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A Benders decomposition approach to product location in carousel storage systems

Author

Listed:
  • Raymond G. Vickson

    (University of Waterloo)

  • Elkafi Hassini

    (McMaster University)

  • Nader Azad

    (University of Ontario Institute of Technology)

Abstract

In this paper we discuss the problem of locating items within carousel bins in order to minimize the average carousel rotational distance per retrieval. We consider two cases: (1) a single two-dimensional carousel and (2) a group of two one-dimensional carousels. The corresponding problems are formulated as mixed-integer programs. In the second problem we apply concepts from Markovian performance evaluation methods to write the objective functions in a simple linear form. We also define a set of uniqueness constraints that significantly reduces the size of the solution feasibility space. We then apply Benders decomposition algorithm to solve both problems. We develop a closed form solution for the dual subprobem and present numerical results to show the efficiency of the proposed solution methodology.

Suggested Citation

  • Raymond G. Vickson & Elkafi Hassini & Nader Azad, 2020. "A Benders decomposition approach to product location in carousel storage systems," Annals of Operations Research, Springer, vol. 284(2), pages 623-643, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:2:d:10.1007_s10479-019-03274-3
    DOI: 10.1007/s10479-019-03274-3
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    References listed on IDEAS

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    1. Mokhtar S. Bazaraa & Hanif D. Sherali, 1980. "Benders' partitioning scheme applied to a new formulation of the quadratic assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(1), pages 29-41, March.
    2. Kaufman, L. & Broeckx, F., 1978. "An algorithm for the quadratic assignment problem using Bender's decomposition," European Journal of Operational Research, Elsevier, vol. 2(3), pages 207-211, May.
    3. Guenov, Marin & Raeside, Robert, 1992. "Zone shapes in class based storage and multicommand order picking when storage/retrieval machines are used," European Journal of Operational Research, Elsevier, vol. 58(1), pages 37-47, April.
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