Heuristic search for the stacking problem

This paper presents the Stacking Problem, a hard combinatorial optimization problem concerning handling and storage of items in a warehouse, where they are handled by a crane and organized into stacks. We define the problem, study its complexity class, and present a mathematical programming model to solve it. In order to tackle mediumor large-scale instances, we propose a simulation-based algorithm using semi-greedy construction heuristics. This simple approach allows for multiple constructions, finding solutions within reasonable time even for large instances. Three semi-greedy heuristics are proposed and compared in an extensive computational experiment, where we study the relation between the number of constructions and the best solution obtained using each heuristic.