Optimal Pricing, Ordering, and Replenishment Policies in a Multi-Item Inventory System for Deteriorating Items Under Time-Varying Backlogging Rate

In today's advanced society, customers are influenced by products full of choices. For more sales, the retailer should maintain an inventory of each variety of items. These varieties have been seen in most food shops, fruit shops, fashion shops, electronic shops, etc., where the products deteriorate with time elapse. Depending on the customer's demand, the stock out time of different deteriorating items is different. Assimilating all these varieties, in this paper, we have developed a multi-item inventory model for deteriorating items where demands depend on the sales price of the product. Shortages are allowed and partially backlogged with a time-dependent backlogging rate. The multi-item mechanism's prime objective is to find the optimal sales price, order quantity, time length up to zero inventory, and cycle length to maximize the retailer's overall profit. Finally, numerical examples are provided to illustrate the model with some managerial insights.