A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages

Yajaira Cardona-Valdés, Samuel Nucamendi-Guillén, Rodrigo E. Peimbert-García, Gustavo Macedo-Barragán and Eduardo Díaz-Medina
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Yajaira Cardona-Valdés: Centro de Investigación en Matemáticas Aplicadas, Universidad Autónoma de Coahuila, Blvd. V. Carranza s/n. Col. República Oriente, Saltillo C.P. 25280, Coahuila, Mexico
Samuel Nucamendi-Guillén: Facultad de Ingeniería, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico
Rodrigo E. Peimbert-García: School of Engineering and Sciences, Tecnológico de Monterrey, Eugenio Garza Sada 2501 Sur, Monterrey, Nuevo León 64849, Mexico
Gustavo Macedo-Barragán: Facultad de Ingeniería, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico
Eduardo Díaz-Medina: Facultad de Ingeniería, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico

Mathematics, 2020, vol. 8, issue 6, 1-16

Abstract: This paper addresses the multi-product, multi-period capacitated lot sizing problem. In particular, this work determines the optimal lot size allowing for shortages (imposed by budget restrictions), but with a penalty cost. The developed models are well suited to the usually rather inflexible production resources found in retail industries. Two models are proposed based on mixed-integer formulations: (i) one that allows shortage and (ii) one that forces fulfilling the demand. Both models are implemented over test instances and a case study of a real industry. By investigating the properties of the obtained solutions, we can determine whether the shortage allowance will benefit the company. The experimental results indicate that, for the test instances, the fact of allowing shortages produces savings up to 17% in comparison with the model without shortages, whereas concerning the current situation of the company, these savings represent 33% of the total costs while preserving the revenue.

Keywords: capacitated lot sizing; mixed integer formulation; retail; inventory; shortages (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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