Models for two-dimensional bin packing problems with customer order spread

Abstract

In this paper, we address an extension of the classical two-dimensional bin packing (2BPP) that considers the spread of customer orders (2BPP-OS). The 2BPP-OS addresses a set of rectangular items, required from different customer orders, to be cut from a set of rectangular bins. All the items of a customer order are dispatched together to the next stage of production or distribution after its completion. The objective is to minimize the number of bins used and the spread of customer orders over the cutting process. The 2BPP-OS gains relevance in manufacturing environments that seek minimum waste solutions with satisfactory levels of customer service. We propose integer linear programming (ILP) models for variants of the 2BPP-OS that consider non-guillotine, 2-stage, restricted 3-stage, and unrestricted 3-stage patterns. We are not aware of integrated approaches for the 2BPP-OS in the literature despite its relevance in practical settings. Using a general-purpose ILP solver, the results show that the 2BPP-OS takes more computational effort to solve than the 2BPP, as it has to consider several symmetries that are often disregarded by the traditional 2BPP approaches. The solutions obtained by the proposed approaches have similar bin usage and significantly better metrics of customer satisfaction concerning the approaches that neglect the customer order spread.