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.

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Persistent URL dx.doi.org/10.1016/0360-8352(89)90005-3
Journal Computers and Industrial Engineering
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