Irregular Performance Measures

  • Xiaoqiang Cai
  • Xianyi Wu
  • Xian Zhou
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 207)


This Chapter covers stochastic scheduling problems with irregular performance measures. Section 3.1 is focused on models where both the earliness and tardiness costs are functions of the completion time deviations from the due date. In Section 3.2, we consider the problem where the tardiness cost is a fixed charge once a job is late, whereas the earliness cost depends on the amount of completion time deviation from the due date. Section 3.3 addresses the completion time variance problem, a model that has been studied in the scheduling field for decades. We will show that, a common structure of the optimal schedule for an E/T problem appears as a V-shape around a due date. We will derive such properties for each model, characterize the analytic optimal solutions when possible, and develop solution algorithms based on the optimality properties. We will show that dynamic programming algorithms can usually be established based on V-shape properties.


  1. Baker, K. R., & Scudder, G. D. (1990). Sequencing with earliness and tardiness penalties: A review. Operations Research, 38, 22–36.CrossRefGoogle Scholar
  2. Benmansour, R., Allaoui, H., & Artiba, A. (2012). Stochastic single machine scheduling with random common due date. International Journal of Production Research, 50, 3560–3571.CrossRefGoogle Scholar
  3. Boxma, O. J., & Forst, F. G. (1986). Minimizing the expected weighted number of tardy jobs in stochastic flow shops. Operations Research Letters, 5, 119–126.CrossRefGoogle Scholar
  4. Buzacott, J. A., & Shanthikumar, J. G. (1993). Stochastic models of manufacturing systems. Englewood Cliffs: Prentice Hall.Google Scholar
  5. Cai, X.Q.i, & Zhou, X. (1997b). Scheduling jobs with random processing times to minimize weighted completion time variance. Annals of Operations Research, 70, 241–260.Google Scholar
  6. Cai, X.Q.i, & Zhou, X. (1999). Stochastic scheduling on parallel machine subject to random breakdowns to minimize expected costs for earliness and tardy cost. Operations Research, 47, 422–437.Google Scholar
  7. Cai, X. Q., & Tu, F. S. (1996). Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early-tardy penalties. Naval Research Logistics, 43, 1127–1146.CrossRefGoogle Scholar
  8. Cai, X. Q., & Zhou, X. (1997a). Scheduling stochastic jobs with asymmetric earliness and tardiness penalties. Naval Research Logistics, 44, 531–557.CrossRefGoogle Scholar
  9. Coffman, E. G., Jr., Flatto, L., & Wright, P. E. (1993). Optimal stochastic allocation of machines under waiting-time constraints. SIAM Journal on Computing, 22, 332–348.CrossRefGoogle Scholar
  10. Eilon, S., & Chowdhury, I. G. (1977). Minimizing waiting time variance in the single machine problem. Management Science, 23, 567–575.CrossRefGoogle Scholar
  11. Emmons, H., & Pinedo, M. (1990). Scheduling stochastic jobs with due dates on parallel machines. European Journal of Operational Research, 47, 49–55.CrossRefGoogle Scholar
  12. Federgruen, A., & Mosheiov, G. (1997). Single machine scheduling problems with general breakdowns, earliness and tardiness costs. Operations Research, 45, 66–71.CrossRefGoogle Scholar
  13. Hino, C. M., Ronconi, D. P., & Mendes, A. B. (2005). Minimizing earliness and tardiness penalties in a single-machine problem with a common due date. European Journal of Operational Research, 160, 190–201.CrossRefGoogle Scholar
  14. Hoogeveen, J. A. (2005). Multicriteria scheduling. European Journal of Operational Research, 167, 592–623.CrossRefGoogle Scholar
  15. Lauff, V., & Werner, F. (2004). Scheduling with common due date, earliness and tardiness penalties for multimachine problems: A survey. Mathematical and Computer Modelling, 40, 637–655.CrossRefGoogle Scholar
  16. Luenberger, D. G. (1984). Linear and nonlinear programming. Reading: Addison-Wesley.Google Scholar
  17. Merten, A. G., & Muller, M. E. (1972). Variance minimization in single machine sequencing problems. Management Science, 18, 518–528.CrossRefGoogle Scholar
  18. Panwalker, S. S., Smith, M. L., & Seidmann, A. (1982). Common due date assignment to minimize total penalty for the one machine scheduling problem. Operations Research, 30, 391–399.CrossRefGoogle Scholar
  19. Ronconi, D. P., & Powell, W. B. (2010). Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming. Journal of Scheduling, 13, 597–607.CrossRefGoogle Scholar
  20. Sarin, S. C., Erel, E., & Steiner, G. (1991). Sequencing jobs on a single machine with a common due date and stochastic processing times. European Journal of Operational Research, 51, 287–302.CrossRefGoogle Scholar
  21. Wan, G., & Yen, B. P.-C. (2009). Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs. European Journal of Operational Research, 195, 89–97.CrossRefGoogle Scholar
  22. Wu, H.-C. (2010). Solving the fuzzy earliness and tardiness in scheduling problems by using genetic algorithms. Expert Systems with Applications, 37, 4860–4866.CrossRefGoogle Scholar
  23. Xu, H. S., Kumar, S. P. R., & Mirchandani, P. B. (1992). Scheduling stochastic jobs with increasing hazard rate on identical parallel machines. Computers and Operations Research, 19, 535–543.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Xiaoqiang Cai
    • 1
  • Xianyi Wu
    • 2
  • Xian Zhou
    • 3
  1. 1.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatin, N.T.Hong Kong SAR
  2. 2.Department of Statistics and Actuarial ScienceEast China Normal UniversityShanghaiPeople’s Republic of China
  3. 3.Department of Applied Finance and Actuarial StudiesMacquarie UniversityNorth RydeAustralia

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