Markov decision process for multi-manned mixed-model assembly lines with walking workers

Abstract

Product customization and frequent market changes force manufacturing companies to employ mixed-model instead of simple assembly lines. To well adjust the line’s capacity to production requirements, the line can benefit from the concept of reconfigurability. Our study deals with a reconfigurable mixed-model assembly line where tasks can be dynamically assigned to stations at each takt, workers can move among stations at the end of each takt, and the order of entering product models is infinite and unknown. The equipment assignment to stations occurs at the line design stage, and equipment duplication is allowed. The dynamic task assignment and workers’ movements among stations is a Markov Decision Process (MDP) that can be translated as a Linear Program (LP). As a result, the line design problem is formulated as a Mixed-Integer Linear Program (MILP) that integrates the MDP model. We propose some reduction rules and a decomposed transition process to reduce the model. The new MILP models taking into account stochastic parameters are built to solve the stochastic and robust problems, with the objectives of expected total cost minimization in all takts and total cost minimization in the worst takt, respectively. Computational experiments with benchmark and generated instances demonstrate the performance of the proposed MDP models. The managerial insights provided in the paper show the superiority of the dynamic task assignment over the model-dependent and fixed assignments usually studied in the literature.