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Article

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

1
Centro de Investigación en Matemáticas Aplicadas, Universidad Autónoma de Coahuila, Blvd. V. Carranza s/n. Col. República Oriente, Saltillo C.P. 25280, Coahuila, Mexico
2
Facultad de Ingeniería, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico
3
School of Engineering and Sciences, Tecnológico de Monterrey, Eugenio Garza Sada 2501 Sur, Monterrey, Nuevo León 64849, Mexico
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Current address: School of Engineering, Macquarie University. Balaclava Road, North Ryde, Sydney 2109, Australia.
Mathematics 2020, 8(6), 878; https://doi.org/10.3390/math8060878
Received: 23 April 2020 / Revised: 21 May 2020 / Accepted: 26 May 2020 / Published: 1 June 2020
(This article belongs to the Special Issue Advances and Novel Approaches in Discrete Optimization)
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. View Full-Text
Keywords: capacitated lot sizing; mixed integer formulation; retail; inventory; shortages capacitated lot sizing; mixed integer formulation; retail; inventory; shortages
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MDPI and ACS Style

Cardona-Valdés, Y.; Nucamendi-Guillén, S.; Peimbert-García, R.E.; Macedo-Barragán, G.; Díaz-Medina, E. A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages. Mathematics 2020, 8, 878. https://doi.org/10.3390/math8060878

AMA Style

Cardona-Valdés Y, Nucamendi-Guillén S, Peimbert-García RE, Macedo-Barragán G, Díaz-Medina E. A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages. Mathematics. 2020; 8(6):878. https://doi.org/10.3390/math8060878

Chicago/Turabian Style

Cardona-Valdés, Yajaira, Samuel Nucamendi-Guillén, Rodrigo E. Peimbert-García, Gustavo Macedo-Barragán, and Eduardo Díaz-Medina. 2020. "A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages" Mathematics 8, no. 6: 878. https://doi.org/10.3390/math8060878

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