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Scheduling and lot streaming in two‐machine open shops with no‐wait in process

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  • Nicholas G. Hall
  • Gilbert Laporte
  • Esaignani Selvarajah
  • Chelliah Sriskandarajah

Abstract

We study the problem of minimizing the makespan in no‐wait two‐machine open shops producing multiple products using lot streaming. In no‐wait open shop scheduling, sublot sizes are necessarily consistent; i.e., they remain the same over all machines. This intractable problem requires finding sublot sizes, a product sequence for each machine, and a machine sequence for each product. We develop a dynamic programming algorithm to generate all the dominant schedule profiles for each product that are required to formulate the open shop problem as a generalized traveling salesman problem. This problem is equivalent to a classical traveling salesman problem with a pseudopolynomial number of cities. We develop and test a computationally efficient heuristic for the open shop problem. Our results indicate that solutions can quickly be found for two machine open shops with up to 50 products. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005

Suggested Citation

  • Nicholas G. Hall & Gilbert Laporte & Esaignani Selvarajah & Chelliah Sriskandarajah, 2005. "Scheduling and lot streaming in two‐machine open shops with no‐wait in process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 261-275, April.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:3:p:261-275
    DOI: 10.1002/nav.20065
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    1. Giorgio Carpaneto & Paolo Toth, 1980. "Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem," Management Science, INFORMS, vol. 26(7), pages 736-743, July.
    2. I.N. Kamal Abadi & Nicholas G. Hall & Chelliah Sriskandarajah, 2000. "Minimizing Cycle Time in a Blocking Flowshop," Operations Research, INFORMS, vol. 48(1), pages 177-180, February.
    3. Nicholas G. Hall & Chelliah Sriskandarajah, 1996. "A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process," Operations Research, INFORMS, vol. 44(3), pages 510-525, June.
    4. Sartaj Sahni & Yookun Cho, 1979. "Complexity of Scheduling Shops with No Wait in Process," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 448-457, November.
    5. Dan Trietsch & Kenneth R. Baker, 1993. "Basic Techniques for Lot Streaming," Operations Research, INFORMS, vol. 41(6), pages 1065-1076, December.
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