On the packing process in a shoe manufacturer

Abstract

This paper addresses a shoe packing problem that is motivated by an industry application and involves two main stages: (i) packing shoes into suitable boxes and (ii) loading the packed shoes into three dimensional open-dimension containers. This is the first study dealing with the packing of small boxes into several containers where each container has all three dimensions open. Assigning shoes to a minimum number of box types is achieved using a 0–1 program, whereas the loading problem is tackled via a mixed-integer nonlinear program that minimizes the total volume of the container. That latter model is linearized by using a simple summation of the container dimensions, which is compared against a more elaborated linearization scheme. The effectiveness and efficiency of the proposed scheme are demonstrated with numerical experiments using real-world instances.

Keywords:

• Packing
• practice of OR
• non-linear programming
• shoe manufacturer

Additional information

Funding

The first author’s research was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PEst-OE/MAT/UI0297/2014 (Centro de Matemática e Aplicações); Third and fourth authors were partially supported by UID/MAT/00212/2019 - financed by FEDER through the - Programa Operacional Factores de Competividade, Fundação para a Ciência e Tecnologia; This initiative was supported by COST Action TD1409, Mathematics for Industry Network (MI-NET), COST is supported by the EU Framework Programme Horizon 2020.