Production Smoothing and Inventory Control

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Abstract
Let production of a product be continuous and subject to the following costs the direct cost of production is proportional to the rate of output, the cost of changing the rate is proportional to the size of the change, with (possibly) different coefficients for upward and downward shifts, the cost of storage is proportional to the stock level, and there is a proportional penalty for backlogs. No orders are lost demands for the product arise at random intervals and the number of units demanded is a random variable with known distribution. The problem is to find the optimal policy of adjusting the rate of production to stock. It is shown that there exists a zone of control depending on the stock level such that no adjustment is made as long as the rate of production falls inside this zone and the rate is brought to its nearest endpoint when it has fallen outside the zone. A discrete version of this problem has been programmed on the IBM 650 Results of some computations are presented.

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