The analysis of optimal price control model in matching problem between production and sales

This paper presents a mathematical model under the assumptions of linear demand and inventory function for investigating the matching problem between production and sales. The main purpose of this paper is to analyze the optimal sales rate at each time t through different pricing strategies so as to achieve the maximum profit in a specific time. The results revealed that the optimal inventory policies including Zero Inventory for Whole Interval, Non-Zero Inventory for Whole Interval, and Partly-Zero Inventory for Whole Interval can be determined through the establishment of the Matching Index which is composed of unit inventory cost, price ceiling, the demand elasticity, sales horizon and unit production cost. Furthermore, a sensitivity analysis is performed.