有限资源下串联排队系统的动态定价及其在汽车检测场的应用  

Dynamic pricing in a tandem queue under limited resources and it’s application to automotive inspection yards

作　　者：马双凤 郭伟 MA Shuangfeng;GUO Wei(School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210023,China;School of Statistics,University of International Business and Economics,Beijing 100029,China)

机构地区：[1]南京财经大学应用数学学院,南京210023 [2]对外经济贸易大学统计学院,北京100029

出　　处：《系统工程理论与实践》2023年第12期3653-3667,共15页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(61973084,62070206)。

摘　　要：本文考虑了有限资源约束下串联排队系统的速率控制以及动态定价问题.管理者不仅需要制定合适的动态价格来增加收益,还需要在资源有限的约束下,为串联的两个服务台分配合适的资源,达到减少成本,提高总体社会福利的目的.文中首先采用灵敏度分析技术求得依赖于状态的最优到达率和两个服务台各自的最优服务率.通过边际收益函数,建立了价格和到达率之间的关系表达式.然后在已得到的最优速率基础上,利用递归算法给出平均逗留时间,进而得到依赖于状态的最优价格.最后将上述理论应用到汽车检测场的动态定价问题之中.This paper considers the rate control and dynamic pricing in a tandem queue with limited resources.To improve the long-run average social welfare,managers not only need to set appropriate dynamic prices to increase revenue,but also need to allocate appropriate resources to two servers with limited resources with the goal of reducing costs.This paper uses sensitivitybased optimization to obtain the optimal state-dependent arrival rates and service rates firstly.Through the marginal revenue function,the relationship between price and arrival rate is established.Then,based on the optimal rates,the sojourn time is derived by using a recursive algorithm and the corresponding dynamic prices are also given.Finally,the above theory is applied to the dynamic pricing in an automobile inspection company.

关 键 词：串联排队 灵敏度优化 速率控制 动态定价 

分 类 号：O226[理学—运筹学与控制论]