Mathematical modeling of some perishable items in inventory

Abstract

Consider a particular (or group of) perishable item(s) for example: meat, fish, fruit, snacks etc., the product (item) spends t ϵ (0, T] number of days on the shelf with a starting quantity m, at time t. The item has a cost price per unit and selling price per unit at time t (t varies with time per day). A discount dt is introduced at time t. After expiration date, it must be disposed of at a cost; hence it is optimal to give a discount. We formulate a mathematical model to determine the profit and the optimal discount to be given at time t so as to minimize loss. Sensitivity analysis was carried out to determine the best time to sell the item under a discount regime.