More Stochastic Scheduling Models

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


This chapter discusses some other scheduling problems and models that do not fall into the categories presented in Chapters 2–9. Section 10.1 considers the problem to minimize a random variable of performance measure under stochastic order, which produces stronger results than the common approach of minimizing the expected value of the measure. Section 10.2 introduces the concept of “team-work tasks”, in which each job is processed by a team of different processors working on designated components of the job, and derives a number of corresponding optimal scheduling policies.


Schedule Problem Completion Time Export Market Maximum Lateness Total Completion Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Alidaee, B., & Womer, N. K. (1999). Scheduling with time dependent processing times: Review and extensions. Journal of the Operational Research Society, 50, 711–720.CrossRefGoogle Scholar
  2. Amoura, A. K., Bampis, E., Kenyon, C., & Manoussakis, Y. (2002). Scheduling independent multiprocessor tasks. Algorithmica, 32, 247–261.CrossRefGoogle Scholar
  3. Arbib, C., Pacciarelli, D., & Smriglio, S. (1999). A three-dimensional matching model for perishable production scheduling. Discrete Applied Mathematics, 92, 1–15.CrossRefGoogle Scholar
  4. Bachman, A., Janiak, A., & Kovalyov, M. Y. (2002). Minimizing the total weighted completion time of deteriorating jobs. Information Processing Letters, 81, 81–84.CrossRefGoogle Scholar
  5. Bianco, L., Blazewicz, J., Dell’Olmo, P., & Drozdowski, M. (1995). Scheduling multiprocessor tasks on a dynamic configuration of dedicated processors. Annals of Operations Research, 58, 493–517.CrossRefGoogle Scholar
  6. Blackburn, J., & Scudder, G. (2009). Supply chain strategies for perishable products: The case of fresh produce. Production and Operations Management, 18, 129–137.CrossRefGoogle Scholar
  7. Blazewicz, J., Ecker, K., Schmidt, G., & Weglarz, J. (1993). Scheduling in computer and manufacturing systems. Berlin: Springer.CrossRefGoogle Scholar
  8. Blazewicz, J., Drozdowski, M., & Weglarz, J. (1994). Scheduling multiprocessor tasks – A survey. Microcomputer Applications, 13, 89–97.Google Scholar
  9. 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
  10. Brown, M., & Solomon, H. (1973). Optimal issuing policies under stochastic field lives. Journal of Applied Probability, 10, 761–768.CrossRefGoogle Scholar
  11. Browne, S., & Yechiali, U. (1989). Dynamic priority rules for cyclic type queues. Advances in Applied Probability, 10, 432–450.CrossRefGoogle Scholar
  12. Browne, S., & Yechiali, U. (1990). Scheduling deteriorating jobs on a single processor. Operations Research, 38, 495–498.CrossRefGoogle Scholar
  13. 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
  14. Cai, X.Q.i, & Zhou, X. (2005). Single-machine scheduling with exponential processing times and general stochastic cost functions. Journal of Global Optimization, 31, 317–332.Google Scholar
  15. Cai, X.Q.i, & Zhou, X. (2013, to appear). Optimal policies for perishable products when transportation to export market is disrupted. Production and Operations Management. doi: 10.111/poms.12080.Google Scholar
  16. Cai, X. Q., & Zhou, X. (2004). Deterministic and stochastic scheduling with team-work tasks. Naval Research Logistics, 51, 818–840.CrossRefGoogle Scholar
  17. Cai, X. Q., Lee, C.-Y., & Li, C. L. (1998). Minimizing total flow time in two-processor task systems with prespecified processor allocations. Naval Research Logistics, 45, 231–242CrossRefGoogle Scholar
  18. Cai, X. Q., Lee, C.-Y., & Wong, T. L. (2000). Multi-processor task scheduling to minimize the maximum tardiness and the total completion time. IEEE Transactions on Robotics and Automation, 16, 824–830.CrossRefGoogle Scholar
  19. Chang, C., & Yao, D. (1993). Rearrangement, majorization and stochastic scheduling. Mathmatics of Operations Research, 18(3), 658–684.CrossRefGoogle Scholar
  20. Chopra, S., & Meindl, P. (2001). Supply chain management: Strategy, planning, and operation. Upper Saddle River: Prentice Hall.Google Scholar
  21. Cooper, W. L. (2001). Pathwise properties and performance bounds for a perishable inventory system. Operations Research, 49, 455–466.CrossRefGoogle Scholar
  22. Drozdowski, M. (1996). Scheduling multiprocessor tasks – An overview. European Journal of Operational Research, 94, 215–230.CrossRefGoogle Scholar
  23. Fawcett, P., Mcleish, R., & Ogden, I. (1992). Logistics management. Harlow: Prentice Hall.Google Scholar
  24. Ferguson, M., & Koenigsberg, O. (2007). How should a firm manage deteriorating inventory? Production and Operations Management, 16, 306–321.CrossRefGoogle Scholar
  25. Gehringer, E. F., Siewiorek, D. P., & Segall, Z. (1987). Parallel processing: The Cm experience. Bedford: Digital Press.Google Scholar
  26. Goyal, S. K., & Giri, B. C. (2001). Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134, 1–16.CrossRefGoogle Scholar
  27. Hall, N. G., & Potts, C. N. (2004). Rescheduling for new orders. Operations Research, 52, 440–453.CrossRefGoogle Scholar
  28. Herrmann, J. W. (2006). Rescheduling strategies, policies, and methods. In J. W. Herrmann (Ed.), Handbook of production scheduling (pp. 135–148). New York: Springer.Google Scholar
  29. Hoogeveen, H., Lente, C., & T’kindt, V. (2012). Rescheduling for new orders on a single machine with setup times. European Journal of Operational Research, 223, 40–46.CrossRefGoogle Scholar
  30. Hopkins, A. L., Smith, T. B., III & Lala, J. H. (1978). FTMP – A highly reliable fault-tolerant multiprocessor for aircraft. Proceedings of the IEEE, 66(10), 1221–1239.CrossRefGoogle Scholar
  31. Hsu, V. N. (2000). Dynamic economic lot size model with perishable inventory. Management Science, 46, 1159–1169.CrossRefGoogle Scholar
  32. Jackson, J. R. (1955). Scheduling a production line to minimize maximum tardiness (Research Report 43). Management Science Research Project, UCLA.Google Scholar
  33. Krawczyk, H., & Kubale, M. (1985). An approximation algorithm for diagnostic test scheduling in multi-computer systems. IEEE Transactions on Computers, 34, 869–872.CrossRefGoogle Scholar
  34. Kuo, W., Chien, W. T. K., & Kim, T. (1998). Reliability, yield, and stress burn-in. Boston: Kluwer.CrossRefGoogle Scholar
  35. Liskyla-Peuralahti, J., Spies, M., & Tapaninen, U. (2011). Transport vulnerabilities and critical industries: Experiences from a Finnish stevedore strike. International Journal of Risk Assessment and Management, 15, 222–240.CrossRefGoogle Scholar
  36. Mosheiov, G. (1991). V-shaped policies for scheduling deteriorating jobs. Operations Research, 39, 979–991.CrossRefGoogle Scholar
  37. Nahmias, S. (1982). Perishable inventory theory: A review. Operations Research, 30, 680–708.CrossRefGoogle Scholar
  38. Nandakumar, P., & Morton, T. E. (1993). Near myopic heuristics for the fixed-life perishability problem. Management Science, 39, 1490–1498.CrossRefGoogle Scholar
  39. Pinedo, M. (1983). Stochastic scheduling with release dates and due dates. Operations Research, 31, 559–572.CrossRefGoogle Scholar
  40. Pinedo, M. (2002). Scheduling: Theory, algorithms, and systems (2nd ed.). Englewood Cliffs: Prentice Hall.Google Scholar
  41. Raafat, F. (1991). Survey of literature on continuously deteriorating inventory models. Journal of the Operational Research Society, 42, 27–37.CrossRefGoogle Scholar
  42. 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
  43. Shaked, M., & Shanthikumar, J. G. (1994). Stochastic orders and their applications. Boston: Academic.Google Scholar
  44. Shanthikumar, J. G., & Yao, D. D. (1991). Bivariate characterization of some stochastic order relations. Advances in Applied Probability, 23, 642–659.CrossRefGoogle Scholar
  45. Snyder, L. V., Atan, Z., Peng, P., Rong, Y., Schmitt, A. J., & Sinsoysal, B. (2010, submitted). OR/MS models for supply chain disruptions: A review. Social Science Research Network.
  46. Starbird, S. A. (1988). Optimal loading sequences for fresh-apple storage facilities. Operations Research, 39, 911–917.CrossRefGoogle Scholar
  47. Stevenson, W. J. (2009). Operations management (10th ed.). New York: McGraw-Hill.Google Scholar
  48. Tadei, R., Trubian, M., Avendano, J. L., DellaCroce, F., & Menga, G. (1995). Aggregate planning and scheduling in the food industry: A case study. European Journal of Operational Research, 87, 564–573.CrossRefGoogle Scholar
  49. Vakharia, A. J., & Yenipazarli, A. (2009). Managing supply chain disruptions. Foundations and Trends in Technology, Information and Operations Management, 2, 243–325.CrossRefGoogle Scholar
  50. Wilson, M. C. (2007). The impact of transportation disruptions on supply chain performance. Transportation Research Part E: Logistics and Transportation Review, 43, 295–320.CrossRefGoogle Scholar
  51. Zhao, C., & Tang, H. (2010). Rescheduling problems with deteriorating jobs under disruptions. Applied Mathematical Modelling, 34, 238–243.CrossRefGoogle Scholar
  52. Zhou, X., & Cai, X. Q. (1997). General stochastic single-machine scheduling with regular cost functions. Mathematical and Computer Modeling, 26, 95–108.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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