Dynamic Pricing Model of a Deteriorating Item with Price-dependent Demand

Dynamic pricing for a single deteriorating item during a finite sales cycle was studied under the condition that demand rate depended linearly on sales price. Two dynamic pricing models were developed respectively when initial inventory level was known or unknown based on optimal control theory. The objective was to maximize the item’s total profit during the sales cycle. According to analysis, these two models could be respectively formulated as Lagrange problem and Boelza problem with control variable’s constraints. Optimal pricing policies were obtained for each problem above when they were solved by Pontryagin maximum principle. Numerical simulation were done for the first problem and the results showed that the optimal pricing policy changed in three cases under the case of different parameter values.