An M/M/c queue model for hub covering location problem

The hub location problem appears in a variety of applications including airline systems, cargo delivery systems, and telecommunication network design. Hub location problems deal with finding the location of hub facilities and the allocation of demand nodes to these located hub facilities. We conside...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 54; no. 11; pp. 2623 - 2638
Main Authors: Mohammadi, Mehrdad, Jolai, Fariborz, Rostami, Hamideh
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.12.2011
Elsevier
Subjects:
algorithms
Artificial Intelligence
Calculus of variations and optimal control
Combinatorics
Combinatorics. Ordered structures
Computer Science
Designs and configurations
Evolutionary computations
Exact sciences and technology
Facilities planning and design
Hub covering location
Imperialist Competitive Algorithm
linear models
Location
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
probability
probability distribution
Queuing
Sciences and techniques of general use
Signal and Image Processing
transportation
trucks
Evolutionary computations
Facilities planning and design
Queuing
Hub covering location
Imperialist Competitive Algorithm
Location
Transportation system
Covering problem
Optimization method
Probability distribution
Non linear programming
Location problem
Linear model
Mathematical model
Queue
Random variable
Computer aided analysis
Mathematical programming
Optimal algorithm
System design
Linear programming
Computational complexity
Constrained optimization
Numerical analysis
Scientific computation
Genetic algorithm
Applied mathematics
Optimal solution
Telecommunication network
ISSN:0895-7177, 1872-9479
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Summary:The hub location problem appears in a variety of applications including airline systems, cargo delivery systems, and telecommunication network design. Hub location problems deal with finding the location of hub facilities and the allocation of demand nodes to these located hub facilities. We consider a hub-and-spoke network problem with crowdedness or congestion in the system. The transportation time and the rate of arrived trucks to each hub are random variables. In addition, a hub cannot service all trucks simultaneously and it has some restrictions like capacity constraint and the service time limitations. Hubs, which are the most crowded parts of network, are modeled as M/M/c queuing systems. In the application of the proposed model for a cargo transportation system, the number of trucks follows Poisson probability distribution in the queuing system. In this paper at first a nonlinear mathematical programming is presented to find an optimal solution for the considered problem. A probabilistic constraint is included to ensure that the probability of b trucks in a queue is less than a threshold value θ for each hub. Then, we transfer the introduced nonlinear constraints of the mathematical programming model to the linear constraints. Due to the computational complexity of the resulted model, we propose an improved meta-heuristic based on Imperialist Competitive Algorithm and Genetic Algorithm to find near optimal solution of the problem. The performance of the solutions found by the proposed improved meta-heuristic is compared with those of pure GA and those of the mathematical programming model.
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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.06.038