We investigate a single-period inventory problem in which the demand is stochastic (exponential) and the amount received is also stochastic (normal or gamma). Specifically, two cases are discussed: (i) where the standard deviation of the amount received is dependent upon the quantity requisitioned; and (ii) where it is independent of the quantity requisitioned. The case when the amount received is normally distributed was considered in earlier works by Noori and Keller (INFOR 24, 1-11 (1986) (3]), who proposed a special numerical scheme to solve the total cost equation for optimal order and, hence, fails to provide a complete range of results. We use an algorithm which succeeds under all conditions. An interesting result has been found for Case (ii). Here, if the amount received is a normal variate, the cost function provides a unique optimal order quantity; but for the gamma variate case, the stationary value of the cost function need not have a global minimum. We also discuss explicitly the variation of the optimal orde quantity wiht various costs and with parameters of the distribution.

Computers and Industrial Engineering
Sprott School of Business

Kumar, U, & Kumar, V. (1989). An inventory model with an uncertain match between the amount requisitioned and the amount received. Computers and Industrial Engineering, 16(1), 27–36. doi:10.1016/0360-8352(89)90005-3