Integrated bin packing and lot-sizing problem considering the configuration-dependent bin packing process

This paper addresses a practical production problem in an aviation manufacturing factory that focuses on the production of composite aeronautic products, where packing and assembling are two major operations conducted in the production process. We extract a novel integer programming model that integrates bin packing with the multi-level lot-sizing problem, which is characterized by re-configurable bins and configuration-dependent processing time. To obtain tighter lower bounds, we decompose the original model into a master problem and several sub-problems based on the Dantzig–Wolfe framework. To accelerate the column generation process, we develop a bi-level dynamic programming algorithm to solve the sub-problems exactly. A hybrid algorithm that combines the column generation and the fix-and-optimize heuristic is proposed to generate high-quality upper bounds. We first evaluate the quality of the lower bounds obtained from the linearly relaxed restricted master problem and then demonstrate the competitiveness of the proposed heuristic algorithm in terms of the solution quality and computational efficiency by comparing it with CPLEX, a commercial solver. In addition, we conduct sensitivity analysis of the bi-level dynamic programming to investigate the impact of the processing time required by the configuration-based bins. Moreover, a case study was conducted, which demonstrated the effect on cost reduction by shortening the length of unit time period in the planning horizon.