Investigating sensitivity and the impact of information of pricing decisions in an M/M/1/∞ queueing model

We consider a model for optimal pricing for a job shop. The problem is formulated as a single server queueing model, where an arriving customer enters the system if his reward (drawn from a stochastic variable) exceeds the sum of the price charge of his job plus the expected waiting costs. The optimal price is found with respect to profit optimization and welfare optimization. Two models are formulated. The first model, called NINF, contains only steady state queue information. The other model, called QL, contains more detailed information because here an arriving customer is informed about the number of customers already in the system. The main interpretation of the models is how complex an information system should the job shop provide to its customers. We show that for both criteria functions it pays off, except for a special case, to use the more detailed information system. In the paper we also investigate how sensitive the pricing decision and its outcome on the criteria functions are on the variance of the reward distribution, which in the paper is assumed to be uniformly distributed. Concerning welfare optimization we show that a decreased variance always results in a decreased welfare contribution while concerning profit optimization a decreased variance can result in both a decreased as well as an increased profit contribution.