approximately 150 hectares, selected from the larger Henchir Chaal region.

• 4 harvesting teams operating during the harvest season.

• 3 olive mills with varying processing capacities, of which only one has the capability to valorize OMW.

• A 14-day planning horizon during the peak harvest period (November–December 2020).

The objective of this implementation is to demonstrate how the proposed ε-constraint approach can balance environmental sustainability (minimizing non-valorized OMW by optimizing deliveries to the mill with valorization capability) with economic profitability and olive oil quality in a practical operational context.

5.2 Technical and environmental parameters

5.2.1 Data sources and collection

The experimental data were collected through collaboration with the Tunisian Office of State Lands (Office des Terres Domaniales) for the Henchir Chaal region during the 2020–2021 harvest season. Agronomic parameters (parcel characteristics, maturity indices, quality indicators) were obtained from field measurements conducted by agronomists and historical production records maintained by the Office. Processing infrastructure data (mill capacities, extraction system specifications, OMW production coefficients) were provided by the three participating olive mills based on operational logs and technical documentation. Economic parameters (olive oil prices, harvesting costs, transportation costs, processing fees, and waste management costs) reflect actual market conditions and contractual agreements during the study period. Environmental parameters (lagooning capacities and land spreading limits) were obtained from environmental permits issued to the mills by Tunisian regulatory authorities. All parameters were validated through consultation with local agronomists and mill operators to ensure representativeness of typical operational conditions in semi-intensive Tunisian olive estates. While the complete model implementation is publicly available at https://github.com/ARGOUBI25/olive-harvest-optimization, raw operational data remain confidential per institutional agreements with participating producers and the Office of State Lands.

The integrated analysis of our case study relies on a comprehensive set of technical, economic, and environmental parameters characterizing the Henchir Chaal olive production system. Table 3 presents the spatial and agronomic characteristics of the 18 olive plots studied, covering a total area of 150 hectares with an average productivity of 2.7 tons/day. These plots show significant variability in terms of maturity index (3.6 to 5.3), a determining factor for optimizing oil quality.

Table 3

Table 3. Characteristics of olive groves in Henchir Chaal (2020–2021 season).

The processing infrastructure consists of three mills (see Table 4) with daily capacities ranging from 12 to 55 tons. A critical aspect for our environmental analysis is the asymmetric distribution of valorization capacities: only Mill P1 has an OMW valorization facility (20.0 m³/day), while Mills P2 and P3 are not equipped with such facilities, thus creating a significant structural constraint. The extraction systems also differ, with P1 and P3 employing three-phase systems (generating 1.2 m³ of OMW per ton of olives) and P2 using a two-phase system (0.8 m³ of OMW per ton).

Table 4

Table 4. Characteristics of oil mills in Henchir Chaal (2020–2021 season).

Olive oil quality parameters varied throughout the harvest period, with increasing oil content and decreasing acidity as the season progressed. The oil extraction rate (ATR) ranged from 0.16 to 0.22 tons of oil per ton of olives, with an average of 0.19 across all parcels.

For the quality objective function, the following weights were used based on industry standards and local market preferences:

${\omega }_1=0.5,{\omega }_2=0.25,{\omega }_3=0.15,{\omega }_4=0.10$

The economic parameters included:

• Average selling price of olive oil: 11,200 TND/ton (with daily variations of ±5%).

• Harvesting costs: 85–120 TND/ton (varying by parcel and team).

• Transportation costs: 20–45 TND/ton (depending on the distance between parcels and mills).

• Processing costs: 150–200 TND/ton (varying by mill).

• OMW management costs: Lagooning (18–25 TND/ m³), Spreading (12–16 TND/ m³).

The OMW production coefficient α was set at 1.2 m³ per ton of processed olives for mills using three-phase extraction systems (P1 and P3), and at 0.8 m³ per ton for the two-phase system (P2), based on actual measurements during the 2020–2021 season. These interdependent parameters form the basis of our environmental and economic optimization model.

5.3 Implementation of the ε-constraint method

The model was implemented in Python 3.9+ using the Gurobi optimizer, executed on an Intel Core i7 workstation equipped with 32GB of RAM. The complete implementation, including the MILP formulation and ε-constraint method implementation, is publicly available at https://github.com/ARGOUBI25/olive-harvest-optimization. For problem instances reflecting typical olive harvest scenarios in Tunisia (15–20 parcels, 3–5 mills, and a 10–15 day planning horizon), optimal solutions were obtained within acceptable computational times (under 30 min), confirming the model's suitability for practical operational planning.

This comprehensive solution framework equips decision-makers with a clear understanding of the environmental–economic trade-offs inherent in olive oil production, thereby facilitating environmentally informed decisions on harvest scheduling and waste management in line with circular economy principles and sustainability objectives.

In accordance with the AUGMECON2 methodology detailed in Section 3, we first constructed the payoff table by optimizing each objective independently. Table 5 presents the resulting data, where the diagonal elements (in bold) indicate the optimal values for each objective, and the off-diagonal elements show the corresponding values of the other objectives when only one objective is being optimized.

Table 5

Table 5. Payoff table for the henchir chaal case study.

Based on this payoff table, the following ranges for the ε values were established:

$Z_2\in \left[3,925.8,6,854.1\right],Z_3\in \left[871,230,1,356,780\right]$

Following the proposed methodology, these ranges were divided into p₂ = 5 and p₃ = 10 equal intervals, respectively, resulting in a total of 66 optimization problems to be solved (after eliminating dominated solutions).

5.4 Multi-objective vs. single-objective performance comparison

To establish the novelty and practical necessity of the multi-objective optimization framework, this subsection provides a systematic comparison between single-objective and multi-objective approaches. The analysis demonstrates that single-objective optimization, while computationally simpler, produces operationally unbalanced solutions that fail to address the inherently multi-dimensional nature of sustainable olive oil production.

5.4.1 Single-objective performance and inherent trade-offs

Table 5 reveals fundamental conflicts between the three objectives, quantifying the performance degradation that occurs when prioritizing one dimension at the expense of others. Each row represents an extreme solution obtained by optimizing a single objective while allowing the others to deteriorate freely.

Environmental-centric scenario (Min Z₁): Minimizing non-valorized OMW achieves the best environmental outcome (105.6 m³ of non-valorized waste), representing optimal waste management performance. However, this environmental focus comes at substantial economic cost: profit is limited to 982,456 TND, representing a 374,324 TND loss (27.6% reduction) compared to profit-maximizing strategies. Quality performance is moderate (4,236.2 units), falling 38.2% below the quality-optimal solution. This scenario reflects operations where environmental compliance dominates decision-making, potentially at the expense of economic viability.

Quality-centric scenario (Max Z₂): Maximizing olive oil quality yields the highest quality score (6,854.1 units), ensuring premium product positioning and extra virgin certification. However, this quality focus produces the worst economic outcome (871,230 TND profit), representing a 485,550 TND sacrifice (35.8% reduction) relative to profit optimization. Environmental performance deteriorates significantly, with non-valorized OMW reaching 398.2 m³—a 277% increase compared to the environmentally optimal solution. This scenario reflects premium quality strategies that may be economically unsustainable and environmentally problematic.

Profit-centric scenario (Max Z₃): Maximizing economic profit achieves 1,356,780 TND, representing the upper bound of financial performance. However, this economic focus produces severe environmental degradation: non-valorized OMW reaches 512.8 m³, representing a 385% increase (407.2 m³ additional waste) compared to environmentally optimal operations. Quality suffers dramatically, dropping to 3,925.8 units—a 42.7% reduction that potentially disqualifies production from extra virgin classification and premium market access. This scenario reflects short-term profit maximization that violates environmental regulations and compromises market positioning.

Table 6 provides a structured comparison of these single-objective extremes, highlighting the severe imbalances inherent in mono-dimensional optimization.

Table 6

Table 6. Comparative performance: single-objective vs. multi-objective optimization.

Quantification of conflicts: The magnitude of these trade-offs reveals why single-objective approaches are fundamentally inadequate for olive oil production planning:

• Environment vs. profit: Achieving optimal environmental performance (Min Z₁) sacrifices 27.6% of potential profit. Conversely, maximizing profit increases environmental burden by 385%.

• Quality vs. profit: Prioritizing quality (Max Z₂) reduces profit by 35.8%. Conversely, profit maximization degrades quality by 42.7%, jeopardizing premium market positioning.

• Quality vs. environment: Environmental optimization (Min Z₁) reduces quality by 38.2% compared to quality-focused strategies. Quality maximization (Max Z₂) increases OMW by 277%.

These sharp trade-offs demonstrate that single-objective solutions are operationally infeasible in real-world contexts where producers must simultaneously satisfy environmental regulations (e.g., Tunisia's 80% valorization target), maintain quality standards for market access (extra virgin certification requiring acidity <0.8%), and achieve economic viability to sustain operations.

5.4.2 Multi-objective framework: value proposition and novelty

The ε-constraint implementation addresses the limitations of single-objective optimization by generating 66 Pareto-efficient solutions that systematically explore the trade-off space between environmental performance, oil quality, and economic profitability. This multi-objective framework provides several critical advantages:

1. Explicit trade-off visualization: Rather than presenting three extreme, unbalanced solutions, the Pareto frontier reveals the full spectrum of feasible compromises. Decision-makers can observe how incremental improvements in one objective affect the others, enabling informed prioritization based on organizational constraints and stakeholder preferences.

2. Stakeholder negotiation support: Olive oil production involves multiple stakeholders with competing interests: producers prioritize profit, regulators enforce environmental compliance, processors demand quality consistency, and communities require environmental protection. The Pareto set provides a common analytical framework for identifying mutually acceptable compromise solutions rather than imposing unilateral optimization of one party's preferred objective.

3. Adaptive management capability: External conditions change over time—environmental regulations tighten, market premiums for quality fluctuate, and economic pressures vary with commodity prices. The multi-objective approach generates a portfolio of solutions from which decision-makers can select based on current conditions, rather than requiring complete model re-optimization when priorities shift.

4. Synergy identification: The Pareto frontier reveals regions where modest sacrifices in one objective yield disproportionate gains in another—“win-win” opportunities invisible in single-objective analysis. For instance, our analysis identifies solutions that achieve 81% of maximum profit (104,580 TND vs. 356,780 TND) while reducing non-valorized OMW by 54% (236.2 m³ vs. 512.8 m³) and maintaining quality scores 48% higher than profit-maximizing scenarios (5,842.6 vs. 3,925.8 units). Such balanced solutions represent the practical operational regimes most likely to achieve simultaneous regulatory compliance, market competitiveness, and environmental stewardship.

5. Regulatory feasibility: Single-objective optimization often produces solutions that violate implicit constraints. The profit-maximizing solution (Max Z₃) generates 512.8 m³ of non-valorized OMW, which, given the limited valorization capacity (20 m³/day at Mill P1), would require intensive lagooning and land spreading that approaches or exceeds regulatory limits. Multi-objective optimization explicitly incorporates these trade-offs, ensuring solutions remain within feasible operational bounds.

Bi-objective scenarios not separately analyzed: While some multi-objective frameworks explore pairwise combinations (e.g., optimizing environment and profit while ignoring quality), such bi-objective approaches remain inadequate for olive oil production systems where all three dimensions are simultaneously constrained by regulations (environmental limits), market standards (quality certification), and economic viability (profit thresholds). Our three-objective formulation reflects the operational reality that producers cannot selectively ignore any dimension: environmental non-compliance incurs legal penalties, quality deficiencies eliminate premium market access, and economic losses threaten operational continuity. The ε-constraint method enables direct exploration of the three-dimensional Pareto frontier without requiring intermediate bi-objective simplifications.

5.4.3 Comparative performance analysis

To quantitatively demonstrate the superiority of the multi-objective approach, we compare a representative balanced solution from the Pareto frontier against the three single-objective extremes:

Balanced multi-objective solution: Selected from the Pareto frontier based on the compromise principle (equidistant from all three ideal points in normalized objective space), this solution achieves:

• Z₁ = 236.2 m³ (non-valorized OMW).

• Z₂ = 842.6 quality units.

• Z₃ = 104, 580 TND profit.

Performance comparison:

• vs. Min Z₁ (Environment): The balanced solution sacrifices 124% additional OMW (236.2 vs. 105.6 m³) but gains 12.4% profit (104,580 vs. 82,456 TND) and 38% quality improvement (5,842.6 vs. 4,236.2 units). This trade-off represents a manageable environmental compromise in exchange for substantial economic and quality gains.

• vs. Max Z₂ (Quality): The balanced solution accepts a 14.8% quality reduction (5,842.6 vs. 6,854.1 units) but gains 26.8% profit improvement (104,580 vs. 71,230 TND) and 40.7% OMW reduction (236.2 vs. 398.2 m³). This demonstrates that near-optimal quality can be maintained while significantly improving environmental and economic performance.

• vs. Max Z₃ (Profit): The balanced solution sacrifices 18.6% profit (104,580 vs. 356,780 TND) but achieves 53.9% OMW reduction (236.2 vs. 512.8 m³) and 48.8% quality improvement (5,842.6 vs. 3,925.8 units). This modest profit sacrifice enables regulatory compliance and premium market access—critical for long-term sustainability.

This comparative analysis reveals that the balanced multi-objective solution achieves:

• 81% of maximum profit (vs 100% in Max Z₃, 72% in Min Z₁, 64% in Max Z₂).

• 85% of maximum quality (vs 100% in Max Z₂, 62% in Min Z₁, 57% in Max Z₃).

• Environmental performance 54% better than profit-maximizing scenarios.

These metrics demonstrate that multi-objective optimization achieves no dimension below 80% of its optimum, while single-objective solutions routinely sacrifice 35%–65% of performance in non-prioritized dimensions.

5.4.4 Establishing novelty: why multi-objective optimization is essential

This comparative analysis establishes three core contributions that justify the multi-objective formulation:

1. Operational infeasibility of single-objective solutions: Our quantitative analysis demonstrates that single-objective optimization produces extreme solutions incompatible with real-world operational requirements. Profit maximization violates environmental regulations (512.8 m³ OMW approaches lagoon capacity limits); quality maximization is economically unsustainable (35.8% profit loss); environmental optimization lacks economic viability (27.6% profit sacrifice). None of these extreme solutions represent implementable operational strategies for Tunisian olive oil producers facing simultaneous regulatory, market, and financial pressures.

2. Trade-off quantification for policy design: The Pareto frontier provides policymakers with explicit visibility into the costs of regulatory tightening. For instance, our analysis shows that reducing non-valorized OMW from 512.8 m³ (profit-optimal) to 236.2 m³ (balanced solution) costs 252,200 TND in foregone profit per planning period. Such quantification enables evidence-based policy design, where regulators can calibrate environmental standards based on documented economic impacts rather than arbitrary targets.

3. Decision support for heterogeneous stakeholders: Olive oil production involves stakeholders with divergent priorities. The Pareto frontier transforms these competing interests from ideological conflicts into quantified trade-offs amenable to negotiation. Rather than debating whether “environment” or “profit” should dominate, stakeholders can identify specific solutions that satisfy minimum acceptable thresholds across all dimensions—a form of collaborative decision-making impossible with single-objective optimization.

In summary, the novelty of our multi-objective framework lies not merely in its methodological sophistication, but in its fundamental alignment with the multi-dimensional nature of sustainable agricultural production. By explicitly addressing environmental, quality, and economic objectives simultaneously, the approach generates operationally feasible solutions that reflect the complex reality of olive oil supply chain management under binding regulatory and market constraints.

5.5 Environmental performance analysis

The primary environmental objective of the model is to maximize the valorization of OMW while complying with strict regulatory constraints. Figure 3 illustrates the distribution of OMW management across different disposal pathways.

Figure 3

Figure 3. Daily OMW generation and management pathways.

Our results show that the optimal solution achieves an overall valorization rate of 12.8% of total OMW generated, significantly below the regulatory target of 80%. This relatively low valorization rate reflects the limited availability of valorization facilities in Henchir Chaal, where only one such facility (Mill P1) exists. Despite the model's inherent preference for valorization (motivated by environmental and economic objectives), the strict constraints on valorization capacity ($V_{max}^{fp}=20.0$ m³/day for P1 only) limit what can be achieved in practice. The remaining 87.2% is distributed between authorized lagoon storage (48.5%) and controlled land spreading (38.7%), both maintained within regulatory limits but constituting the majority of waste management solutions.

Table 7 provides a comprehensive overview of the environmental performance indicators, with particular attention to greenhouse gas emissions (CO₂-equivalent).

Table 7

Table 7. Summary of OMW management outcomes and environmental indicators.

This analysis highlights a critical infrastructural gap in the region's olive oil sector: despite the environmental and economic benefits of valorization, the limited capacity of the existing facility creates a bottleneck in achieving circular economy goals. Moreover, the current system generates around 68.5 tons of CO₂-equivalent emissions, mainly due to transportation and lagoon operations, underscoring the climate relevance of these waste management choices.

5.6 Regulatory compliance

A critical aspect of the model is ensuring strict adherence to environmental regulations regarding waste management capacity. Figure 4 presents the daily utilization of lagoon capacity B_p and land spreading limits E_f throughout the planning horizon.

Figure 4

Figure 4. Daily utilization of environmental capacity constraints.

The results confirm that at no point does the model violate the regulatory constraints. However, the system operates close to capacity limits for both lagoon storage (peak utilization of 97.8% on day 8) and land spreading (peak utilization of 99.1% on day 7). This near-saturation of traditional disposal methods demonstrates the system's vulnerability to harvest volume fluctuations and underscores the urgent need for expanded valorization infrastructure to relieve pressure on these limited disposal pathways.

5.7 Environmental-economic trade-offs

To explore the sensitivity of economic outcomes to environmental constraints and valorization capacity, we conducted a series of hypothetical scenarios. Figure 5 illustrates the resulting relationship between valorization capacity expansion and environmental-economic performance.

Figure 5

Figure 5. Impact of valorization capacity on environmental-economic performance.

The analysis reveals several key insights:

• Baseline: The current limited valorization capacity (20 m³/day at Mill P1 only) achieves only moderate environmental performance (12.8% valorization rate) while constraining economic potential, with a profit of 104,580 TND.

• 50% increase: Raises the valorization rate to 17.5% (+4.7 percentage points) and profit to 120,450 TND (+15.2%).

• Doubling capacity: Achieves a valorization rate of 23.6% and increases profit to 136,740 TND (+30.8%).

• Installations in all mills: Adding valorization facilities in all three mills could reach a valorization rate of approximately 60%–70%, still short of the 80% regulatory target.

Table 8 summarizes the detailed results of our sensitivity analysis.

Table 8

Table 8. Sensitivity analysis of valorization capacity and environmental constraints.

5.8 Quality performance

Figure 6 presents the distribution of key quality attributes (acidity and peroxide index) across mills, which are critical for maintaining extra virgin olive oil certification.

Figure 6

Figure 6. Distribution of quality indicators across mills.

The average acidity level across all production was 0.64%, below the 0.8% threshold required for extra virgin classification, with 91.7% of daily production meeting this standard. Peroxide values averaged 12.3 meq O₂/kg, well below the regulatory limit of 20 meq O₂/kg. Table 9 summarizes these results.

Table 9

Table 9. Quality performance by mill.

5.9 Spatial optimization and logistics

Figures 7, 8 present complementary spatial analyses of the optimized harvest and transport plan. Figure 7 displays the optimized allocation of harvesting teams and transportation flows, with annotations highlighting transport-intensive zones and the routing structure needed to reach valorization-capable mills.

Figure 7

Figure 7. Optimized harvesting and transport routes with CO₂ intensity overlay.

Figure 8

Figure 8. Choropleth map of transport-related CO₂ emissions across olive groves.

Figure 8 provides a choropleth map of cumulative transport-related CO₂ emissions (in tons) across olive groves in the study area. Emissions hotspots correspond to remote parcels located far from the only valorization-equipped mill (P1).

Overall, the model achieves an average transport distance of 18.2 km per ton of harvested olives, resulting in a 14.6% reduction in transport-related CO₂ emissions compared to current practices. However, due to the concentration of valorization infrastructure in a single location, certain plots incur longer travel distances, intensifying local emissions despite the global optimization.

6 Discussion and practical implications

6.1 Key findings and system vulnerabilities

The results of this study reveal critical insights into the challenges and opportunities for transitioning Tunisia's olive oil sector toward circular economy principles. Three core findings emerge from our analysis:

1. Infrastructure bottleneck: Valorization capacity represents the principal constraint to achieving circular economy objectives in the sector. Despite optimization of harvest scheduling and transport logistics, only 12.8% of OMW is currently valorized due to the presence of a single valorization facility (Mill P1). This structural limitation fundamentally restricts the industry's capacity to meet environmental targets.

2. Regulation-infrastructure misalignment: Environmental regulations imposing strict limits on lagooning and land spreading have not been accompanied by corresponding investments in valorization infrastructure. This regulatory-infrastructure gap creates significant economic and operational challenges for producers who must comply with environmental standards without adequate infrastructural support.

3. Investment scenarios: Our analysis indicates that expanding valorization capacity—particularly through a distributed network of facilities across multiple mills—offers the most balanced trade-off between environmental performance and economic viability. While full compliance with the 80% valorization target remains challenging, a pragmatic benchmark of 60%–70% valorization becomes achievable with strategic infrastructure investment.

The findings highlight several critical dimensions that warrant further discussion:

• System vulnerability and operational resilience: The current system operates near saturation limits, with lagoon and land-spreading capacities reaching peaks of 97.8% and 99.1%, respectively. This proximity to maximum capacity indicates significant vulnerability to production variations or logistical disruptions. Building operational resilience through buffer capacities and adaptive scheduling protocols emerges as an essential requirement for system stability.

• Environmental-economic trade-offs: The incremental valorization scenarios demonstrate diminishing marginal returns beyond certain expansion thresholds. Profit gains plateau after doubling valorization capacity, suggesting that unlimited infrastructure investment may not yield proportional benefits.

• Spatial inequality: Our spatial analysis reveals significant CO₂ emission hotspots resulting from extended transport routes to the centralized valorization facility. This creates inequitable distribution of environmental impacts, with remote production areas bearing disproportionate environmental and logistical burdens.

• Policy integration: The results point to the necessity for integrated policy approaches that simultaneously address environmental regulations, infrastructure development, and logistical optimization. Transport-related emissions are unevenly distributed across the region, highlighting the need for spatial considerations in sustainability planning.

6.2 Stakeholder-specific implementation guidelines

Translating optimization results into actionable strategies requires stakeholder-specific guidance that addresses the distinct operational contexts of grove managers, mill operators, and policy makers.

6.2.1 For olive grove managers

Olive grove managers face the operational challenge of balancing harvest timing, quality preservation, and logistics coordination. Our results provide several actionable insights:

• Harvest scheduling optimization: Prioritize early-to-mid season harvesting (days 3–8 in our 14-day horizon) when quality parameters remain favorable (average acidity 0.59%–0.64%) and valorization capacity at Mill P1 has not yet saturated. Late-season harvesting (days 10–14) forces greater reliance on lagooning and land spreading as valorization capacity depletes, increasing environmental impact by 23%–31% per ton processed.

• Strategic mill allocation: Given the asymmetric distribution of valorization capacity (only Mill P1 equipped with 20 m³/day capacity), producers located within 15–20 km of P1 should negotiate preferential access to this facility, even if processing costs are 8%–12% higher than alternatives. Our sensitivity analysis demonstrates that the environmental and long-term reputational benefits of valorization access outweigh marginal cost increases, particularly as regulatory enforcement intensifies.

• Quality threshold targeting: The quality-profit trade-off analysis indicates that investments in pre-harvest quality management yield returns up to 15% when product quality enables extra virgin classification. However, pursuing maximum quality (Max Z₂ scenario) sacrifices 35.8% profit. A practical strategy targets 85%–90% of maximum attainable quality (5,800–6,200 quality units in our case study) rather than absolute optimization, as marginal improvements beyond this threshold yield diminishing economic returns.

• Collaborative logistics arrangements: The spatial analysis reveals that transport-related CO₂ emissions are highly uneven, with remote groves bearing disproportionate burdens. Grove managers should establish cooperative scheduling agreements with neighboring producers to consolidate transport loads, reducing per-unit emissions by 14%–18% through shared logistics. Our model provides a template for such collaborative planning by demonstrating optimal routing patterns.

6.2.2 For mill operators

Mill operators control the critical nexus between harvest operations and waste management, making their strategic decisions pivotal for system-wide sustainability:

• Valorization infrastructure investment priorities: The sensitivity analysis (Table 8) provides clear investment guidance. Doubling current valorization capacity (from 20 to 40 m³/day) increases profit by 30.8% while improving valorization rates from 12.8% to 23.6%. Return-on-investment calculations suggest that for mills processing 800–1,200 tons per season, valorization infrastructure investments of 150,000–200,000 TND achieve payback periods of 3–4 seasons, assuming regulatory compliance benefits and avoided lagooning costs.

• Dynamic processing capacity management: Mills operate closest to capacity limits during days 6–9 of the harvest season, with utilization rates reaching 89%–94%. Operators should implement dynamic pricing mechanisms that incentivize off-peak deliveries (days 1–3 and 12–14), offering 5%–8% processing fee discounts for producers who can schedule flexibly. This demand smoothing reduces peak-period bottlenecks and enables more consistent valorization throughput, improving overall environmental performance.

• Quality screening protocols: The quality compliance analysis shows that 91.7% of production achieves extra virgin standards (acidity <0.8%) under optimal scheduling. However, 8.3% of batches require rejection or downgrading, representing 98–124 tons per season. Mill operators should implement rapid quality screening protocols (portable acidity testers, moisture analyzers) at intake points to reject substandard batches before processing begins, avoiding contamination of high-quality production runs and reducing unnecessary OMW generation from low-value processing.

• External valorization partnerships: With only 12.8% valorization achieved due to single-mill capacity constraints, operators should proactively develop partnerships with external valorization facilities (composting operations, biogas plants, pharmaceutical extraction firms). Our analysis indicates that securing contracts for an additional 15–20 m³/day of external valorization capacity would increase system-wide valorization rates to 28%–32%, substantially relieving pressure on lagooning and spreading pathways while generating potential revenue streams from valorized products.

• Two-phase vs. three-phase system evaluation: Mill P2's two-phase system generates 33% less OMW per ton (0.8 vs. 1.2 m³/ton) compared to three-phase systems at P1 and P3. However, two-phase systems typically require higher capital investment (15%–20% premium) and may produce slightly lower oil yields (2%–3% reduction). Operators planning system upgrades should evaluate this trade-off: in regions with severe valorization constraints and high lagooning costs, the OMW reduction from two-phase systems can justify the capital premium within 5–7 years.

6.2.3 For policy makers and regulators

Policy makers face the challenge of designing regulations that achieve environmental objectives without compromising the economic viability of the olive oil sector:

• Phased regulatory implementation: The most critical finding for policy makers is the fundamental mismatch between regulatory targets (80% valorization mandate) and infrastructure reality (12.8% achieved with current capacity). Our analysis demonstrates that even with perfect optimization, existing infrastructure cannot approach regulatory targets. Policy makers should adopt a phased approach: (i) immediate target of 25%–30% valorization (achievable with modest infrastructure expansion), (ii) intermediate target of 50%–60% within 5 years (requires distributed valorization network across multiple mills), (iii) long-term target of 80% within 10–15 years (requires comprehensive regional valorization infrastructure). This graduated approach maintains regulatory pressure while allowing time for necessary capital investment.

• Targeted investment incentive design: The sensitivity analysis quantifies the economic barriers to valorization infrastructure: doubling capacity requires investments of 150,000–200,000 TND per mill with 3–4 season payback periods under current market conditions. Policy makers should design targeted programs: (i) capital subsidies covering 40%–50% of valorization infrastructure costs, (ii) accelerated depreciation allowances for environmental equipment, (iii) preferential access to low-interest green financing, and (iv) tax credits for OMW valorization volumes exceeding baseline thresholds. Our cost-benefit analysis suggests that subsidies exceeding 35%–40% of capital costs would stimulate 60%–80% of mills to invest within 3–5 years.

• Spatially differentiated regulatory standards: The spatial analysis reveals significant geographic heterogeneity in infrastructure access and transport burdens. Rather than uniform national standards, regulators should consider spatially differentiated requirements: (i) higher valorization mandates (40%–50%) for mills in regions with existing valorization infrastructure, (ii) intermediate targets (25%–35%) for remote regions requiring transport to centralized facilities, and (iii) transitional allowances for small-scale producers (<500 tons/season) with limited infrastructure access. This differentiated approach maintains environmental ambition while accommodating practical constraints.

• Market-based policy instruments: Beyond command-and-control regulation, policy makers should explore market mechanisms: (i) tradeable valorization credits allowing mills with excess capacity to sell credits to constrained operators, creating economic incentives for infrastructure investment in optimal locations, (ii) environmental certification programs providing price premiums (8%–12% above commodity rates) for olive oil produced under verified low-OMW-impact systems, and (iii) public procurement preferences requiring government entities to source from certified sustainable producers. Our economic analysis suggests that 10%–15% price premiums for sustainable production would shift 50%–60% of producers toward voluntary over-compliance with environmental standards.

6.2.4 Universal implementation principles

Three cross-cutting principles emerge for successful implementation across all stakeholder groups:

1. Embrace multi-objective thinking: Single-objective optimization invariably fails in complex agricultural systems where environmental, economic, and quality dimensions are tightly coupled. Stakeholders at all levels should adopt multi-objective frameworks for planning and evaluation, explicitly quantifying trade-offs rather than treating objectives as lexicographically ordered priorities. Our ε-constraint methodology provides a replicable template for such decision support in other agricultural contexts.

2. Plan for operational variability: Our case study represents average conditions during the 2020–2021 season, but real operations face harvest volume fluctuations (±15%–25%), quality variations (±10%–18%), and processing disruptions. Stakeholders should maintain operational buffers: valorization capacity 20% above average demand, lagoon reserves 15%–20% below maximum capacity, flexible harvest scheduling windows allowing 2–3 day delays without quality degradation.

3. Foster industry collaboration: The spatial optimization results demonstrate that system-wide efficiency requires coordination across independently operated groves, mills, and transport providers. Industry associations should facilitate: (i) harvest coordination platforms enabling real-time scheduling optimization across multiple producers, (ii) shared quality monitoring data improving pre-harvest decision-making, and (iii) collaborative transport arrangements. Our model shows that coordinated scheduling can reduce transport emissions by 14.6% compared to decentralized decision-making.

6.3 Study limitations

While this research provides valuable insights for sustainable olive oil production planning, several limitations warrant acknowledgment:

Temporal and spatial scope: Our case study focuses on a 14-day planning horizon during the 2020–2021 harvest season in Henchir Chaal, representing peak-period operations in a single region. Results may not fully capture inter-seasonal variability in yields, quality, and weather conditions, geographic differences in infrastructure availability across Tunisia's diverse olive-producing regions, and long-term dynamics such as climate change impacts on olive phenology.

Deterministic optimization framework: The MILP formulation assumes perfect information regarding quality parameters, processing capacities, and waste generation coefficients. In practice, producers face significant uncertainty: olive yields vary ±15%–25% based on weather conditions, quality indicators exhibit ±10%–18% measurement variability, and processing efficiency fluctuates with equipment condition. Stochastic or robust optimization extensions would provide solutions more resilient to real-world uncertainties.

Simplified valorization modeling: Our model treats valorization as a capacity-constrained binary variable, abstracting from the heterogeneity of valorization pathways. In reality, different technologies (composting, anaerobic digestion, phenolic extraction, and biochar production) have distinct capital costs, throughput capacities, product values, and secondary environmental impacts. Explicit modeling of technology-specific attributes would enable more nuanced investment guidance.

Economic parameter stability: Cost and price parameters reflect 2020–2021 market conditions specific to Henchir Chaal. Olive oil markets exhibit substantial volatility: international prices fluctuate ±20%–30% annually based on global production, and processing costs respond to energy price shocks. Sensitivity analysis to economic parameters would strengthen confidence in the robustness of recommendations across diverse economic scenarios.

Behavioral and institutional factors: The optimization model assumes rational decision-making and perfect compliance with computed schedules. Actual implementation faces behavioral barriers: producer risk aversion may favor familiar practices, incomplete information may lead to suboptimal harvest timing, coordination failures among independent producers may prevent collaborative logistics, and power imbalances between producers and mills may distort optimal allocation patterns.

Environmental impact scope: While our analysis focuses on OMW management and CO₂ emissions from transport, comprehensive sustainability assessment would incorporate water consumption, agrochemical inputs, biodiversity impacts, soil erosion, and full life-cycle assessment including packaging and distribution. Our OMW-centric focus addresses the most acute environmental pressure point but represents one component of holistic sustainability.

Scalability considerations: The case study examines a medium-scale system (18 groves, 150 hectares, 3 mills, 800–1,200 tons/season). Findings may not directly transfer to smallholder systems (<50 hectares) where infrastructure investments lack economies of scale, industrial-scale operations (>500 hectares) where continuous processing alters operational dynamics, or different agro-climatic zones with distinct productivity profiles.

6.4 Future research directions

The limitations outlined above, combined with emerging trends in olive oil production and circular economy implementation, suggest several promising avenues for future research:

Stochastic optimization under uncertainty: Develop stochastic programming formulations that explicitly model uncertainty in yield (±15%–25%), quality (±10%–18%), and processing capacity (±8%–12%). Two-stage stochastic models with recourse decisions would better reflect operational flexibility in managing uncertainty.

Technology-specific valorization analysis: Expand the valorization component to explicitly model competing technologies with distinct capital costs, throughput capacities, and product values. Multi-criteria evaluation incorporating technology readiness levels, market maturity, and regulatory acceptance would guide strategic investment prioritization.

Multi-season planning with climate adaptation: Extend the planning horizon to multi-season frameworks (3–5 years) incorporating inter-annual yield variability, long-term infrastructure investment decisions, and climate change adaptation scenarios projecting temperature increases (+1.5–2.5°C by 2050) and precipitation changes.

Regional-scale network optimization: Scale the analysis to provincial or national levels, optimizing valorization infrastructure networks across 20–50 mills and 100–300 estates, addressing optimal location and sizing of shared facilities, waste transport network design, and economies of scale in centralized vs. distributed infrastructure.

Integrated supply chain analysis: Extend the optimization boundary upstream (nursery selection, irrigation scheduling, pest management) and downstream (bottling, distribution, retail) to capture full supply chain interactions, with attention to quality-differentiated pricing, sustainability certification schemes, and blockchain-based traceability systems.

Behavioral implementation research: Complement optimization modeling with behavioral analysis addressing producer risk perception, technology adoption barriers, cooperative formation mechanisms, power dynamics in producer-mill relationships, and policy instrument effectiveness through quasi-experimental evaluation of pilot programs.

Circular economy integration: Broaden the scope beyond OMW to comprehensive circular strategies including valorization of solid residues through pyrolysis or gasification, integration with adjacent sectors, industrial symbiosis networks where OMW phenolic compounds become inputs for pharmaceutical or cosmetic industries, and life-cycle assessment quantifying net environmental benefits.

Policy mechanism design: Develop and test alternative policy instruments including performance-based incentives vs. capital subsidies, tradeable valorization permits creating markets for environmental compliance, spatial differentiation of standards, and public-private partnership models for financing regional infrastructure.

Machine learning integration: Integrate optimization with machine learning for quality prediction using satellite imagery, dynamic rescheduling algorithms adjusting operations based on real-time utilization, reinforcement learning agents adapting strategies based on operational experience, and mobile decision support applications.

Comparative international analysis: Replicate the framework across diverse contexts (Spain, Italy, Greece, Morocco, and California) to identify universal principles vs. context-specific adaptations, benchmark Tunisia's performance, evaluate how different regulatory regimes shape sustainability transitions, and assess potential for international knowledge exchange.

These research directions collectively address the technical, economic, behavioral, and institutional dimensions required for systemic transformation of olive oil production toward environmental sustainability.

7 Conclusion

This study developed an integrated multi-objective optimization framework for sustainable agricultural supply chain management that simultaneously addresses operational efficiency, environmental compliance, and product quality. Applied to Mediterranean olive oil production, the framework demonstrates how circular economy principles can be embedded directly into supply chain decision-making while ensuring regulatory compliance.

The analysis reveals a critical infrastructure bottleneck: despite achieving 14.6% reduction in transport emissions and maintaining regulatory compliance, olive mill wastewater valorization remained limited to 12.8% due to insufficient processing capacity. This finding demonstrates that sustainable supply chain transformation requires coordinated infrastructure investment alongside operational optimization.

The framework makes three key contributions to sustainable supply chain management. Methodologically, treating environmental constraints as hard optimization limits rather than penalties provides robust regulatory compliance while revealing win-win operational strategies. From a decision support perspective, the ε-constraint approach enables systematic exploration of trade-offs, showing that strategic valorization capacity expansion could achieve 60%–70% waste recovery while improving profits by 30.8%. The spatial analysis reveals important equity considerations, with remote areas bearing disproportionate environmental burdens from centralized processing infrastructure.

For practitioners, the research demonstrates that supply chain sustainability requires integrated decision-making across traditionally siloed functions rather than end-of-pipe environmental management. The infrastructure analysis provides specific investment guidance: decentralized valorization networks offer the most promising pathway for achieving regulatory targets while maintaining competitiveness.

Several limitations indicate future research directions. The deterministic approach should incorporate uncertainty from weather variability and market fluctuations. Social sustainability dimensions warrant explicit integration beyond implicit benefits of environmental and economic improvements. Broader geographic validation would strengthen transferability across diverse agricultural contexts.

The olive oil sector's sustainability transformation offers broader lessons: environmental constraints define opportunity spaces rather than limitations, and competitive advantage emerges from supply chain designs that create value through resource efficiency. This framework provides both theoretical foundation and practical tools for agricultural supply chains to achieve this transformation while maintaining economic viability essential for long-term sustainability.

Data availability statement

The optimization model implementation and code are publicly available at https://github.com/ARGOUBI25/olive-harvest-optimization. Raw operational data from participating producers and mills remain confidential per institutional agreements with the Tunisian Office of State Lands (Office des Terres Domaniales) and cannot be publicly shared. Researchers interested in accessing aggregate data for validation purposes may contact the corresponding author with specific requests, which will be evaluated on a case-by-case basis subject to institutional approval.

Author contributions

MA: Conceptualization, Investigation, Software, Writing – original draft, Writing – review & editing. KM: Conceptualization, Funding acquisition, Investigation, Writing – review & editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This research was supported by the Deanship of Scientific Research at King Faisal University, Saudi Arabia [Grant number KFU254524].

Acknowledgments

The authors would like to express their sincere gratitude to the Deanship of Scientific Research at King Faisal University for supporting this research. The authors also thank their respective institutions, the University of Sousse and King Faisal University, for providing the necessary academic environment and resources. Special thanks go to the teams involved in data collection and simulation testing, whose contributions were instrumental in the completion of this study.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was used in the creation of this manuscript. All core research contributions, methodology, mathematical models, data analysis, results, and conclusions are entirely the original work of the author(s). The AI assistance was limited to editorial and structural improvements without altering the substance, findings, or technical accuracy of the research. All factual content, citations, and research claims have been verified by the author(s).

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References

Agence Nationale pour la Maǐtrise de l'Energie (2022). Tunisia low carbon strategy 2030. Government Report.

Google Scholar

Anvari, S., Aguado, R., Jurado, F., Fendri, M., Zaier, H., Larbi, A., et al. (2024). Analysis of agricultural waste/byproduct biomass potential for bioenergy: the case of Tunisia. Energy Sustain. Dev. 78:101367. doi: 10.1016/j.esd.2023.101367

Crossref Full Text | Google Scholar

Behzadi, G., O'Sullivan, M. J., Olsen, T. L., and Zhang, A. (2018). Agribusiness supply chain risk management: a review of quantitative decision models. Omega 79, 21–42. doi: 10.1016/j.omega.2017.07.005

Crossref Full Text | Google Scholar

Bei, H., Yu, M., Yang, T., and Murcio, R. (2025). Optimization of intermodal transportation routes for perishable goods considering customer satisfaction. Res. Transport. Bus. Manag. 59:101261. doi: 10.1016/j.rtbm.2024.101261

Crossref Full Text | Google Scholar

Belamkar, P., Biswas, S., Baidya, A., Majumder, P., and Bera, U. K. (2023). Multi-objective optimization of agro-food supply chain networking problem integrating economic viability and environmental sustainability through type-2 fuzzy-based decision making. J. Clean. Prod. 421:138294. doi: 10.1016/j.jclepro.2023.138294

Crossref Full Text | Google Scholar

Brandenburg, M., Govindan, K., Sarkis, J., and Seuring, S. (2014). Quantitative models for sustainable supply chain management: developments and directions. Eur. J. Oper. Res. 233, 299–312. doi: 10.1016/j.ejor.2013.09.032

Crossref Full Text | Google Scholar

Cairns, G., Roberts, J., Kallis, G., Martinez-Alier, J., and Norgaard, R. B. (2009). Paper assets, real debts: an ecological-economic exploration of the global economic crisis. Crit. Perspect. Int. Bus. 5, 14–25. doi: 10.1108/17422040910938659

Crossref Full Text | Google Scholar

Cinelli, M., Coles, S. R., and Kirwan, K. (2014). Review analysis of the potentials of multi criteria decision analysis methods to conduct sustainability assessment. Ecol. Indic. 46, 138–148. doi: 10.1016/j.ecolind.2014.06.011

Crossref Full Text | Google Scholar

Costanza, R., de Groot, R., Sutton, P., van der Ploeg, S., Anderson, S. J., Kubiszewski, I., et al. (2014). Changes in the global value of ecosystem services. Global Environ. Change 26, 152–158. doi: 10.1016/j.gloenvcha.2014.04.002

Crossref Full Text | Google Scholar

Donner, M., Erraach, Y., López-i Gelats, F., Manuel-i Martin, J., Yatribi, T., Radić, I., et al. (2022). Circular bioeconomy for olive oil waste and by-product valorisation: actors' strategies and conditions in the mediterranean area. J. Environ. Manage. 321:115836. doi: 10.1016/j.jenvman.2022.115836

PubMed Abstract | Crossref Full Text | Google Scholar

Enaime, G., Bacaoui, A., Yaacoubi, A., and Belaqziz, M. (2020). Phytotoxicity assessment of olive mill wastewater treated by different technologies: effect on seed germination of maize and tomato. Environ. Sci. Pollut. Res. 27, 21125–21136. doi: 10.1007/s11356-019-06672-z

PubMed Abstract | Crossref Full Text | Google Scholar

Fernandez-Lobato, L., López-Sánchez, Y., Baccar, R., Fendri, M., and Vera, D. (2022). Life cycle assessment of the most representative virgin olive oil production systems in Tunisia. Sustain. Product. Consumpt. 32, 908–923. doi: 10.1016/j.spc.2022.06.002

Crossref Full Text | Google Scholar

Food and Agriculture Organization (2020). Greenhouse gas emissions from agriculture. Available online at: http://www.fao.org/3/cb1993en/CB1993EN.pdf (Accessed March 15, 2025).

Google Scholar

Geissdoerfer, M., Savaget, P., Bocken, N. M. P., and Hultink, E. J. (2017). The circular economy-a new sustainability paradigm? J. Clean. Prod. 143, 757–768. doi: 10.1016/j.jclepro.2016.12.048

Crossref Full Text | Google Scholar

Haimes, Y. Y., Lasdon, L. S., and Wismer, D. A. (1971). On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans. Syst. Man, Cybern. 1, 296–297. doi: 10.1109/TSMC.1971.4308298

Crossref Full Text | Google Scholar

Harremöes, P., Gee, D., MacGarvin, M., Stirling, A., Keys, J., Wynne, B., et al. (2002). The Precautionary Principle in the 20th Century: Late Lessons From Early Warnings. London: Routledge.

Google Scholar

Jarboui, R., Sellami, F., Azri, C., Gharsallah, N., and Ammar, E. (2010). Olive mill wastewater evaporation management using PCA method: case study of natural degradation in stabilization ponds (Sfax, Tunisia). J. Hazard. Mater. 176, 992–1005. doi: 10.1016/j.jhazmat.2009.11.140

Crossref Full Text | Google Scholar

Jayarathna, C. P., Agdas, D., Dawes, L., and Yigitcanlar, T. (2021). Multi-objective optimization for sustainable supply chain and logistics: a review. Sustainability 13:13617. doi: 10.3390/su132413617

Crossref Full Text | Google Scholar

Karaouzas, I., Skoulikidis, N. T., Giannakou, U., and Albanis, T. A. (2011). Spatial and temporal effects of olive mill wastewaters to stream macroinvertebrates and aquatic ecosystems status. Water Res. 45, 6334–6346. doi: 10.1016/j.watres.2011.09.014

PubMed Abstract | Crossref Full Text | Google Scholar

Keskes, M., Zouari, A., Houssin, R., Dhouib, D., and Renaud, J. (2024). “Prioritization of circular olive oil production in Tunisia based on multi-criteria decision-making within a sustainable life cycle framework,” in Optimization in Agri-Food Supply Chain: Recent Studies in Agrifood Supply Chain and Animal Industry, 143–160. doi: 10.1002/9781394316977.ch8

Crossref Full Text | Google Scholar

Kirchherr, J., Reike, D., and Hekkert, M. (2017). Conceptualizing the circular economy: an analysis of 114 definitions. Resour. Conserv. Recycl. 127, 221–232. doi: 10.1016/j.resconrec.2017.09.005

Crossref Full Text | Google Scholar

Kumar, A., Mangla, S. K., Luthra, S., Rana, N. P., and Dwivedi, Y. K. (2020). Challenges in perishable food supply chains for sustainability management: a developing economy perspective. Bus. Strat. Environ. 29, 1809–1831. doi: 10.1002/bse.2470

Crossref Full Text | Google Scholar

Lahyani, R., Khemakhem, M., and Semet, F. (2015). Rich vehicle routing problems: from a taxonomy to a definition. Eur. J. Oper. Res. 241, 1–14. doi: 10.1016/j.ejor.2014.07.048

Crossref Full Text | Google Scholar

Liu, J., Dietz, T., Carpenter, S. R., Alberti, M., Folke, C., Moran, E., et al. (2007). Complexity of coupled human and natural systems. Science 317, 1513–1516. doi: 10.1126/science.1144004

PubMed Abstract | Crossref Full Text | Google Scholar

Masri, R., and Hamza, E. (2011). A stochastic linear program for Tunisian olive oil production chain. Int. J. Oper. Quantit. Manag. 17, 147–160.

Google Scholar

Mavrotas, G. (2009). Effective implementation of the ϵ-constraint method in multi-objective mathematical programming problems. Appl. Math. Comput. 213, 455–465. doi: 10.1016/j.amc.2009.03.037

Crossref Full Text | Google Scholar

Mavrotas, G., and Florios, K. (2013). An improved version of the augmented ϵ-constraint method (augmecon2) for finding the exact pareto set in multi-objective integer programming problems. Appl. Math. Comput. 219, 9652–9669. doi: 10.1016/j.amc.2013.03.002

Crossref Full Text | Google Scholar

Meftah, O., Guergueb, Z., Braham, M., Sayadi, S., and Mekki, A. (2019). Long term effects of olive mill wastewaters application on soil properties and phenolic compounds migration under arid climate. Agric. Water Manag. 212, 119–125. doi: 10.1016/j.agwat.2018.07.029

Crossref Full Text | Google Scholar

Mekki, A., Dhouib, A., and Sayadi, S. (2006). Changes in microbial and soil properties following amendment with treated and untreated olive mill wastewater. Microbiol. Res. 161, 93–101. doi: 10.1016/j.micres.2005.06.001

PubMed Abstract | Crossref Full Text | Google Scholar

Mirabella, N., Castellani, V., and Sala, S. (2014). Current options for the valorization of food manufacturing waste: a review. J. Clean. Prod. 65, 28–41. doi: 10.1016/j.jclepro.2013.10.051

Crossref Full Text | Google Scholar

Modica, G., Pulvirenti, A., Spina, D., Bracco, S., D'Amico, M., and Di Vita, G. (2024). Clustering olive oil mills through a spatial and economic gis-based approach. Cleaner Environ. Syst. 14:100207. doi: 10.1016/j.cesys.2024.100207

Crossref Full Text | Google Scholar

Moglie, M., Biancini, G., Norici, A., Mugnini, A., and Cioccolanti, L. (2024). Valorization of olive mill wastewater for arthrospira platensis production. Cell Rep. Sustain. 1:100017. doi: 10.1016/j.crsus.2024.100017

Crossref Full Text | Google Scholar

Rockström, J., Steffen, W., Noone, K., Persson, A., Chapin, F. S., Lambin, E. F., et al. (2009). A safe operating space for humanity. Nature 461, 472–475. doi: 10.1038/461472a

PubMed Abstract | Crossref Full Text | Google Scholar

Ruggeri, M., De Luca, F., Ungolo, A., Vigani, B., Paredes, A. J., Russo, E., et al. (2024). Olive mill wastewater: from by-product to smart antioxidant material. Int. J. Pharm. 8:100301. doi: 10.1016/j.ijpx.2024.100301

PubMed Abstract | Crossref Full Text | Google Scholar

Seuring, S., and Müller, M. (2008). From a literature review to a conceptual framework for sustainable supply chain management. J. Clean. Prod. 16, 1699–1710. doi: 10.1016/j.jclepro.2008.04.020

Crossref Full Text | Google Scholar

Spina, D., Borrello, M., Selvaggi, R., Chinnici, G., Hamam, M., Cembalo, L., et al. (2025). Transitioning towards a circular economy agri-food model: strategies to move from goals to objectives in the olive oil sector. J. Clean. Prod. 520:146130. doi: 10.1016/j.jclepro.2025.146130

Crossref Full Text | Google Scholar

Steffen, W., Richardson, K., Rockström, J., Cornell, S. E., Fetzer, I., Bennett, E. M., et al. (2015). Planetary boundaries: guiding human development on a changing planet. Science 347:1259855. doi: 10.1126/science.1259855

Crossref Full Text | Google Scholar

U.S. Environmental Protection Agency (2018). Idling reduction for agricultural equipment. Available online at: http://www.epa.gov/verified-diesel-tech/idling-reduction-agricultural-equipment (Accessed March 15, 2025).

Google Scholar

Vaz, T., Quina, M. M., Martins, R. C., and Gomes, J. (2024). Olive mill wastewater treatment strategies to obtain quality water for irrigation: a review. Sci. Total Environ. 931:172676. doi: 10.1016/j.scitotenv.2024.172676

PubMed Abstract | Crossref Full Text | Google Scholar

Velenturf, A. P. M., and Purnell, P. (2021). Principles for a sustainable circular economy. Sustain. Prod. Consumpt. 27, 1437–1457. doi: 10.1016/j.spc.2021.02.018

Crossref Full Text | Google Scholar

Yang, J., Li, C., Teng, J., Zhang, Y., Wang, Y., Hou, Y., et al. (2024). Multi-objective optimization and life cycle assessment of mass-integrated combined heat and power system. Sci. Total Environ. 951:175811. doi: 10.1016/j.scitotenv.2024.175811

PubMed Abstract | Crossref Full Text | Google Scholar

Yengue, J.-L., Rialland-Juin, C., and Servain, S. (2008). “The wine country, between landscape and promoting tool: the example of Chinon and Saint-Nicolas-de-Bourgueil Vineyards (France),” in VIIéme International Terroir Congress (Suisse), 727–733.

Google Scholar