Price and Service Capacity Decisions of Queueing Systems with Loss-averse Customers
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 behav-ior 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 differ-ences 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 strate-gies 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.
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