A new technique to optimize the functions of fuzzy profit of queuing models: Application to a queuing model with publicity and renouncement

In this paper we model, using the Queuing Theory, the situation in which the manager of some facilities wishes to maximize the profit generated by the same. The manager tries to attract customers and the effectiveness of his publicity politic is measured in the fraction of customers who renounce. In this paper, unlike the classic models, we consider that the service time of the only server of the facilities behave with uncertainty, which may be represented by means of a fuzzy number. The objective is to determine the rate to be paid by every customer for his service and the level of publicity which the manager must utilize to maximize his profits. The consideration of service times as fuzzy numbers implies that the function to be optimized has fuzzy coefficients, this is why it is necessary to use fuzzy optimization for the solution of the problem and, in addition, a new technique is proposed in order to optimize the functions of fuzzy profit of queuing models. To demonstrate the validity of the proposed proceeding is resolved satisfactorily, and applied as an example, a system of fuzzy queues, which is often found in real situations. The fuzzy queuing systems are more realistic than the crisp systems commonly used in many practical situations. Besides, the extension of the queuing decision models to fuzzy environment allows these models to have further applications. © 2008 Elsevier Ltd. All rights reserved.