DYNAMIC PRICING AND GOODWILL INVENTORY MODEL FOR DETERIORATING ITEMS

Abstract

In this model, a dynamic goodwill problem for perishable objects with advertisement effort is studied. The spoilage of
perishable products that takes place over time causes not only quantitative loss but results in an economic loss that occurs
due to a reduction in consumption rate. Together with deterioration, selling price and advertisement of the products also play
a vital role in the profit of a firm and customer’s consumptions rate. It is more difficult for a company to solve a problem that
includes different dynamic strategies. The goodwill effect is positively affected by the advertisements and decays due to
forgetfulness. This paper studies dynamic pricing and advertisement efforts for deteriorating objects. The demand rate is a
function of the selling price, goodwill effect, and market potential. A dynamic inventory model is developed to maximize the
total profit function of the retailer for the decision variable i.e. cycle time and order quantity. The dynamic selling price,
advertisement efforts, and goodwill effect are calculated through Pontryagin’s maximum principle. A numerical example and
sensitivity analysis are done related to the different inventory parameters. The model also provides some managerial
implications for different decision variables.