Abstract: A customer’s satisfaction with a service is greatly affected by her expectations of the service attributes, with higher expectations often leading to lower utility and vice versa. Such expectations are known as reference points, and such customers are said to be reference-dependent customers. Loss aversion reflects customer behavior in the sense that compared with reference points on price and delay, losses are more painful than equal-sized gains. There is a substantial body of anecdotal and empirical evidence of customer loss aversion on price and delay attributes.Also, time is less fungible than money, and time cannot be easily saved or stored. These differences imply that people may have different degrees of loss aversion toward money and time attributes. In this study, we examine customers’ loss aversion behavior toward both price and delays in service systems where the degree of customers’ loss aversion to these attributes is different.
   We model a service system with congestion as a queueing system. Customers compare these two attributes with their rational expectations of outcomes, with losses being more painful than equal-sized gains being pleasant. Therefore, the customer’s overall expected utility from a service includes her intrinsic and gain-loss utilities. Intrinsic utility measures the direct effects of service attributes. Gain-loss utility measures the deviation of the net monetary reward and delay based on her reference points. There are different coefficients that reflect the degree of loss aversion to price and delays. We first examine customers’ equilibrium queueing strategies. We find that, unlike the traditional case in which loss aversion is not considered, there may exist three equilibrium strategies, one of which is preferred in the sense that customers’ utility is the highest at this equilibrium. Based on this, with the objective of profit maximization, we obtain three strategies on price and service capacity for different unit service capacity costs. If the unit service capacity cost is small or large, the manager will adopt strategies to attract all potential customers. However, if the unit service capacity cost is in the middle range, the manager may only attract some of the potential customers or even may not operate the system. Finally, the effect of loss aversion coefficients on the system is discussed. The results illustrate that when customers are more loss-averse to price, the optimal price and the optimal profit will increase, but when customers are more loss-averse to waiting, the optimal price and the optimal profit will decrease. However, the change in service capacity’s strategy is closely related to the unit service capacity cost.
   The management insights of this study are as follows: (1)Due to the change in the loss aversion coefficient, the threshold of unit service capacity cost will change. Managers should adopt different strategies in different threshold ranges;hence, they should pay attention to customers’ loss aversion behavior. (2)When the unit service capability cost is small or large, appropriate pricing and service capability strategies can be adopted to serve all potential customers, but when the unit service capability cost is in the middle range, appropriate strategies can be adopted to serve some potential customers, or even choose not to operate the system. (3)Managers should not ignore customers’ loss aversion towards price, however, they can ignore their loss aversion towards waiting.
   Our study will examine the reference effect on service systems when customers are loss averse toward both price and waiting time. We show that both customers’ equilibrium joining strategies, systems’ pricing and service capacity decisions are significantly different from the results without considering the reference effect. We hope our study will stimulate empirical research testing our analytical results in different service systems, such as those in the healthcare field and at call centers. Future research may also consider analyzing customers’ loss-averse behavior in observable queues.

Key words: loss-averse customers, queueing system, equilibrium analysis, pricing, service capacity

摘要： 针对顾客对价格和等待的损失厌恶行为,本文研究了排队系统关于价格和服务能力的决策问题。基于顾客对价格和等待有不同的损失厌恶程度,首先分析了损失厌恶型顾客的均衡进队策略,发现存在多重均衡,其中有一个为个人偏好均衡。随后,以利润最大化为目标,得到了不同单位服务能力成本下的三种价格和服务能力策略。如果单位服务能力成本较小或较大,管理者会采取策略吸引所有潜在顾客进入,而如果处于中间范围,管理者可能只会吸引部分潜在顾客进入,甚至可能不运营系统。最后,损失厌恶系数对系统影响的结果表明:当顾客对价格的损失厌恶程度增加时,最优价格和最优利润都会增加,而当顾客对等待的损失厌恶程度增加时,最优价格和最优利润都会减小,但服务能力策略的变化均与单位服务能力成本密切相关。

关键词: 损失厌恶型顾客, 排队系统, 均衡分析, 价格, 服务能力