This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many p...This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.71201027,71272085,71390334,and 11271356973 Project under Grant No.2010CB731400+3 种基金Humanity and Social Science Youth Foundation of Ministry of Education of China under Grant No.12YJC630260Guangdong Natural Science Foundation under Grant No.S2012040007919Foundation for Distinguished Young Talents in Higher Education of Guangdong under Grant No.LYM11121the Open Fund of Chongqing Key Laboratory of Logistics under Grant No.CQKLL12003
文摘This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.
