Single-Machine Order Acceptance and Scheduling Problem Considering Setup Time and Release Date Relations
Bicakci, Papatya S.
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This paper focuses on a make-to-order production system, where rejection of some orders is inevitable due to limited production capacity. In such a system, accepting all orders may cause overloads, order delays, and customer dissatisfaction. For this reason, firms tend to reject some orders. The order acceptance and scheduling problem is defined as deciding simultaneously which orders to be selected and how to schedule these selected orders. An extension of this problem with sequence-dependent setup times and release dates has been rarely studied, and the existing studies suggest that setup activities wait for the release date to be performed. However, in real production environments this may not be the case. Therefore, this paper examines the relationships between setup times and release dates considering the overall scheduling literature. Previous scheduling studies define two different relationships concerning setup times and release dates. One of them considers setup time is completely dependent on release date, and the other one claims that they are completely independent. In this paper, a new relationship is addressed to propound that setup time may be partially dependent on the release date. The paper also proposes a new mixed integer linear programming formulation withO(n(2)) binary decision variables andO(n(2)) constraints. It includes a detailed computational analysis by solving available instances in the literature, which suggests that existing formulation can solve the test problems to optimality with up to 10 orders in a given time limit. Our proposed formulation, however, can solve the test problems to optimality with up to 50 orders within the same time limit. According to the findings, our approach seems to be more suitable for real-life applications, and the proposed formulation is extremely faster than the existing one.