Abstract
We consider the following problem. There are m different items. For each, deterministic stationary demand is expected. By switching machine setting, each item is produced without shortage so as to minimize (discounted) inventory holding cost, but incur thereby a switching cost each time we modify the setting. This paper presents a computational theory generating the optimal lot size schedule of this problem by quasi-variational inequalities. Namely, (i) formulating the problem into dynamic programming and deriving a system of quasi-variational inequalities, we characterise the solution of the optimal cost function as the maximum element of a set of functions defined appropriately. (ii) We derive the optimal policy, which is stationary and indexpolicy.
