A Heuristic Model for Spare Parts Stocking Based on Markov Chains

Ernesto Armando Pacheco-Velázquez, Manuel Robles-Cárdenas, Saúl Juárez Ordóñez, Abelardo Ernesto Damy Solís and Leopoldo Eduardo Cárdenas-Barrón ()
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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

Mathematics, 2023, vol. 11, issue 16, 1-21

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.

Keywords: inventory; spare parts; Markov chains; decision analysis; optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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