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Optimizing the allocation of components to kits in small‐lot, multiechelon assembly systems

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  • J. F. Chen
  • W. E. Wilhelm

Abstract

The kitting problem in multiechelon assembly systems is to allocate on‐hand stock and anticipated future deliveries to kits so that cost is minimized. This article structures the kitting problem and describes several preprocessing methods that are effective in refining the formulation. The model is resolved using an optimizing approach based on Lagrangian relaxation, which yields a separable problem that decomposes into a subproblem for each job. The resulting subproblems are resolved using a specialized dynamic programming algorithm, and computational efficiency is enhanced by dominance properties devised for that purpose. The Lagrangian problem is resolved effectively using subgradient optimization and a specialized branching method incorporated in the branch‐and‐bound procedure. Computational experience demonstrates that the specialized approach outperforms the general‐purpose optimizer OSL. The new solution approach facilitates time‐managed flow control, prescribing kitting decisions that promote cost‐effective performance to schedule. © 1994 John Wiley & Sons. Inc.

Suggested Citation

  • J. F. Chen & W. E. Wilhelm, 1994. "Optimizing the allocation of components to kits in small‐lot, multiechelon assembly systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(2), pages 229-256, March.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:2:p:229-256
    DOI: 10.1002/1520-6750(199403)41:23.0.CO;2-H
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    1. Marshall L. Fisher, 1973. "Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I," Operations Research, INFORMS, vol. 21(5), pages 1114-1127, October.
    2. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    3. Peter J. Billington & John O. McClain & L. Joseph Thomas, 1983. "Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction," Management Science, INFORMS, vol. 29(10), pages 1126-1141, October.
    4. Slowinski, Roman, 1981. "Multiobjective network scheduling with efficient use of renewable and nonrenewable resources," European Journal of Operational Research, Elsevier, vol. 7(3), pages 265-273, July.
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    1. Gunther, H. O. & Gronalt, M. & Piller, F., 1996. "Component kitting in semi-automated printed circuit board assembly," International Journal of Production Economics, Elsevier, vol. 43(2-3), pages 213-226, June.
    2. Alex X. Zhang, 1997. "Demand Fulfillment Rates In An Assembleto‐ Order System With Multiple Products And Dependent Demands," Production and Operations Management, Production and Operations Management Society, vol. 6(3), pages 309-324, September.

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