Diversification under yield randomness in inventory models

In this paper we consider the case of random yield and diversification in two different inventory models. It is assumed that two sources (suppliers) exist who ship an amount which is a random function of the amount requisitioned. Since they may charge different prices and their reliability (in terms of the variance of the yield random variable) may be different, diversification may be more desirable than using a single supplier. We analyze this problem for both the EOQ model and the newsboy model. Analytic results for the optimal order quantities and the minimum cost are obtained for the EOQ model. Convexity of the objective function is also discussed. We develop the necessary conditions for the newsboy model and propose an approximate solution technique. The concavity of the expected profit function is shown. Numerical examples are provided for both models.