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A Heuristic Model for Spare Parts Stocking Based on Markov Chains

Author

Listed:
  • Ernesto Armando Pacheco-Velázquez

    (Tecnologico de Monterrey, School of Engineering and Sciences, Calle del Puente 222, Ejidos de Huipulco, Mexico City 14380, Mexico)

  • Manuel Robles-Cárdenas

    (Tecnologico de Monterrey, School of Engineering and Sciences, Av. Eduardo Monroy Cárdenas 2000, San Antonio Buenavista, Toluca 50110, Estado de Mexico, Mexico)

  • Saúl Juárez Ordóñez

    (Tecnologico de Monterrey, School of Engineering and Sciences, Av. Carlos Lazo 100, Santa Fe, Mexico City 01389, Mexico)

  • Abelardo Ernesto Damy Solís

    (Tecnologico de Monterrey, School of Engineering and Sciences, Av. General Ramón Corona 2514, Nuevo México, Zapopan 45138, Jalisco, Mexico)

  • Leopoldo Eduardo Cárdenas-Barrón

    (Tecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Nuevo León, Mexico)

Abstract

Spare parts management has gained significant attention in recent years due to the considerable costs associated with backorders or excess inventory. This article addresses the challenge of determining the optimal number of spare parts to stock, assuming that the parts can be repaired. When an item fails, it is promptly sent for repair in a workshop. The time between failures and the repair time are assumed to follow an exponential distribution, although it should be noted that the results could be adapted to other distributions as well. This study introduces a heuristic method to find the optimal inventory level that minimizes the total cost, considering holding inventory, backorder, and repair costs. The research offers a valuable decision-making framework for determining the number of spare parts needed to minimize inventory costs, based on just two parameters: (1) the ratio of time to repair and time to failure, and (2) the ratio of the inventory holding cost of a spare part per day to the daily cost of an idle machine. To the best of our knowledge, there are no similar methodologies in the existing literature. The proposed method is straightforward to implement, employing graphs and simple computations. Therefore, it is anticipated to be highly beneficial for practitioners seeking a quick and reliable estimator of the optimal number of spare parts to stock for critical components.

Suggested Citation

  • Ernesto Armando Pacheco-Velázquez & Manuel Robles-Cárdenas & Saúl Juárez Ordóñez & Abelardo Ernesto Damy Solís & Leopoldo Eduardo Cárdenas-Barrón, 2023. "A Heuristic Model for Spare Parts Stocking Based on Markov Chains," Mathematics, MDPI, vol. 11(16), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3550-:d:1218800
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    References listed on IDEAS

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    2. Yonit Barron, 2024. "Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment," Mathematics, MDPI, vol. 12(9), pages 1-30, April.

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