Scheduling parallel mixed-model assembly lines with cross-line item transfers

This paper investigates a system of parallel, identical assembly lines, where items can either remain on the same line or transfer to another line. The objective is to minimise the makespan or a cost function. First, the system is analysed under deterministic assumptions using a mixed-integer linear programming (MILP) model. The effects of transfers and in-transfer storage on the makespan are examined. Then, a Markov Decision Process (MDP) solution is introduced for stochastic conditions, where item arrivals and process times are uncertain. An MDP-based heuristic is developed to handle large-scale systems with many stages. Its performance, which considers both the makespan and transfer costs, is compared with a simplified myopic method. Results indicate that the makespan increases with the process time variability by 13% in the MILP model and 16% in the MDP solution. Transfers improve performance, reducing makespan by an average of 10%, both by the MILP and the MDP. In the deterministic case, both transfers and in-transfer storage lead to notable improvements, with makespan reductions of 5% to 13%. In the stochastic case, the number of stages and the transfer cost parameter affect the choice of the best policy.