Analysis of a dynamic lot-sizing problem with production capacity constraint

We study a capacitated dynamic lot-sizing problem with special cost structure involving setup cost, freight cost, production cost, and inventory holding cost. We investigate two cases of the problem categorized by whether the maximal production capacity in one period is an integral multiple of the capacity of a container and reveal the special structure of an optimal solution for each case. In the case where the maximal production capacity is an integral multiple of a container's capacity, the T-period problem is solved using polynomial effort by a network algorithm. For the other case, the problem is transformed into a shortest path problem, and a network-based algorithm combining dynamic programming is proposed to solve it in polynomial time. Numerical examples are presented to illustrate application of the algorithms to solve the two cases of the problem.