Exploiting packing components in general-purpose integer programming solvers

Abstract

The problem of packing boxes into a large box is often only a part of a complex problem. For example in furniture supply chain applications, one needs to decide what trucks to use to transport furniture between production sites and distribution centres and stores, such that the furniture fits inside. Such problems are often formulated and sometimes solved using general-purpose integer programming solvers. This chapter studies the problem of identifying a compact formulation of the multi-dimensional packing component in a general instance of integer linear programming, reformulating it using the discretisation of Allen–Burke–Mareček, and solving the extended reformulation. Results on instances of up to 10,000,000 boxes are reported.