Exact methods for order acceptance and scheduling on unrelated parallel machines

Abstract This paper studies an order acceptance and scheduling (OAS) problem on unrelated parallel machines to maximize the total net revenue of accepted orders, which is the difference between sum of revenues and total weighted tardiness. Two mixed-integer programming (MIP) models are formulated, which are further improved with various enhancement techniques. A formulation-based branch-and-bound algorithm is developed in an attempt to handle complicated instances following the principle of “divide and conquer”. Extensive computational experiments on various instances are conducted, and the results demonstrate the efficiency of the enhancement techniques for the formulations, as well as the effectiveness and efficiency of the formulation-based branch-and-bound algorithm. The proposed branch-and-bound algorithm can optimally solve instances with up to 50 jobs and different number of machines within the time limit of half an hour.

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