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Minimizing flow time on a single machine with job classes and setup times

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  • A. J. Mason
  • E. J. Anderson

Abstract

We examine the static sequencing problem of ordering the processing of jobs on a single machine so as to minimize the average weighted flow time. It is assumed that all jobs have zero ready times, and that the jobs are grouped into classes with the property that setup tasks are only required when processing switches from jobs of one class to jobs of another class. The time required for each setup task is given by the sum of a setdown time from the previous class and a setup time for the new class. We show that an algorithm presented in the literature for solving a special case of this problem gives suboptimal solutions. A number of properties of the optimal solution are derived, and their use in algorithms is evaluated. Computational results are presented for both a branch‐and‐bound procedure and a simpler depth‐first search.

Suggested Citation

  • A. J. Mason & E. J. Anderson, 1991. "Minimizing flow time on a single machine with job classes and setup times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 333-350, June.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:3:p:333-350
    DOI: 10.1002/1520-6750(199106)38:33.0.CO;2-0
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    References listed on IDEAS

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    1. Lucio Bianco & Salvatore Ricciardelli & Giovanni Rinaldi & Antonio Sassano, 1988. "Scheduling tasks with sequence‐dependent processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 177-184, April.
    2. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    3. Wlodzimierz Szwarc & Jatinder N. D. Gupta, 1987. "A flow‐shop problem with sequence‐dependent additive setup times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 619-627, October.
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    1. Esaignani Selvarajah & George Steiner, 2009. "Approximation Algorithms for the Supplier's Supply Chain Scheduling Problem to Minimize Delivery and Inventory Holding Costs," Operations Research, INFORMS, vol. 57(2), pages 426-438, April.
    2. Grundel, Soesja & Çiftçi, Barış & Borm, Peter & Hamers, Herbert, 2013. "Family sequencing and cooperation," European Journal of Operational Research, Elsevier, vol. 226(3), pages 414-424.
    3. José Niño-Mora, 2020. "Fast Two-Stage Computation of an Index Policy for Multi-Armed Bandits with Setup Delays," Mathematics, MDPI, vol. 9(1), pages 1-36, December.
    4. Kenneth R. Baker, 1999. "Heuristic procedures for scheduling job families with setups and due dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(8), pages 978-991, December.
    5. Kramer, Arthur & Iori, Manuel & Lacomme, Philippe, 2021. "Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization," European Journal of Operational Research, Elsevier, vol. 289(3), pages 825-840.

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