On the EOQ Models with Advertisement-Price-Dependent Demand and Quantity Discount with Expiration Date Under Shortage

This paper presents inventory models for items that deteriorate over time and have a maximum lifetime. The demand for these items is influenced by advertising frequency and the selling price. The holding cost for each item is proportional to the purchase cost. Two inventory models are developed with and without backlogging. The decision variables include advertising frequency, selling price, stock-out period, and order cycle. This study also examines the impact of quantity discounts and identifies optimal solutions that maximize total profit per unit time for both models. We establish necessary and sufficient conditions for the existence and uniqueness of global optimal solutions for total profits. To solve the mixed integer nonlinear inventory models, we propose two solution algorithms. Numerical examples are used to illustrate the solution process with graphical representations. We conduct sensitivity analyses on optimal solutions with respect to model parameters to provide theoretical results and managerial insights. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.