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 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Probability in the Engineering and Informational Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.