Inventory Model (Q, R) With Period of Grace, Quadratic Backorder Cost and Continuous Lead Time

Abstract

The paper considers the simple economic order model where the period of grace is operating, the lead time is continuous and the backorder cost is quadratic. The lead time follows a gamma distribution. The expected backorder cost per cycle is derived and averaged over all the states of the lead time L. Next we obtain the expected on hand inventory. The Lead time is taken as a Normal variate. The expected backorder costs are, derived after which the expected on hand inventory is derived. The cost inventory costs for constant lead times is then averaged over the states of the lead times which is taken as a normal distribution.