Optimization models for the flow-shop scheduling problem with multiple orders per job

This study investigates the flow-shop scheduling problem with multiple orders per job. We also consider the ready times of all orders, multiple product types within all orders, and the sequence-dependent setup times between the product types. Both lot processing machines and item processing machines are also discussed. Two scheduling problems are proposed. The performance measure is the total weighted completion time of all orders. We present two different mixed binary integer programming (BIP) formulation methods for each proposed problem; one method is based on dichotomous restrictions and the other method adopts the concept of assignment problem. Thus, four mixed BIP models are developed to optimally solve the two scheduling problems. Different formulation methods are also compared with each other for each proposed problem on the same benchmark problem data set.