Setup cost stability region for the multi-level dynamic lot sizing problem

In this paper the multi-level dynamic lot sizing problem is investigated in which setup costs are parameters and the range within which setup costs can vary without changing the optimal solution is determined. The computations are significantly shortened by the fact that the holding cost function is convex in the number of setups. The topic also raises the problem of convexity of a multi-variable integer function and the search for the neighbouring integer points of the minimum.