On the packing process in a shoe manufacturer - Vieira, Manuel V. C. (2020)
This paper addresses a shoe packing problem that is motivated by an industry applicationand involves two main stages: (i) packing shoes into suitable boxes and (ii) loading thepacked shoes into three dimensional open-dimension containers. This is the first study deal-ing with the packing of small boxes into several containers where each container has allthree dimensions open. Assigning shoes to a minimum number of box types is achievedusing a 0–1 program, whereas the loading problem is tackled via a mixed-integer nonlinearprogram that minimizes the total volume of the container. That latter model is linearized byusing a simple summation of the container dimensions, which is compared against a moreelaborated linearization scheme. The effectiveness and efficiency of the proposed schemeare demonstrated with numerical experiments using real-world instances.