Domain-Independent Dynamic Programming and Constraint Programming Approaches for Assembly Line Balancing Problems with Setups

We propose domain-independent dynamic programming (DIDP) and constraint programming (CP) models to exactly solve type 1 and type 2 assembly line balancing problem with sequence-dependent setup times (SUALBPs). The goal is to assign tasks to assembly stations and to sequence these tasks within each station while satisfying precedence relations specified between a subset of task pairs. Each task has a given processing time and a setup time dependent on the previous task on the station to which the task is assigned. The sum of the processing and setup times of tasks assigned to each station constitute the station time and the maximum station time is called the cycle time. For the type 1 SUALBP (SUALBP-1), the objective is to minimize the number of stations, given a maximum cycle time. For the type 2 SUALBP (SUALBP-2), the objective is to minimize the cycle time, given the number of stations. On a set of diverse SUALBP instances, experimental results show that our approaches significantly outperform the state-of-the-art mixed integer programming models for SUALBP-1. For SUALBP-2, the DIDP model outperforms the state-of-the-art exact approach based on logic-based Benders decomposition. By closing 76 open instances for SUALBP-2, our results demonstrate the promise of DIDP for solving complex planning and scheduling problems. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods and Analysis. Funding: This work was supported by Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2020-04039]. 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.2024.0603 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0603 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .