Set partitioning and column generation heuristics for capacitated lotsizing

This paper discusses set partitioning and column generation heuristics for the multi item single level capacitated dynamic lotsizing problem. Most previous research efforts reported in literature use the single item uncapacitated problem solutions as candidate plans. In this paper a different approach is proposed in which candidate plans are also generated by some well-known mutli item capacitated dynamic lotsizing heuristics. The LP relaxation of a set partitioning model is solved and rounded to obtain an integer solution. A number of heuristics are subsequently applied to improve upon this initial solution. Heuristics are also used to convert the possibly fractional solution from the column generation step to a feasible integer one. The present methods are compared with other common sense heuristics. Computational experience shows that the methods perform best for problems with fewer periods than items, but are quite good on average.