Polynomial time algorithms for the constant capacitated single-item lot sizing problem with stepwise production cost

This paper presents two polynomial time algorithms for the constant capacitated lot sizing problem with a batch production. We give several optimality properties for the general problem. Assuming constant production capacity, constant batch size and WagnerWhitin cost structure, we derive O(T ) and O(T ) time algorithms respectively for the case with production capacity multiple of the batch size and for the case with arbitrary fixed capacities.