Optimization of Both Order Quantity and Reorder Point for the Continuous Review Inventory Model with Variable Lead Time and Price-Quantity Discount

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In this paper, we propose a mixed integer optimization approach for solving the inventory problem with variable lead time, reorder point, crashing cost and price-quantity discount. Chang and Chang study a continous review inventory model in which lead time is a decision variable under price-quantity discount. However, their study cannot find the optimal solution due to the flaws in the modeling and the solution procedure. We present a complete procedure to find the optimal solution for the model. In addition to the above contribution, we also apply the minimax distribution free approach to the model to devise a practical procedure which can be used without specific information on demand distribution.