A tabu search algorithm for order acceptance and scheduling

Order acceptance and scheduling decisions arise when the limited production capacity entails a manufacturer to select among incoming orders. In this paper, we consider an order acceptance and scheduling problem in a single machine environment where the orders are processed without preemption and a sequence dependent setup time is incurred between processing of every consecutive order. The problem is defined formally as follows. A set of incoming orders is available at time zero. Each incoming order i is identified with a release date, ri, a processing time, pi, a due date, di, a deadline, d̄i, the maximum revenue, ei, the weight (tardiness penalty), wi, and a sequence dependent setup time where sji denotes the setup time when order j immediately precedes order i in the processing sequence. In this problem setting, ei shows the maximum revenue that the manufacturer can gain if this order is accepted and the tardiness of the order is zero. However, if the order is tardy, the revenue that the manufacturer can gain from this order, Ri, decreases linearly with its tardiness, Ti. The manufacturer may complete order i until its deadline d̄i, but for each time unit beyond its due date, a tardiness penalty cost of wi is incurred. No revenue can be gained from order i if its completion time exceeds its deadline, d̄i, and the revenue of order i equals to zero at its deadline. To ensure this, we set wi to ei/(d̄i-di) for each order i. Tardiness of order i is Ti = max(0, Ci − di), where Ci is the completion time of order i. Then revenue from order i is Ri = ei Ii−wi Ti. Here, Ii is an indicator that equals to 1 if order i is accepted, and 0 otherwise. Our aim is to find an optimal set of accepted orders and an optimal schedule for them that maximizes the manufacturer’s total revenue,