Lot-sizing and cyclic scheduling for multiple products in a flow shop

This paper considers a production-inventory system in which optimal batch sizes are determined for n products that are processed on m machines in a flow shop. The total cost function for this system is derived by considering three cost components: inventory cost in work-in-process, the final products inventory cost and the machine setup labor cost. In order to make the optimal solution realizable, it is assumed that all products have the same processing cycle time. The capacity constraint considered during the derivation of the optimal lot sizes acts as an additional constraint. Two heuristic algorithms are developed in order to obtain the optimal solution. An important part of these algorithms is the modeling of the recursive relations among the production waiting times and machine idle times. These algorithms are not only used in deriving the optimal solution but also in providing the production schedules. A numerical example is also demonstrated along with the conclusion and indication for future research.