Bi-objective vibration damping optimization for congested location–pricing problem

• A bi-objective mathematical model is presented for a location–queuing–pricing problem.
• This paper considers M/M/m/K queuing system at each facility while M/M/1 is usual in the literature.
• Unlike previously published papers which consider the same price at all facilities we consider different prices.
• We developed a multi-objective vibration damping optimization to find Pareto solutions.
• Taguchi method is also implemented using a response metric to tune the parameters.

This paper presents a bi-objective mathematical programming model for the restricted facility location problem, under a congestion and pricing policy. Motivated by various applications such as locating server on internet mirror sites and communication networks, this research investigates congested systems with immobile servers and stochastic demand as M/M/m/k queues. For this problem, we consider two simultaneous perspectives; (1) customers who desire to limit waiting time for service and (2) service providers who intend to increase profits. We formulate a bi-objective facility location problem with two objective functions: (i) maximizing total profit of the whole system and (ii) minimizing the sum of waiting time in queues; the model type is mixed-integer nonlinear. Then, a multi-objective optimization algorithm based on vibration theory (so-called multi-objective vibration damping optimization (MOVDO)), is developed to solve the model. Moreover, the Taguchi method is also implemented, using a response metric to tune the parameters. The results are analyzed and compared with a non-dominated sorting genetic algorithm (NSGA-II) as a well-developed multi-objective evolutionary optimization algorithm. Computational results demonstrate the efficiency of the proposed MOVDO to solve large-scale problems.