Heavy traffic analysis of dynamic cyclic policies : a unified treatment of the single machine scheduling problem

154 Pages·1996·4 MB·English

by  Markowitz, David Maxwell

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Heavy Traffic Analysis of Dynamic Cyclic
Policies: A Unified Treatment of theSingle
Machine Scheduling Problem
David M. Markowitz and Lawrence M. Wein
#3925-96-MSA September, 1996
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HEAVY TRAFFIC ANALYSIS OF DYNAMIC
CYCLIC POLICIES: A UNIFIED TREATMENT OF
THE SINGLE MACHINE SCHEDULING PROBLEM
David M. Markowitz
Logistics Management Institute
McLean. \'A 22102
Lawrence M. Wein
Sloan School of Management. ALLT.
Cambridge. ALA 02139
ABSTRACT
This paper examines how setups, due-dates and the mix of standardized and customized
products affect the scheduling of a single machine operating in a dynamic and stochastic
environment. We restrict ourseh'es to the class of d}'namic cyclic policies, where the
machine busy/idle policy and lot-sizing decisions are controlled in a dynamic fashion,
but different products must be produced in a fixed sequence. .As in earlier work, we
conjecture that an a\-eraging principle holds for this queueing system in the heavy traffic
limit, and optimize over the class of dynamic cyclic policies. The results allow for a
detailed discussion of the interactions between the due-date, setup and product mix
facets of the problem.
September 1996