On the packing process in a shoe manufacturer
Manuel V.C. Vieira, Flora Ferreira, José C. M. Duque, Rui M.P. Almeida
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.