Multiple-type, two-dimensional bin packing problems: Applications and algorithms

In this paper the authors consider a class of bin selection and packing problems (BPP) in which potential bins are of various types, have two resource constraints, and the resource requirement for each object differs for each bin type. The problem is to select bins and assign the objects to bins so as to minimize the sum of bin costs while meeting the two resource constraints. This problem represents an extension of the classical two-dimensional BPP in which bins are homogeneous. Typical applications of this research include computer storage device selection with file assignment, robot selection with work station assignment, and computer processor selection with task assignment. Three solution algorithms have been developed and tested: a simple greedy heuristic, a method based on simulated annealing (SA) and an exact algorithm based on Column Generation with Branch and Bound (CG). An LP-based method for generating tight lower bounds was also developed (LB). Several hundred test problems based on computer storage device selection and fine assignment were generated and solved. The heuristic solved problems up to 100 objects in less than a second; average solution value was within about 3% of the optimum. SA improved solutions to an average gap of less than 1% but a significant increase in computing time. LB produced average lower bounds within 3% of optimum within a few seconds. CG is practical for small to moderately-sized problems - possibly as many as 50 objects.