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A heuristic approach for multiple item and location ordering problem with quantity discount and capacity constraint

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  • Peng-Sheng You

    (National Chia-Yi University Chia-Yi)

Abstract

This paper addresses a geographically distributed vending machine inventory control problem where the multiple product choices in every vending machine and the varied demand for each product in every location's vending machine exist. The ordering quantity for each product and the desirable number of each product type in a vending machine must be simultaneously decided to maximize the total expected profit. Considering that the ordering costs are in piece-wise function and only one type of product is allocated in a slot of a vending machine, the proposed problem correlates to the piece-wise constrained nonlinear integer-programming problem. There is difficulty in deriving the exact optimal solutions to this problem since its computational complexity appears to be a nondeterministic polynomial problem. This paper presents a novel heuristic approach in finding (1) the ordering quantity for each product, (2) the product types, and (3) the corresponding quantity allocated in each vending machine. The numerical results show the effectiveness of the proposed methodology in solving the aforementioned problem. In this paper, the solutions found by this study's approach are as well as those found by the brute-force method, and if not equivalent, perform better than those by the Lingo software.

Suggested Citation

  • Peng-Sheng You, 2005. "A heuristic approach for multiple item and location ordering problem with quantity discount and capacity constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 307-316, March.
    • Handle: RePEc:pal:jorsoc:v:56:y:2005:i:3:d:10.1057_palgrave.jors.2601811
    DOI: 10.1057/palgrave.jors.2601811
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    References listed on IDEAS

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    1. Wee, Hui-Ming, 1999. "Deteriorating inventory model with quantity discount, pricing and partial backordering," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 511-518, March.
    2. Benton, W. C. & Park, Seungwook, 1996. "A classification of literature on determining the lot size under quantity discounts," European Journal of Operational Research, Elsevier, vol. 92(2), pages 219-238, July.
    3. Chung, Chia-Shin & Hum, Sin-Hoon & Kirca, Omer, 1996. "The coordinated replenishment dynamic lot-sizing problem with quantity discounts," European Journal of Operational Research, Elsevier, vol. 94(1), pages 122-133, October.
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    Cited by:

    1. Ding, Xiaohui & Chen, Caihua & Li, Chongshou & Lim, Andrew, 2021. "Product demand estimation for vending machines using video surveillance data: A group-lasso method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).

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