Periodic inventory model with controllable lead time where backorder rate depends on protection interval

In this paper, a period review inventory model with controllable lead time has been considered where shortages are partially backlogged. The backorder rate is dependent on the backorder discount and the length of the protection interval, which is sum of the review period and the lead time. Two cases have been discussed for protection interval demand which are (a) Demand distribution is known (Normal Distribution) (b) Demand distribution is unknown (Minimax distribution). Further, algorithms have been developed which jointly optimize the backorder discount, the review period and the lead time for each case. Numerical examples are also presented to illustrate the results.