On the Throughput-Wip Trade-Off in Queueing Systems, Diminishing Returns and the Threshold Property: A Linear Programming Approach

Economics Working Paper 276

24 Pages Posted: 28 Jun 1998

See all articles by José Niño Mora

José Niño Mora

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Abstract

We present a new unifying framework for investigating throughput-WIP (Work-in-Process) optimal control problems in queueing systems, based on reformulating them as linear programming (LP) problems with special structure: We show that if a throughput-WIP performance pair in a stochastic system satisfies the Threshold Property we introduce in this paper, then we can reformulate the problem of optimizing a linear objective of throughput-WIP performance as a (semi-infinite) LP problem over a polygon with special structure (a threshold polygon). The strong structural properties of such polygones explain the optimality of threshold policies for optimizing linear performance objectives: their vertices correspond to the performance pairs of threshold policies. We analyze in this framework the versatile input-output queueing intensity control model introduced by Chen and Yao (1990), obtaining a variety of new results, including (a) an exact reformulation of the control problem as an LP problem over a threshold polygon; (b) an analytical characterization of the Min WIP function (giving the minimum WIP level required to attain a target throughput level); (c) an LP Value Decomposition Theorem that relates the objective value under an arbitrary policy with that of a given threshold policy (thus revealing the LP interpretation of Chen and Yao's optimality conditions); (d) diminishing returns and invariance properties of throughput-WIP performance, which underlie threshold optimality; (e) a unified treatment of the time-discounted and time-average cases.

JEL Classification: C61, C63, M11

Suggested Citation

Niño Mora, José, On the Throughput-Wip Trade-Off in Queueing Systems, Diminishing Returns and the Threshold Property: A Linear Programming Approach. Economics Working Paper 276, Available at SSRN: https://ssrn.com/abstract=102634 or http://dx.doi.org/10.2139/ssrn.102634

José Niño Mora (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
(34-3) 542 26 73 (Phone)
(34-3) 542 17 46 (Fax)

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