| Popis: |
In this paper we consider a version of the dynamic lot size model wherein set-up and unit production costs are assumed to be non-increasing over time. The objective is to characterize the manner in which the optimal solutions change if set-up costs are proportionately changed for each period, e.g., if (at) is the vector of set-up costs over time for the given problem, then in what manner will an optimal solution change for set-up costs given by (αa t), α a positive scalar. One of the main results is that if set-up costs are proportionately decreased, then the number of regeneration points is nondecreasing and the kth regeneration point of the perturbed problem occurs at least as early as the kth regeneration point of the original problem. In particular, if set-up costs are proportionately decreased, then the first period batch size can only decrease. We also show that these results do not necessarily hold for more general reductions in set-up costs. |
