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Finding and identifying optimal inventory levels for systems with common components

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  • Nonås, Sigrid Lise

Abstract

In this article, we consider the problem of finding the optimal inventory level for components in an assembly system where multiple products share common components in the presence of random demand. Previously, solution procedures that identify the optimal inventory levels for components in a component commonality problem have been considered for two product or one common component systems. We will here extend this to a three products system considering any number of common components. The inventory problem considered is modeled as a two stage stochastic recourse problem where the first stage is to set the inventory levels to maximize expected profit while the second stage is to allocate components to products after observing demand. Our main contribution, and the main focus of this paper, is the outline of a procedure that finds the gradient for the stochastic problem, such that an optimal solution can be identified and a gradient based search method can be used to find the optimal solution.

Suggested Citation

  • Nonås, Sigrid Lise, 2009. "Finding and identifying optimal inventory levels for systems with common components," European Journal of Operational Research, Elsevier, vol. 193(1), pages 98-119, February.
  • Handle: RePEc:eee:ejores:v:193:y:2009:i:1:p:98-119
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    References listed on IDEAS

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    1. Haugland, Dag & Wallace, Stein W., 1988. "Solving many linear programs that differ only in the righthand side," European Journal of Operational Research, Elsevier, vol. 37(3), pages 318-324, December.
    2. Jonsson, Henrik & Silver, Edward A., 1989. "Optimal and heuristic solutions for a simple common component inventory problem," Engineering Costs and Production Economics, Elsevier, vol. 16(4), pages 257-267, July.
    3. Jonsson, Henrik & Jornsten, Kurt & Silver, Edward A., 1993. "Application of the scenario aggregation approach to a two-stage, stochastic, common component, inventory problem with a budget constraint," European Journal of Operational Research, Elsevier, vol. 68(2), pages 196-211, July.
    4. Jonsson, Henrik & Silver, Edward A., 1989. "Common component inventory problems with a budget constraint: Heuristics and upper bounds," Engineering Costs and Production Economics, Elsevier, vol. 18(1), pages 71-81, October.
    5. Kenneth R. Baker & Michael J. Magazine & Henry L. W. Nuttle, 1986. "The Effect of Commonality on Safety Stock in a Simple Inventory Model," Management Science, INFORMS, vol. 32(8), pages 982-988, August.
    6. Yigal Gerchak & Michael J. Magazine & A. Bruce Gamble, 1988. "Component Commonality with Service Level Requirements," Management Science, INFORMS, vol. 34(6), pages 753-760, June.
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