Skip to main content Accessibility help

On Optimal Permutation Scheduling in Stochastic Proportionate Flowshops

  • Michael Pinedo (a1), Dequan Shaw (a1) and Xiuli Chao (a2)


Consider m machines in series with unlimited intermediate buffers and n jobs available at time zero. The processing times of job j on all m machines are equal to a random variable Xj with distribution Fj. Various cost functions are analyzed using stochastic order relationships. First, we focus on minimizing where cj is the weight (holding cost) and Tj the completion time of job j. We establish that if are in a class of distributions we define as SIFR, and and are increasing sequences of likelihood ratio-ordered and stochastic-ordered random variables, respectively, the job sequence [1, 2, … n ] is optimal among all static permutation schedules. Second, for arbitrary processing time distributions, if is an increasing sequence of likelihood ratio-ordered (hazard rate-ordered) random variables and the costs are nonincreasing, then a general cost function is minimized by the job sequence [1,2,…, n] in the stochastic ordering (increasing convex ordering) sense.



Hide All
Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing probability models. Silver Spring, MD: To Begin With.
Brown, M. & Solomon, H. (1973). Optimal issuing policies under stochastic field lives. Journal of Applied Probability 10(4):761768.
Chang, C.S., Chao, X., Pinedo, M., & Weber, R. (1992). On the optimality of the LEPT rule and cμ rule for machines in parallel. Journal of Applied Probability (to appear).
Chang, C.S. & Yao, D.D. (1990). Rearrangement, majorization and stochastic scheduling. International Business Machines, Report 16250.
Forst, F.G. (1983). Minimizing total expected cost in the two-machine, stochastic flow shop. O.R. Letters 2(2, 06), pp. 5861.
Ow, P.S. (1985). Focused scheduling in proportionate flowshops. Management Science 31(7, 07), pp. 852869.
Pinedo, M. & Wie, S.H. (1986). Inequalities for stochastic flow shops and job shops. Applied Stochastic Models and Data Analysis 2: 6169.
Pinedo, M. (1985). A note on stochastic shop models in which jobs have the same processing requirement on each machine. Management Science 31 (7, 07), pp. 840846.
Pinedo, M.L. & Rammouz, E. (1988). A note on stochastic scheduling on a single machine subject to breakdown and repair. Probability in the Engineering and Informational Sciences 2: 4149.
Ross, S.M. (1983). Stochastic processes. New York: Wiley & Sons.
Shanthikumar, J.G. & Yao, D.D. (1991). Bivariate characterization of some stochastic order relations. Advances in Applied Probability 23: 642659.
Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: Wiley & Sons.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed