A Benders’ Decomposition Algorithm for Balancing and Sequencing of the Mixed-Model Multi-Manned Assembly Lines

Assembly lines of large-size products usually allow multiple workers to process tasks simultaneously on the same product. Meanwhile, due to the increasing demand of customized products, a diverse product mix with more product models and optional features is necessary. Although line balancing and model sequencing are interwoven, only the balancing problem of the mixed-model multi-manned assembly lines (MMALs) has been explored. In this study, a new mixed-integer linear programming model is proposed for balancing and sequencing of MMALs to minimize the number of workers, the number of stations, and the amount of utility work. An innovative approach based on Benders’ decomposition algorithm (BDA) is developed. Valid inequalities based on maximal cliques are generated to deal with the incompatible tasks which cannot be assigned to the same station to tighten and reduce the size of the formulation. An initial solution based on the greedy algorithm feeds the BDA to accelerate the convergence. Only one branch-and-search tree is built for the master problem to speed up the algorithm, and optimality cuts based on the subproblems are used as lazy cuts. The effectiveness of the proposed BDA is demonstrated by numerical results.

I. Introduction

The assembly line balancing problem (ALBP) is to balance the workload of stations. Simple ALBP (SALBP) is the most studied balancing problem under the hypotheses stated in Baybars [1]. There is only one standardized product, and there is one worker in each station. Due to the increasing demand for products with many customizations, the intense competition, and the changing market, a diverse production mix with more product models and optional features is of increasing importance to industries [2]. Assembly lines are key to the production of high-volume standardized products and the low-volume production of customized products [3]. Additionally, for large-size products, it is possible to allow more than one worker to process tasks on the same product simultaneously [4]. Worker number of each station is determined by the attributes of assigned tasks. An example of mixed-model multi-manned assembly lines (MMALs) can be found in Fig. 1. Fig. 1.

Example of the MMAL.