Inventories, Stock-Outs and Production Smoothing

If stock-outs are ignored and if demand shocks are additive, then optimal behaviour requires that the marginal cost of production (MC) be equated with the expected marginal revenue of increasing expected sales by one unit (EMR). However, with more general demand shocks (and still ignoring stock-outs), the excess of MC over EMR has the same sign as the covariance of the slope of the demand curve and the marginal valuation of inventory. The equality of EMR and MC is also broken by taking account of stock-outs, even if demand shocks are additive. If there is a production lag, then taking account of stock-outs implies that optimal behaviour will be characterized by production smoothing even if the cost of production is linear. Two alternative definitions of production smoothing are presented and optimal behaviour in the presence of stock-outs displays each type of smoothing.