INVENTORY MODEL (M,R,T) CONTINUOUS LEAD TIMES, QUADRATIC BACK ORDER COSTS AND RANDOM SUPPLY (Series 2)

This paper considers the (M,R,T) inventory model in which the backorder costs is a quadratic function of the time of a backorder, lead time is continuous and supply random Results of series 1, which the same model was considered for constant lead times is the basis for deriving this paper’s model. The inventory costs when lead time is constant is averaged over the states of lead time in which the distribution of lead time is assumed to be a gamma distribution. In averaging over the states of lead time extensive use is made of the Bessel function of imaginary argument.