Exploiting Packing Components in General-Purpose Integer Programming Solvers

Abstract: The problem of packing boxes into a large box is often a part of a larger problem. For example in furniture supply chain applications, one needs to decide what trucks to use to transport furniture between production sites and distribution centers 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--Marecek, and and solving the extended reformulation. Results on instances of up to 10000000 boxes are reported.