Lot sizing models with backlog or out-sourcing

This paper addresses a single item capacitated dynamic lot sizing problem. We consider backlogging models as well as out-sourcing models to minimize the total cost. The production, holding and backlogging or out-sourcing cost functions considered in this paper are arbitrary and time-varying. Due to various capacity constraints, it is possible that no feasible solution exists. We give a necessary and sufficient condition for there to be a feasible solution and show that this condition can be checked in polynomial time. When feasible solutions exist, we show that an optimal solution can be obtained in pseudo-polynomial time with dynamic programming algorithms. We then address polynomially solvable special cases of stockout and conservation models. © 2004 IEEE