• Management Science and Financial Engineering
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• v.15 no.2
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• pp.69-100
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• 2009

In this paper, we consider a relatively new two-machine flow shop scheduling problem where the unit time WIP cost increases as a job passes through various stages in the production process, and the objective is to minimize the total WIP (work-in-process) cost. Specifically, we study three special cases of the problem. First, we consider the problem where processing times on machine 1 are identical. Second, the problem with identical processing times on machine 2 is examined. The recognition version of the both problems is unary NP-complete (or NP-complete in strong sense). For each problem, we suggest two simple and intuitive heuristics and find the worst case bound on relative error. Third, we consider the problem where the processing time of a job on each machine is proportional to a base processing time. For this problem, we show that a known heuristic finds an optimal schedule.

• Management Science and Financial Engineering
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• v.17 no.1
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• pp.95-116
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• 2011

This paper considers a flowshop scheduling problem where a customer orders multiple products (jobs) from a production facility. The objectives are to minimize makespan and to minimize the sum of order (batch) completion times. The order cannot be shipped unless all the products in the order are manufactured. This problem was motivated by numerous real world problems encountered by a variety of manufacturers. For the makespan objective, we develop an optimal solution procedure which runs in polynomial time. For the sum of order completion time objective, we establish the complexity of the problem including several special cases. Then, we introduce a simple heuristic and find an asymptotically tight worst case bound on relative error. Finally, we conclude the paper with some implications.