An inventory model for perishable items with price-, stock-, and time-dependent demand rate considering shelf-life and nonlinear holding costs

Nowadays, consumers are more health conscious than before, and their demand of fresh items has intensely increased. In this context, an effective and efficient inventory management of the perishable items is needed in order to avoid the relevant losses due to their deterioration. Furthermore, the demand of products is influenced by several factors such as price, stock, and freshness state, among others. Hence, this research work develops an inventory model for perishable items, constrained by both physical and freshness condition degradations. The demand for perishable items is a multivariate function of price, current stock quantity, and freshness condition. Specific to price, six different price-dependent demand functions are used: linear, isoelastic, exponential, logit, logarithmic, and polynomial. By working with perishable items that eventually deteriorate, this inventory model also takes into consideration the expiration date, a salvage value, and the cost of deterioration. In addition, the holding cost is modelled as a quadratic function of time. The proposed inventory model jointly determines the optimal price, the replenishment cycle time, and the order quantity, which together result in maximum total profit per unit of time. The inventory model has a wide application since it can be implemented in several fields such as food goods (milk, vegetables, and meat), organisms, and ornamental flowers, among others. Some numerical examples are presented to illustrate the use of the inventory model. The results show that increasing the value of the shelf-life results in an increment in price, inventory cycle time, quantity ordered, and profits that are generated for all price demand functions. Finally, a sensitivity analysis is performed, and several managerial insights are provided.