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Simultaneous optimization of efficiency and performance balance measures in single‐machine scheduling problems

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  • Awi Federgruen
  • Gur Mosheiov

Abstract

Manufacturing and service organizations routinely face the challenge of scheduling jobs, orders, or individual customers in a schedule that optimizes either (i) an aggregate efficiency measure, (ii) a measure of performance balance, or (iii) some combination of these two objectives. We address these questions for single‐machine job scheduling systems with fixed or controllable due dates. We show that a large class of such problems can be optimized by solving either a single instance or a finite sequence of instances of the so‐called (SQC) problem, in which the sum of general quasiconvex functions of the jobs' completion times is to be minimized. To solve a single instance of (SQC), we develop an efficient, though pseudopolynomial algorithm, based on dynamic programming. The algorithm generates a solution that is optimal among all schedules whose starting time is restricted to the points of a prespecified (arbitrary) grid. The algorithm is embedded in an iterative procedure, where in each iteration a specific instance of (SQC) is solved. Special attention is given to the simultaneous minimization of the mean and variance of completion times. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • Awi Federgruen & Gur Mosheiov, 1993. "Simultaneous optimization of efficiency and performance balance measures in single‐machine scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(7), pages 951-970, December.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:7:p:951-970
    DOI: 10.1002/1520-6750(199312)40:73.0.CO;2-1
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    1. X. Cai & F. S. Tu, 1996. "Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early‐tardy penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1127-1146, December.
    2. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    3. Chung‐Lun Li & Edward C. Sewell & T. C. E. Cheng, 1995. "Scheduling to minimize release‐time resource consumption and tardiness penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 949-966, September.
    4. Michael X. Weng & Jose A. Ventura, 1996. "Note: “Simultaneous optimization of efficiency and performance balance measures in single‐machine scheduling problems”," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 313-318, March.

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