A modeling-based approach for non-standard packing problems

Abstract

This chapter examines the problem of packing tetris-like items, orthogonally, with the possibility of rotations, into a convex domain, in the presence of additional conditions. An MILP (Mixed Integer Linear Programming) and an MINLP (Mixed Integer Nonlinear Programming) models, previously studied by the author (Fasano, Solving Non-standard Packing Problems by Global Optimization and Heuristics. SpringerBriefs in Optimization, Springer Science + Business Media, New York, 2014), are surveyed. An efficient formulation of the objective function, aimed at maximizing the loaded cargo, is pointed out for the MILP model. The MINLP one, addressed to the relevant feasibility sub-problem, has been conceived to improve approximate solutions, as an intermediate step of a heuristic process. A space-indexed model is further introduced and the problem of approximating polygons by means of tetris-like items investigated. In both cases an MILP formulation has been adopted. An overall heuristic approach is proposed to provide effective solutions in practice. One chapter of this book focuses on the relevant computational aspects (Gliozzi et al., Container loading problem MIPbased heuristics solved by CPLEX: an experimental analysis. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, Springer Science + Business Media, New York, 2015).