A Logic-Based Benders Decomposition for the Car Resequencing Problem with a Painted Body Storage

The cost of producing diverse cars depends on the sequence in which they are arranged in the body shop, paint shop, and assembly shop. Before entering the downstream assembly shop, the upstream car sequence shared by the body shop and paint shop is readjusted via the painted body storage, which consists of several first-in-first-out lanes. The car resequencing problem addressed in this paper requires determining the upstream and downstream sequences and the car-to-lane assignment to minimize the total cost of the three shops. We propose a nested logic–based Benders decomposition approach with three levels, where each car is assigned a body and a color in the first level to determine the upstream sequence. In the second level, cars are rearranged by determining their configurations and downstream positions. A feasible assignment of cars to lanes is sought in the third level to respect this sequence change. We provide a mathematical formulation for each level and propose two shortest-path problem reformulations for the first level, where solving the first reformulation is equivalent to a k-shortest-path problem. The second reformulation is a shortest-path model restricted by demand constraints. A lower bound, valid inequalities, and a heuristic method are also proposed as enhancements. Computational results show that our approach can handle instances of up to 120 cars, about 10 times more than previous studies. A sensitivity analysis is conducted to provide some managerial insights. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: Financial support for this work was provided by the Canadian Natural Sciences and Engineering Research Council (NSERC) [Grant 2021-04037] and the National Natural Science Foundation of China [Grant 72372087]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0904 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0904 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .