On optimal permutation scheduling in stochastic proportionate flowshops

Document Type

Article

Publication Date

1-1-1992

Abstract

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 nj=1 cjETj, where Cj is the weight (holding cost) and Tj the completion time of job j. We establish that if [fj]nj=1 are in a class of distributions we define as SIFR, and {cj-1 Xj}nj=1 and [xj]nj=1 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 [Inline Formula] is an increasing sequence of likelihood ratio-ordered (hazard rate-ordered) random variables and the costs [Inline Formula] are nonincreasing, then a general cost function is minimized by the job sequence {1,2,…, n} in the stochastic ordering (increasing convex ordering) sense. © 1992, Cambridge University Press. All rights reserved.

Identifier

84976074628 (Scopus)

Publication Title

Probability in the Engineering and Informational Sciences

External Full Text Location

https://doi.org/10.1017/S0269964800002709

e-ISSN

14698951

ISSN

02699648

First Page

513

Last Page

523

Issue

4

Volume

6

Grant

DDM-9101179

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS