Determining Optimal Reorder Intervals in Capacitated Production-Distribution Systems

Peter L. Jackson, William L. Maxwell and John A. Muckstadt
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Peter L. Jackson: College of Engineering, Cornell University, Ithaca, New York 14853
William L. Maxwell: College of Engineering, Cornell University, Ithaca, New York 14853
John A. Muckstadt: College of Engineering, Cornell University, Ithaca, New York 14853

Management Science, 1988, vol. 34, issue 8, 938-958

Abstract: The problem of determining consistent and realistic reorder intervals in complex production-distribution environments was formulated as a large scale, nonlinear, integer programming problem by Maxwell and Muckstadt (Maxwell, W. L., J. A. Muckstadt. 1985. Establishing consistent and realistic reorder intervals in production-distribution systems. Oper. Res. 33(6, November--December) 1316--1341.). They show how the special structure of the problem permits its solution by a standard network flow algorithm. In this paper, we review the Maxwell-Muckstadt model, provide necessary and sufficient conditions that characterize the solution, and show that the optimal partition of nodes in the production-distribution network is invariant to an arbitrary scaling of the set-up and holding cost parameters. We consider two capacitated versions of the model: one with a single constrained work center, and the other with multiple constrained work centers. For single constraint problems, the invariance corollary provides a simple closed-form solution. For the multiple work center problem, the invariance corollary is exploited in the development of a Lagrange multiplier method of solution. The technique is illustrated by means of a small example problem and a problem taken from a real industrial setting.

Keywords: production scheduling; lot-sizing; nonlinear programming applications (search for similar items in EconPapers)
Date: 1988
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Citations: View citations in EconPapers (21)

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