Joint optimization of dynamic pricing and replenishment cycle considering variable non-instantaneous deterioration and stock-dependent demand

Inventory control and pricing are two of the most important topics of business and academic researches. In this paper, an optimal control approach is taken to find optimal dynamic prices and replenishment cycle simultaneously with the aim of maximizing the total profit of a non-instantaneous deteriorating item. The deterioration rate is not considered fixed, but rather increases after some time. Furthermore an expiration date is considered at which time any unsold inventory becomes worthless and should be discarded. Customer demand depends on selling price and displayed inventory level. We address the problem at two steps. First assuming that the replenishment cycle is given, the optimal dynamic pricing is obtained by using Pontryagin's maximum principle. Then, a one-dimensional algorithm is designed to obtain the joint optimal solution. Numerical examples are used to illustrate the theoretical results, perform the sensitivity analysis, and provide real life interpretations. Finally, the paper is concluded and directions for future research are highlighted.