Two-warehouse supply chain model under preservation technology and stochastic demand with shortages

This article develops an inventory model for deteriorating items with price-dependent stochastic demand. To maintain the freshness of the deteriorating items, preservation technology is being applied. Due to stochastic demand, retailers might face shortages considered partial backlogging. The retailer orders the items based on the forecasting of the stochastic demand, then keeps those items in their warehouse and the remaining items in a rented warehouse. This work aims to develop a suitable inventory model for finding the optimal selling price, cycle time when all items of the rented warehouse are sold, the replenishment cycle time, and the investment cost of preservation technology. We formulate the mathematical model with a solution procedure and provide the related theorems. We illustrate the concavity of the expected profit function using numerical examples. In conclusion, we discuss the implementation of the proposed model.