The shape of the yield and its impact on inventory decisions

We consider an inventory model with stochastic demand, positive lead time and random yield where ordering decisions are made according to a linear inflation rule. In case of a positive lead times the complexity of such inventory systems increases distinctly. Due to positive lead times, the inventory position contains no longer a term for outstanding orders but the estimated quantity of goods to be delivered after a known positive lead time period, which differ from the realized deliveries. Thus, a forecast error occurs in each period. In previous research this forecast error was assumed to be normally distributed which is not an appropriate assumption in case of symmetric yield. Since yield skewness can’t be neglected, we propose to fit a skew normal distribution or a generalized extreme value distribution on the forecast error to account for the yield skewness. A numerical study reveals that the proposed approaches are excellent and outperform existing ones.