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Algorithms for the item assortment problem: An application to vending machine products

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Abstract

We consider the item assortment problem of a vending machine. Our goal is to determine the optimal assortment of items and the optimal replenishment cycle time of the vending machine. We model the problem as mathematical programming problems. We formulate this problem as an integer linear programming problem to get tight lower bounds and apply the column generation method for its linear relaxation problem. We also propose two algorithms to get upper bounds, one based on tabu search and the other on multiple start local search. Our numerical experiments on a real world instance and randomly generated instances show that our methods generate good solutions within a reasonable computational time.

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References

  1. R. Anupindi, M. Dada and S. Gupta, Estimation of consumer demand with stock-out based substitution: an application to vending machine products. Management Sci.,17, No.4 (1998), 406–423.

    Google Scholar 

  2. G.N. Frederickson and D.B. Johnson, The complexity of selection and ranking inX +Y and matrices with sorted columns. J. Comput. Syst. Sci.,24 (1982), 197–208.

    Article  MATH  MathSciNet  Google Scholar 

  3. Z. Galil and N. Megiddo, A fast selection algorithm and the problem of optimum distribution of effort. J. ACM,26 (1979), 58–64.

    Article  MATH  MathSciNet  Google Scholar 

  4. T. Ibaraki and N. Katoh, Resource Allocation Problems: Algorithmic Approaches. MIT Press, Cambridge, MA, 1988.

    MATH  Google Scholar 

  5. P.C. Gilmore and R.E. Gomory, A linear programming approach to the cutting stock problem. Opns. Res.,9 (1961), 849–859.

    Article  MATH  MathSciNet  Google Scholar 

  6. F. Glover, Tabu search I. ORSA J. Comput.,1 (1989), 190–206.

    MATH  MathSciNet  Google Scholar 

  7. F. Glover, Tabu search II. ORSA J. Comput.,2 (1989), 4–32.

    MathSciNet  Google Scholar 

  8. S. Mahajan and G. J. van Ryzin, Retail inventories and consumer choice. Quantitative Models for Supply Chain Management (eds. S. Tayur et al.), Chapter 17, Kluwer, Amsterdam, 1998.

    Google Scholar 

  9. J.P. Matthews, Optimal inventory stocking levels with demand transference among products. Decision Sci.,9 (1978), 129–142.

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science and Technology, Sophia University, Kioityou, Chiyoda-ku, 102-8554, Tokyo, Japan

    Yuichiro Miyamoto

  2. Department of Information Engineering and Logistics, Tokyo University of Mercantile Marine, Etsujima, Koutou-ku, 135-8533, Tokyo, Japan

    Mikio Kubo & Shiho Itoh

  3. Department of Solution and Computation, Fuji Electric Co., Ltd., Fuji-machi, Hino, 191-8502, Tokyo, Japan

    Kenya Murakami

Authors
  1. Yuichiro Miyamoto
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  2. Mikio Kubo
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  3. Shiho Itoh
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  4. Kenya Murakami
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Miyamoto, Y., Kubo, M., Itoh, S. et al. Algorithms for the item assortment problem: An application to vending machine products. Japan J. Indust. Appl. Math. 20, 87 (2003). https://doi.org/10.1007/BF03167464

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  • DOI: https://doi.org/10.1007/BF03167464

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