An integrated model for product mix problem and scheduling considering overlapped operations

Product mix problem is one of the most important decisions made in production systems. Several algorithms have been developed to determine the product mix. Most of the previous works assume that all resources can perform, simultaneously and independently, which may lead to infeasibility of the schedule. In this paper, product mix problem and scheduling are considered, simultaneously. A new mixed-integer programming (MIP) model is proposed to formulate this problem. The proposed model differentiates between process batch size and transfer batch size. Therefore, it is possible to have overlapped operations. The numerical example is used to demonstrate the implementation of the proposed model. In addition, the proposed model is examined using some instances previously cited in the literature. The preliminary computational results show that the proposed model can generate higher performance than conventional product mix model.