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, Eduardo Díaz-Medina

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
15 Downloads (Pure)


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.

Original languageEnglish
Article number878
Pages (from-to)1-16
Number of pages16
Issue number6
Publication statusPublished - Jun 2020
Externally publishedYes

Bibliographical note

Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • capacitated lot sizing
  • mixed integer formulation
  • retail
  • inventory
  • shortages


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