Optimal manufacturing of a two product mix

The paper considers a machine that works constantly and produces two types of fluid products, one type of product at a time. Whenever there is a positive amount of both types of products, the products are mixed immediately and shipped away. Whenever mixing is infeasible the product that is currently being produced accumulates inventory. The goal is to minimize the long-run average as well as the discounted costs of running such an operation. Inventory incurs a linear holding cost for each type of product. Also, whenever switching from the production of one type of product to the other, a fixed switching cost is incurred. It is found that a stationary periodic policy is optimal. The optimal solution for the long-run average cost criterion is described by closed form formulas. As a special case, it is shown that the (s,S) policy for the textbook EOQ inventory model is indeed optimal over the class of all policies. Also, a theorem that proves the optimality of cyclic policies within a particular set of policies is introduced in a very general setting.