Computationally efficient solution of the multi-item, capacitated lot-sizing problem

The problem of multi-item, single-level, dynamic lotsizing in the presence of a single capacitated resource is addressed. A model based on variable redefinition is developed leading to a solution strategy based on a branch-and-bound search with sharp low bounds. The multi-item low bound problems are solved by column generation with the capacity constraints as the linking constraints. The resulting subproblems separate into as many single-item, uncapacitated lotsizing problems as there are items. These subproblems are solved as shortest-path problems. Good upper bounds are also generated by solving an appropriate minimum-cost network flow problem at each node of the branch-and-bound tree. The resulting solution scheme is very efficient in terms of computation time. Its efficiency is demonstrated by computational testing on a ste of benchmark problem instances and is attributable to the sharpness of the lower bounds, the efficiency with which the low bound problems are solved and the frequent generation of good upper bounds; all of which leading to a high exclusion rate.