Optimal dynamic pricing for non-instantaneous deteriorating items dependent on price and time demand

This paper establishes a dynamic pricing model for non-instantaneous deteriorating products to maximise the companies' profit. The demand rate depends on time as well as the sales price. The optimal dynamic price strategy, optimal sale period and the maximal total profit are derived to solve the problem by applying Pontryagin's maximum principle. Meanwhile, uniform pricing and two-part pricing models are introduced to compare with the dynamic pricing model. Finally, numerical examples are carried out to investigate that the dynamic pricing was better than the other two static pricing strategies. Moreover, some managerial conclusions and appropriate measures for decision makers have been obtained by discussing the sensitiveness of the main parameters.