Economic order quantity for perishables with decreasing willingness to purchase during their life cycle

In an inventory management model for perishables, depletion due to interacting with the demand is of importance, but also, damage to products is a relevant variable. This article considers that demand and sales phenomena do not always go hand-in-hand. The demand process relates to the willingness to acquire products in good condition, giving the customer the power to evaluate the quality of the product before an effective purchase takes place. We also considered the cost of disposing of unsold units, besides the conventional costs for storage and procurement. We then proposed a mathematical model to derive the Economic Order Quantity (EOQ) under specific conditions, in order to minimize the expected management cost of perishables, assuming constant demand and linearly decreasing purchase probability during the product life cycle. We proposed several random instances and validate the mathematical model using simulation. We then found the optimal parameters for the inventory policy using a third-order numerical approximation. Last, we developed a sensitivity analysis over the product life cycle to prove that the proposed model approximates to a traditional EOQ model for perishables when life cycle is sufficiently large.