A minimax distribution free procedure for mixed inventory models involving variable lead time with fuzzy lost sales

Recently, the continuous review inventory models with allowable shortages have been extended to include variable lead time, where a fixed fraction of the demand during the stockout period is backordered. However, in practice, the backorder (or lost sales) rate may change slightly due to some uncertainties. To incorporate this reality, this article attempts to apply the fuzzy set concepts to deal with the uncertain lost sales rate. For a situation where information about the lead time demand distribution is partial, we utilize the minimax distribution free procedure to find the optimal inventory strategy in the fuzzy sense. Two numerical examples are given to illustrate the results.