An Economic Order Quantity Model for Imperfect and Deteriorating Items with Freshness and Inventory-Level-Dependent Demand

The sale of many products is influenced by the characteristics of the products and the behaviour of the consumers. This is particularly true of food items. Consumers of most food items want them fresh; thus, while items that are edible but have lost some of their freshness might be sold, the demand usually drops, and the closer the expiry date, the lower the demand for such products. Another factor that is known to affect the sale of many items is the attractiveness of the stocking pattern. Seeing a large stock of consumable items tends to attract consumers; hence the stock level dependence of demand. An additional characteristic of such products is that they continue to deteriorate; thus affects both the quality and quantity of such items, as the overly deteriorated ones are removed from the stock of saleable items. Consequently, the stock level reduces owing to both demand and deterioration. This description fits many agricultural products such as fruits and vegetables. Another characteristic of such products is the possibility of their being imperfect when they are received, as some stock might be damaged by harvesting, handling, or transportation. In this research, we develop a mathematical model to determine the optimal lot size for an item having all these characteristics, with the profit function as the model objective. We used a case of banana as the numerical illustration. Sensitivity analyses of important model parameters were conducted to demonstrate the model’s robustness. The findings were that the date of expiry, the scale of demand, and the selling price of perfect products were the main constituents that affected their profitability. This model should find ready application in most stores where fresh consumable food items such as fruits and vegetables are managed.