This paper is the continuation of a previous work (Fasano 2004), dedicated to a MIP formulation for non-standard three-dimensional packing issues, with additional conditions. The Single Bin Packing problem (Basic Problem) is considered and its MIP formulation shortly surveyed, together with some possible extensions, including balancing, tetris-like items and non-standard domains. A MIP-based heuristic is proposed to solve efficiently the Basic Problem or any possible extension of it, susceptible to a MIP formulation. The heuristic is a recursive procedure based on a non-blind local search philosophy. The concept of abstract configuration, concerning the relative positions between items, is introduced: the relative positions of items, determined by any abstract configuration, give rise to a feasible solution in an unbounded domain. The heuristic generates a sequence of good abstract configurations and solves, step by step, a reduced MIP model by fixing the relative positions of items, corresponding to the current abstract configuration.
Accepted for pubblication in '4OR A Quarterly Journal of Operations Research'