Optimizing price, order quantity, and backordering level using a nonlinear holding cost and a power demand pattern

  1. Cárdenas-Barrón, Leopoldo Eduardo 1
  2. Sicilia, Joaquín 2
  3. Mandal, Buddhadev 1
  4. San-José, Luis A. 3
  5. Abdul-Jalbar, Beatriz 2
  1. 1 Instituto Tecnológico y de Estudios Superiores de Monterrey
    info

    Instituto Tecnológico y de Estudios Superiores de Monterrey

    Monterrey, México

    ROR https://ror.org/03ayjn504

  2. 2 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

  3. 3 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

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Journal:
Computers & Operations Research

ISSN: 0305-0548

Year of publication: 2021

Volume: 133

Pages: 105339

Type: Article

DOI: 10.1016/J.COR.2021.105339 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Computers & Operations Research

Abstract

It is well-known that the demand rate for some products depends on several factors, such as price, time, and stock, among others. Moreover, the holding cost can vary over time. More specifically, it increases with time since a long period of storage requires more expensive warehouse facilities. This research introduces an inventory model with shortages for a single product where the demand rate depends simultaneously on both the selling price and time according to a power pattern. Shortages are completely backordered. Demand for the product jointly combines the impact of the selling price and a time power function, which is performed as an addition. Furthermore, the holding cost is a power of the time that the product is held in storage. The main objective is to derive the optimal inventory policy such that the total profit per unit of time is maximized. For optimizing the inventory problem, some theo-retical results are derived first to prove that the total profit function is strictly pseudo concave with respect to the decision variables. Next, an efficient algorithm that obtains the optimal solution is provided. The proposed in-ventory model is a general model because it contains several published inventory models as special cases. Some numerical examples are presented and solved to illustrate and validate the proposed inventory model. Also, a sensitivity analysis is conducted in order to highlight and generate significant insights.

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