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Scheduling for parallel dedicated machines with a single server

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  • Celia A. Glass
  • Yakov M. Shafransky
  • Vitaly A. Strusevich

Abstract

This paper examines scheduling problems in which the setup phase of each operation needs to be attended by a single server, common for all jobs and different from the processing machines. The objective in each situation is to minimize the makespan. For the processing system consisting of two parallel dedicated machines we prove that the problem of finding an optimal schedule is N P‐hard in the strong sense even if all setup times are equal or if all processing times are equal. For the case of m parallel dedicated machines, a simple greedy algorithm is shown to create a schedule with the makespan that is at most twice the optimum value. For the two machine case, an improved heuristic guarantees a tight worst‐case ratio of 3/2. We also describe several polynomially solvable cases of the later problem. The two‐machine flow shop and the open shop problems with a single server are also shown to be N P‐hard in the strong sense. However, we reduce the two‐machine flow shop no‐wait problem with a single server to the Gilmore—Gomory traveling salesman problem and solve it in polynomial time. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 304–328, 2000

Suggested Citation

  • Celia A. Glass & Yakov M. Shafransky & Vitaly A. Strusevich, 2000. "Scheduling for parallel dedicated machines with a single server," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(4), pages 304-328, June.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:4:p:304-328
    DOI: 10.1002/(SICI)1520-6750(200006)47:43.0.CO;2-1
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    1. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    2. 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.
    3. Logendran, Rasaratnam & Sriskandarajah, Chelliah, 1993. "Two-machine group scheduling problem with blocking and anticipatory setups," European Journal of Operational Research, Elsevier, vol. 69(3), pages 467-481, September.
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    Cited by:

    1. T.C.E. Cheng & Svetlana A. Kravchenko & Bertrand M. T. Lin, 2019. "Server scheduling on parallel dedicated machines with fixed job sequences," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 321-332, June.
    2. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    3. Wafaa Labbi & Mourad Boudhar & Ammar Oulamara, 2017. "Scheduling two identical parallel machines with preparation constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1531-1548, March.
    4. Nadia Babou & Djamal Rebaine & Mourad Boudhar, 2024. "Solving the two-machine open shop problem with a single server with respect to the makespan," Annals of Operations Research, Springer, vol. 338(2), pages 857-877, July.
    5. Abdelhak Elidrissi & Rachid Benmansour & Nicolas Zufferey & Mohammed Benbrahim & David Duvivier, 2024. "Minimization of maximum lateness on parallel machines with a single server and job release dates," 4OR, Springer, vol. 22(3), pages 351-385, September.
    6. Rachid Benmansour & Oliver Braun & Saïd Hanafi, 2019. "The single-processor scheduling problem with time restrictions: complexity and related problems," Journal of Scheduling, Springer, vol. 22(4), pages 465-471, August.
    7. Ammar Oulamara & Djamal Rebaine & Mehdi Serairi, 2013. "Scheduling the two-machine open shop problem under resource constraints for setting the jobs," Annals of Operations Research, Springer, vol. 211(1), pages 333-356, December.
    8. Sironi, Andrea & Zazzara, Cristiano, 2003. "The Basel Committee proposals for a new capital accord: implications for Italian banks," Review of Financial Economics, Elsevier, vol. 12(1), pages 99-126.
    9. David Füßler & Stefan Fedtke & Nils Boysen, 2019. "The cafeteria problem: order sequencing and picker routing in on-the-line picking systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 727-756, September.
    10. Hosseini, Amir & Otto, Alena & Pesch, Erwin, 2024. "Scheduling in manufacturing with transportation: Classification and solution techniques," European Journal of Operational Research, Elsevier, vol. 315(3), pages 821-843.

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