CAJ | 학술논문

在需求率线性依赖于销售价格的情形下,研究有限销售周期内一次订购模式下单一易变质产品在连续时间上的最优动态定价决策问题。针对给定初始库存水平和初始库存水平待定两种情形,利用最优控制理论分别建立了易变质产品的动态定价模型,目标是最大化产品销售周期内总的销售利润。通过分析,可将问题分别转化为有控制变量约束的拉格郎日问题和波尔扎问题。利用Pontryagin极大值原理求解上述两类问题,均得到系统最优定价决策。对上述第一类问题分别进行了数值仿真,仿真结果表明：不同参数取值情形下,产品最优动态定价决策会在三种情形中变动。
재수구솔선성의뢰우소수개격적정형하,연구유한소수주기내일차정구모식하단일역변질산품재련속시간상적최우동태정개결책문제。침대급정초시고존수평화초시고존수평대정량충정형,이용최우공제이론분별건립료역변질산품적동태정개모형,목표시최대화산품소수주기내총적소수리윤。통과분석,가장문제분별전화위유공제변량약속적랍격랑일문제화파이찰문제。이용Pontryagin겁대치원리구해상술량류문제,균득도계통최우정개결책。대상술제일류문제분별진행료수치방진,방진결과표명：불동삼수취치정형하,산품최우동태정개결책회재삼충정형중변동。
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.