Heuristics for the One-Dimensional Bin Packing Problem with Time Windows

Huibing Cheng¹Jian Tu²Hong He¹Shanshui Zheng¹Dengheng Zheng^1*

• ¹Guangzhou Railway Polytechnic, Guangzhou, China
• ²Jiangxi Institute of Fashion Technology, Nanchang, China

Abstract: This paper introduces and studies the One-Dimensional Bin Packing Problem with Time Windows (1DBPP-TW)—a variant of the bin packing problem (BPP) with critical applications in the logistics industry. Despite extensive research on BPP, existing time-constrained BPP studies focus on variable-sized bins (VSBPPTW), while 1DBPP-TW— featuring homogeneous bins and a requirement for a common time point among items in the same bin—remains understudied. Given the NP-completeness of BPP, heuristic and metaheuristic algorithms are preferred for large-scale instances, as exact methods are computationally infeasible. To address this gap, we propose two efficient algorithms: the Greedy on Time Range (GTR) heuristic (optimized for real-time responsiveness, achieving solutions in ≤0.001s for large instances with deterministic, reliable outputs) and the Iterative Local Search (ILS) metaheuristic (enhanced with three neighborhood operators to improve convergence rate, delivering 7.3% average bin reduction over GTR). We first establish a mathematical model for 1DBPP-TW, then generate two benchmark datasets—optimal solution-known instances (opt) and random instances (rand)—for validation. Experimental results show that GTR and ILS efficiently solve 1DBPP-TW: for medium and large instances, they achieve better computational efficiency and comparable or higher solution quality than the linear programming solver CPLEX within a 3600s time limit. Practically, these algorithms address industry pain points such as low loading efficiency and time window conflicts. Theoretically, this work advances combinatorial optimization theory for time-constrained BPP variants and provides a benchmark for future research.