Sample Path Analysis for Continuous Tandem Production Lines

Authors:
Leyuan Shi;Bor-Ruey Fu;Rajan Suri
Affiliations:
Department of Industrial Engineering, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706;Iomega Corporation, 1821 West Iomega Way, Roy, UT 84067;Department of Industrial Engineering, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706
Venue:
Discrete Event Dynamic Systems
Year:
1999

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Abstract

We considera tandem production line where the product flowing through theline is continuous fluid. We call such a line a continuous tandem(CT) line. We derive a recursive representation for the departuretime of products in CT lines. Next, we apply sample path analysistechniques to prove that the departure time is convex (in thesense of strong stochastic convexity) in the flow rates of themachines. We then prove that the infinitesimal perturbation analysis(IPA) estimate, for the gradient of throughput with respect tomachine flow rates, is strongly consistent.