服务台不可靠的重试排队系统均衡分析

本文研究服务台不可靠的M/M/1常数率重试排队系统中顾客的均衡进队策略, 其中服务台在正常工作和空闲状态下以不同的速率发生故障。在该系统中, 服务台前没有等待空间, 如果到达的顾客发现服务台处于空闲状态, 该顾客可占用服务台开始服务。否则, 如果服务台处于忙碌状态, 顾客可以选择留下信息, 使得服务台在空闲时可以按顺序在重试空间中寻找之前留下信息的顾客进行服务。当服务台发生故障时, 正在被服务的顾客会发生丢失, 且系统拒绝新的顾客进入系统。根据系统提供给顾客的不同程度的信息, 研究队长可见和不可见两种信息情形下系统的稳态指标, 以及顾客基于收入-支出函数的均衡进队策略, 并建立单位时间内服务商的收益和社会福利函数。比较发现, 披露队长信息不一定能提高服务商收益和社会福利。     

服务台不可靠的重试排队系统均衡分析

本文研究服务台不可靠的M/M/1常数率重试排队系统中顾客的均衡进队策略, 其中服务台在正常工作和空闲状态下以不同的速率发生故障。在该系统中, 服务台前没有等待空间, 如果到达的顾客发现服务台处于空闲状态, 该顾客可占用服务台开始服务。否则, 如果服务台处于忙碌状态, 顾客可以选择留下信息, 使得服务台在空闲时可以按顺序在重试空间中寻找之前留下信息的顾客进行服务。当服务台发生故障时, 正在被服务的顾客会发生丢失, 且系统拒绝新的顾客进入系统。根据系统提供给顾客的不同程度的信息, 研究队长可见和不可见两种信息情形下系统的稳态指标, 以及顾客基于收入-支出函数的均衡进队策略, 并建立单位时间内服务商的收益和社会福利函数。比较发现, 披露队长信息不一定能提高服务商收益和社会福利。     

客源充足情境下的customer-intensive服务策略研究

在customer-intensive服务中服务速度越慢,顾客的效用就越高,然而等待时间也随之变长;而服务商则需对服务速度和价格进行决策,以求获得最优收益。本文基于客源丰富的服务垄断商对此问题采用M/M/1排队模型进行了研究,将顾客成本细分为时间成本和焦虑成本,给出了最优服务速度和价格。研究发现,单位焦虑成本的增加造成了服务商收益的减少,但对收益的影响要小于单位时间成本。最后,提出了服务商投入一定的服务成本来减少焦虑成本的策略,以达到获取更高收益的目的,并证明了策略的有效性。     

具有两类平行顾客的M/M/1重试排队系统均衡策略研究

本文研究具有两类平行顾客且服务台可靠的M/M/1重试排队系统的均衡策略.在该排队系统中,两类顾客平行到达,并服从不同参数的负指数分布.当顾客进入系统时,若观察到服务台为空,将立刻开始服务;若观察到服务台处于忙期,则进入重试空间等待重试.在完全可见和几乎可见两种情形下,基于“收益-成本”理论提出合理的效用函数并对两类平行顾客进行均衡分析.此外,建立单位时间的社会收益函数,给出最优社会效益分析.最后运用数值分析直观地表示出随着系统参数的改变,顾客行为策略的变化情况.     

基于排队系统的偏好差异性顾客服务策略分析

在服务商为不同偏好顾客提供差异性服务的排队系统中,其收益受到需求规模、顾客类型等因素影响,如何制定策略才能达到服务特定类型顾客并获取最大收益的目的？本文以服务时间与效果正相关的顾客密集型服务为背景,基于M/M/1模型对服务商为两种偏好顾客提供两种服务的情景进行研究,并将从偏好服务所获基准效用相对较低、较高的顾客分别定义为1类、2类顾客。结果表明,①随着潜在顾客规模的增加,最优策略所适用的3种基本策略依次为公平策略、优先服务2类顾客的策略以及仅服务2类顾客的排他性策略;②3种基本策略的适用范围仅与1类顾客的服务选择标准相关;③在优先服务某类顾客的策略中,有效到达速率及服务速度由另一类顾客的特征决定。     

面向时间敏感型顾客的服务系统速率-成本决策模型

针对一类客户资源集中、时间敏感性强、质量要求高的服务系统决策问题,建立M/M/1排队模型,分析稳定状态下顾客参与服务系统的均衡到达率、服务价格之间的关系以及服务商最优速率.结果表明:服务速率与顾客单位时间等待成本无关,而均衡到达率和服务价格均与顾客单位等待成本呈负相关;当基准服务质量达到一定水平时,企业要提高利润就要追加投资,降低顾客等待效用,提高顾客满意度.     

竞争环境下考虑顾客惰性行为的易逝品动态定价

消费者购买决策的行为倾向对企业的收益管理有着不可忽视的影响。本文在竞争企业动态定价问题中, 考虑了顾客惰性行为——即顾客购买决策的非理性拖延倾向——的影响。证明了库存充足情况下, 多企业多期博弈各销售期都存在唯一的纯策略纳什均衡。数值模拟表明, 顾客惰性对企业的最优价格和企业最大期望收益均造成负面影响, 且对销售低质量产品的企业的负面影响更大。此外, 顾客惰性宽度对各企业最优价格和最大期望收益的影响边际效应递增, 而顾客惰性深度产生的影响边际效应递减。     

基于互补性服务的Geom/Geom/1排队顾客均衡策略研究

主要研究具有两种服务的Geom/Geom/1排队系统,这两种服务提供具有互补性,即顾客只有同时都接受服务才能得到收益.通过建立均衡方程来分析顾客的行为,研究了顾客的收益与花费,得到了利润最大化的服务提供者的到达概率小于社会最优到达概率,并给出了垄断情形下的顾客均衡策略,并说明垄断者的最优价格同时使社会福利达到最优.     

具有两类故障特性的M/M/1排队系统均衡分析

考虑顾客在具有两种故障特性的马尔科夫排队系统中的均衡策略.在该系统中,正常工作的服务台随时都可能发生故障.假设服务台只要发生故障就不再接收新顾客,并且可能出现的故障类型有两种：（1）不完全故障：此类故障发生时,服务台仍有部分服务能力,以较低服务率服务完在场顾客后进行维修;（2）完全故障：此类故障发生时,服务台停滞服务并且立即进行维修,维修结束后重新接收新顾客.顾客到达时为了实现自身利益最大化都有选择是否进队的决策,基于线性“收益-损失”结构函数,分析了顾客在系统信息完全可见和几乎不可见情形下的均衡进队策略,及系统的平均社会收益,并在此基础上,通过一些数值例子展示系统参数对顾客策略行为的影响.     

带有破坏性负顾客的Geo/Geo/1/MWV可修排队系统均衡策略研究

本文研究带有破坏性负顾客的离散时间Geo/Geo/1/MWV可修排队系统的顾客策略行为.当破坏性负顾客到达系统时,会移除正在接受服务的正顾客,同时造成服务台故障.服务台一旦发生损坏,会立刻接受维修,修理时间服从几何分布.服务台在工作休假期间会以较低的服务速率对顾客进行服务.我们求得系统的稳态分布,进一步给出服务台不同状态下的均衡进入率以及系统单位时间的社会收益表达式.最后对均衡进入率和均衡社会收益进行了数值分析.     

社会互动视角下的服务型企业最优运营策略研究

本文主要研究在社会互动的影响下,服务型企业如何制定以价格、服务速率为代表的运营管理策略,从而实现利润最大化。首先,基于M/M/1排队模型对顾客购买决策过程进行建模分析,考虑单个服务型企业在实现利润最大化的目标条件下,社会互动的作用如何影响定价和服务速率决策;其次,研究在竞争市场环境中,社会互动如何影响市场均衡状态下各企业的运营决策和市场份额。结果表明,无论在垄断还是竞争的市场环境中,社会互动对服务型企业的最优运营决策均有不同程度与方向的影响。     

Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations

This paper studies the customers’ equilibrium and socially optimal joining–balking behavior in single-server Markovian queues with multiple working vacations. Different from the classical vacation policies, the server does not completely stop service but maintains a low service rate in vacation state in case there are customer arrivals. Based on different precision levels of the system information, we discuss the observable queues, the partially observable queues, and the unobservable queues, respectively. For each type of queues, we get both the customers’ equilibrium and socially optimal joining–balking strategies and make numerical comparisons between them. We numerically observe that their equilibrium strategy is unique, and especially, the customers’ equilibrium joining probability in vacation state is not necessarily smaller than that in busy state in the partially observable queues. Moreover, we also find that the customers’ individual behavior always deviates from the social expectation and makes the system more congested.     

Equilibrium balking strategies in Markovian queues with working vacations

The equilibrium balking strategies are investigated in the paper for observable and unobservable single-server queues with working vacations. In such an M/M/1 queue with working vacations, the server undertakes the workload with a lower service rate rather than completely stops to work during the vacation period. Upon arrival, the customers decide whether to join or balk the queue based on observation of the queue length and the status of the server, along with the reward-cost structure of the system. Accordingly, four cases with respect to different levels of information are studied and the corresponding Nash equilibria are derived. Finally, the effect of the information levels as well as several parameters on the equilibrium threshold and equilibrium entrance probabilities is illustrated by numerical examples.     

Optimal pricing and inventory policies with reliable and random-yield suppliers: characterization and comparison

In this paper, we study the joint pricing and inventory replenishment problem for a periodic-review inventory system with random demand and dual suppliers, one of the suppliers is reliable but more expensive, the other supplier is less expensive but is unreliable with random yield. We characterize the firm’s optimal policies that simultaneously determine the optimal ordering and pricing decisions in each period over a finite planning horizon, and investigate the impacts of supply source diversification and supplier reliability on the firm and on its customers. We show that having source diversification or higher reliability of suppliers not only increases the firm’s expected profit, but also results in a lower optimal selling price, thus they benefit both the firm and its customers.     

Equilibrium threshold strategies in observable queueing systems under single vacation policy

This paper studies the equilibrium behavior of customers in continuous/discrete time queueing systems under single vacation policy. In the single vacation queueing system, the server can only take exactly one vacation when no customers exist in the system. This scheme is more practical under many specific circumstances. Based on the reward–cost structure, equilibrium behavior is considered in the fully observable and almost observable cases. The threshold strategies in equilibrium are obtained and the stationary system behavior is analyzed under the corresponding strategies. Finally, we illustrate the effect of the information level as well as several parameters on the equilibrium thresholds and social benefits via numerical experiments. The research results could instruct the customers to take optimal strategies and provide the managers with reference information on the pricing problem in the queueing system.     

Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly

This paper analyzes the impact of dynamic and fixed-ratio pricing policies on firm profits and equilibrium prices under competition. Firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times. In each period, customers first purchase from the low price firm and then from the high price firm up to their inventories, provided the prices are lower than the maximum they are willing to pay. The main conclusions of this paper are as follows: although dynamic pricing is a more sophisticated policy than fixed-ratio pricing, it may lead to decreased equilibrium profits; under both pricing policies, one firm assumes the role of a low-cost high-output firm while the other assumes the role of a high-cost low-output firm; and, the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices.     

基于分类服务机制的可预约排队系统设计和服务定价研究

采取合理有效的服务机制和服务定价是确保服务型企业持续有效运行的重要方式,服务提供商设计合理的服务策略可以使得服务收益达到最优。本文以服务可预约的排队系统为研究背景,对服务提供商分类服务机制选择和服务定价策略进行研究。通过考虑由两种服务策略下顾客之间的平均等待时间的对比和顾客等待厌恶心理参数形成的全新顾客服务效用模型,给出服务提供商在不同服务机制下的最优服务策略以及顾客市场规模对其服务策略选择的影响。研究表明,当预约顾客的市场规模相对较小时,服务提供商可以采取分类服务机制,即同时服务预约顾客和未预约顾客以增加服务收益,反之亦然。此外,预约顾客等待厌恶程度能够显著增大服务提供商的服务定价。     

服务水平约束下动态定价与库存管理

本文研究服务水平约束下的动态定价与库存管理问题。企业在有限期内销售某种产品,产品的需求为随机需求,且期望需求依赖于产品价格。在每一期期初,企业需要在满足服务水平约束的条件下同时决定订货量和产品价格。本文首先构建了动态定价和订购联合决策的随机动态规划模型,并证明了最优解的存在性。进一步,通过对最优解的结构进行刻画,将原问题的求解转化为若干子问题的求解,降低了问题求解的难度。通过对最优解的分析发现,当期初库存增大时,产品最优价格降低。通过分析目标服务水平对利润的影响,证明了服务水平与利润之间存在权衡,实现高的服务水平需要承受利润损失。数值模拟表明,相对于传统的静态定价策略,采用动态定价策略可以降低追求服务水平所带来的利润损失,验证了动态定价策略的有效性。     

A capacitated firm’s pricing strategies for strategic consumers with different search costs

This paper studies pricing strategies of a seller with budget constraints facing two types of strategic consumers with different search costs, and proposes three pricing strategies to motivate all consumers to visit his shop. These are the basic price strategy, differentiated compensation strategy and an improved differentiated compensation strategy. Based on the rational expectations paradigm, we characterize the rational expectations equilibrium in the game and propose a basic pricing strategy. In order to address the interplay between price and demand, we further propose a differentiated compensation strategy to improve the basic model. We then compare the differentiated compensation strategy to the basic pricing strategy when both are feasible. We find that selection of the optimal strategy is independent of composition of consumers but is dependent on the seller’s budget level and the difference between the two search costs. If the budget is large enough and the difference between the search costs is small enough, a differentiated compensation strategy can further improve the seller’s profitability. In addition to these findings, we first propose an improved differentiated compensation strategy to further enhance the firm’s profit. We find that the optimal strategy is to implement the improved differentiated compensation strategy when all three strategies are feasible. Interestingly, the firm may benefit from paying a high compensation to the consumers.     

竞争环境下截流问题的选址-价格模型

研究了竞争环境下考虑产品定价的截流设施选址问题。连锁企业在市场上新建设施时,市场上已有属于竞争对手的设施存在,在连锁企业新建设施位置确定之后,两个企业关于产品定价进行双寡头完全信息非合作博弈。定义了效用函数,引入Huff模型,以企业利润最大为目标,建立双层规划模型,证明了模型纳什均衡价格的存在性,并构造启发式算法对模型进行求解。算例分析表明,该算法求解结果较为理想,可用于大中型网络的规划选址问题。