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

Yajaira Cardona-Valdés; Nucamendi-Guillén, Samuel; Rodrigo E. Peimbert-García; Macedo Barragán, Gustavo; Díaz Medina, Eduardo

doi:10.3390/MATH8060878

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

Journal

Mathematics

ISSN

2227-7390

Date Issued

2020

Author(s)

Yajaira Cardona-Valdés

Rodrigo E. Peimbert-García

Macedo Barragán, Gustavo

Type

Resource Types::text::journal::journal article

DOI

10.3390/MATH8060878

URL

https://scripta.up.edu.mx/handle/20.500.12552/2920

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.