Developing a New Bi-Objective Functions Model for a Hierarchical Location-Allocation Problem Using the Queuing Theory and Mathematical Programming

Document Type : Original Manuscript


Department of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran



In this research, a hierarchical location-allocation problem is modeled in a queue framework. The queue model is considered as M/M/1/k, in which system capacity is finite, equals to k. This is the main contribution of the current research. Customer's enters to the system in order to find the service according to a Poisson. In this problem, the hierarchical location-allocation model is considered in two levels. Also, the model has two objective functions: maximizing the total number of demand coverage and minimizing the waiting time of customers in queues to receive services. After modeling and verifying the validity of the presented model, it is solved using NSGA II and MOPSO meta-heuristics.


  • We propose a new M/M/1/K model for the location-allocation problem.
  • The model had two levels of services.
  • Two metaheuristic algorithms including NSGA-II and MOPSO were used to optimize the model.
  • Computational experiments show that the NSGA-II is able to obtain the efficient solutions.


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