The Multi-item DLSP

Abstract

In this chapter we consider algorithms for solving the multi-item DLSP. In Section 5.2 solution procedures are discussed, based on straightforward application of dynamic programming. Although these algorithms give exact solutions, the computation times and the required memory grow rapidly with the size of the problem. Therefore, alternative (approximation) algorithms are considered, that give acceptable solutions in reasonable computation time for problem dimensions as met in practice. Section 5.3 presents the algorithms as proposed by Fleischmann for solving multi-item, single facility problems with zero setup times (1/N/SI/G/A and 1/N/SD/G/A). These algorithms are based on Lagrangean relaxation and dynamic programming to obtain lower bounds, while successive approximation techniques are used to obtain upper bounds. The procedures are embedded in a branch-and-bound routine. In Section 5.4 two heuristics are described for the multi-item single facility DLSP with nonzero setup times (1/N/SI/G/SI). The heuristics are based on column generation techniques. In both heuristics new columns are generated using DP, but the heuristics differ in the way the master problem is solved. The primal heuristic uses standard linear programming, while the dual heuristic uses a dual ascent procedure combined with subgradient optimization.