An Optimal Ordering policy on Both Way Substitutable Two-Commodity Inventory Control System

There are a lot of raw materials, work-in-processes and finished goods in manufacturing industry. Here, the less stock of materials and work-in-processes manufacturing industry has, the worse the rate of the production is. Inversely, the more manufacturing industry has, the more expensive the cost to support them is. Thus, it is important for us to balance them efficiently. In general, inventory problems are to decide appropriate times to produce goods and to determine appropriate quantities of goods. Therefore, inventory problems require as more useful information as possible. For example, there are demand, lead time, ordering point and so on. In this paper, we deal with an optimal ordering policy on both way substitutable two-commodity inventory control system. That is, there is a problem of how to allocate the produced two kinds of goods in a factory to m areas so as to minimize the total expected inventory cost. The demand of each area is probabilistic, and we adopt the exponential distribution as a probability density function of demand. Moreover, we provide numerical examples of the problem.