Abstract
In this paper, in order to maximise total profit, the order acceptance and scheduling problem was generalised by considering some customers with their own orders who do not agree with partial rejection/acceptance of them. Therefore, it was assumed that accepting or rejecting one customer is equal to accepting or rejecting all his orders. In addition, the considered penalty function for scheduling the orders was total weighted lateness. A mathematical programming model, an upper bound, a branch and bound, and an efficient heuristic algorithm were proposed for this problem. It was shown that before starting the problem solving procedure, it is possible to certainly reject or accept some customers. The proposed branch and bound algorithm solved 93% of 810 randomly designed problem instances in a reasonable time. Besides, the heuristic algorithm solved the problem instances with the size of 2,000 customers at most with 0.1% deviation from a lower bound.
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