Constrained order packing: comparison of heuristic approaches for a new bin packing problem

Bin packing problems consist of allocating a set of small parts to a set of large bins by minimizing the number of used bins. Although several boundary conditions have been stated in the past, for example conflicts or restrictions on cutting and rotations, we introduce a set of constraints, which lead to a new problem structure. These constraints are motivated by the precast-concrete-part industry and represent requirements on the ordering of parts and their positions, machinery restrictions and due dates. Furthermore, we solve the problem using several heuristic approaches that are based on algorithms for the standard bin packing problem. Therefore, existing concepts are classified and adapted to fit the new problem, including Simulated Annealing, Genetic Algorithms, Tabu Search methods and SubSetSum based search routines. Finally, all proposed algorithms are tested and obtained results are discussed.