Optimal Pricing for Competitive Service Facilities with Balking and Veering Customers

This paper focuses on determining the optimal pricing strategy for a service providing firm with multiple facilities. The market is involved with some other competing firms providing the same service. The firm and its competitors might devise three different pricing policies as uniform mill pricing, distinct mill pricing and delivered pricing. Customers choose the facilities probabilistically based on their perceived utility to being served. After they received at a congested facility, some of them balk from entering the queue and go directly to another facility rather than coming back to their origins. As a result, the arrival rate for a facility is varying on the level of congestion in all facilities. This situation requires us to find equilibrium point of facilities’ arrival rates. For this purpose, a heuristic procedure is developed. The resulted non-linear and complex model is proposed to solve using a hybrid algorithm of Particle Swarm Intelligence and Differential Evolution, two continuous approximate optimization algorithms. An illustrative example is given to show the model’s applicability and the algorithm’s efficiency. Different scenarios in terms of sensitivity analysis are also mentioned to capture managerial insights.