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A branch‐and‐bound algorithm to minimize total flow time with unequal release dates

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  • Chengbin Chu

Abstract

This article examines the single‐machine scheduling problem to minimize total flow time with unequal release dates. This problem has been proven to be NP‐hard. We present a necessary and sufficient condition for local optimality which can also be considered as a priority rule. On the basis of this condition, we then define a class of schedules which contains all optimal solutions. We present some efficient heuristic algorithms using the previous condition to build a schedule belonging to this subset. We also prove some new dominance theorems, discuss the results found in the literature for this problem, and propose a branch‐and‐bound algorithm in which the heuristics are used to provide good upper bounds. We compare this new algorithm with existing algorithms found in the literature. Computational results on problems with up to 100 jobs indicate that the proposed branch‐and‐bound algorithm is superior to previously published algorithms. © 1992 John Wiley & Sons. Inc.

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  • Chengbin Chu, 1992. "A branch‐and‐bound algorithm to minimize total flow time with unequal release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 859-875, October.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:6:p:859-875
    DOI: 10.1002/1520-6750(199210)39:63.0.CO;2-W
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    1. Potts, C. N. & Van Wassenhove, L. N., 1983. "An algorithm for single machine sequencing with deadlines to minimize total weighted completion time," European Journal of Operational Research, Elsevier, vol. 12(4), pages 379-387, April.
    2. Gupta, Sushil K & Kyparisis, Jerzy, 1987. "Single machine scheduling research," Omega, Elsevier, vol. 15(3), pages 207-227.
    3. Reza H. Ahmadi & Uttarayan Bagchi, 1990. "Lower bounds for single‐machine scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(6), pages 967-979, December.
    4. Lucio Bianco & Salvatore Ricciardelli, 1982. "Scheduling of a single machine to minimize total weighted completion time subject to release dates," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(1), pages 151-167, March.
    5. 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.
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    Cited by:

    1. Adel Kacem & Abdelaziz Dammak, 2021. "Multi-objective scheduling on two dedicated processors," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 694-721, October.
    2. Christos Koulamas, 1997. "Decomposition and hybrid simulated annealing heuristics for the parallel‐machine total tardiness problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 109-125, February.
    3. Hongfeng Wang & Min Huang & Junwei Wang, 2019. "An effective metaheuristic algorithm for flowshop scheduling with deteriorating jobs," Journal of Intelligent Manufacturing, Springer, vol. 30(7), pages 2733-2742, October.
    4. Christos Koulamas, 1996. "A total tardiness problem with preprocessing included," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(5), pages 721-735, August.
    5. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    6. Suresh Chand & Rodney Traub & Reha Uzsoy, 1996. "Single‐machine scheduling with dynamic arrivals: Decomposition results and an improved algorithm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(5), pages 709-719, August.
    7. K. H. Adjallah & K. P. Adzakpa, 2007. "Minimizing maintenance cost involving flow-time and tardiness penalty with unequal release dates," Journal of Risk and Reliability, , vol. 221(1), pages 57-65, March.
    8. Philippe Baptiste & Ruslan Sadykov, 2009. "On scheduling a single machine to minimize a piecewise linear objective function: A compact MIP formulation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 487-502, September.

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