A soft-computing Pareto-based meta-heuristic algorithm for a multi-objective multi-server facility location problem
Graphical abstract
Highlights
► A novel multi-objective facility location model within multi-server queuing framework is developed. ► Three Pareto-based meta-heuristics are proposed to solve the problem with three objectives. ► Taguchi approach is utilized to tune the parameters of the algorithms. ► A new multi-objective response metric is introduced for calibration. ► The algorithms are compared based on their computational time and number of Pareto solutions.
Section snippets
Introduction and motivation
The facility location problems (FLPs) are the ones dealing to locate new facilities along with their demand nodes allocations, for which many models have been developed under different situations so far. On the one hand, the term “location” relates to the modeling, formulation, and solving methodology of a class of problems that can be best described as locating facilities in some given space. On the other hand, the term “allocation” in FLP refers to allocating demand nodes to the located
Problem definition
In this paper, a novel multi-objective MSFLAP model within M/M/m queuing framework is developed in which the system is congested, the demands are stochastic, the servers are immobile, and the capacity, the service level, and selecting the nearest-facility are considered constraints. The applications of such model can be found in medical facilities, post offices, automated teller machines, vending machines, intercity service centers, banks, checkout counters in stores, check-in counters in
The model
Before modeling, the index sets, the parameters, and the decision variables of the model are defined as follow.
- i
an index for a customer i = 1, 2,…, I
- j
an index for a facility containing multiple servers j = 1, 2,…, J
Indices
- P
maximum number of on-duty servers
demand rate of service requested from customer i
service rate of the servers in facility j
demand rate at facility node j
fixed cost of establishing a facility at potential node j
staffing cost for a server at potential node j
traveling time
Parameters
The proposed Pareto-based meta-heuristic algorithm
In this section, a Pareto-based meta-heuristic algorithm called MOHS is proposed to solve the developed triple-objective model of the MSFLP at hand. Moreover, both NSGA-II and NRGA are utilized to validate the results obtained. However, some required multi-objective backgrounds are first defined in the following section.
Applications and comparisons
This section provides the application of the proposed methodology and the performance comparisons of the three meta-heuristic algorithms using a parameter tuning procedure. Before doing this, some multi-objective performance metrics are first introduced.
Conclusion and directs for future researches
In this paper, a multi-objective multi-server facility location-allocation problem with immobile servers and random demands under service capacity, the nearest-facility selection criterion, and service level constraints, was first modeled mathematically. Then, in view of the fact that FLPs are basically NP-Hard, three parameter-tuned Pareto-based multi-objective meta-heuristic algorithms, called MOHS, NSGA-II, and NRGA were proposed to solve the problem. The proposed algorithms were next
Acknowledgments
The authors are thankful for constructive comments of the associate editor and the anonymous reviewers. Taking care of the comments certainly improved the presentation of the manuscript.
References (51)
- et al.
Location analysis: a synthesis and survey
European Journal of Operational Research
(2005) - et al.
Facility location and supply chain management – a review
European Journal of Operational Research
(2009) - et al.
A review of soft computing applications in supply chain management
Applied Soft Computing
(2010) - et al.
A fuzzy queuing location model with a genetic algorithm for congested systems
Applied Mathematics and Computation
(2006) - et al.
A review of congestion models in the location of facilities with immobile servers
European Journal of Operational Research
(2007) - et al.
Budget constrained location problem with opening and closing of facilities
Computers and Operations Research
(2003) A multiple server location-allocation model for service system design
Computers and Operations Research
(2008)- et al.
Shortest path based simulated annealing algorithm for dynamic facility layout problem under dynamic business environment
Expert Systems with Applications
(2009) - et al.
Multi-objective routing within large scale facilities using open finite queueing networks
European Journal of Operational Research
(2000) - et al.
Multi-objective solution of the uncapacitated plant location problem
European Journal of Operational Research
(2003)
Optimizing the throughput, service rate, and buffer allocation in finite queuing networks
Electronic Notes in Discrete Mathematics
Performance optimization of open zero-buffer multi-server queuing networks
Computers and Operations Research
Multiple criteria facility location problems: a survey
Applied Mathematical Modelling
Covering problems in facility location: a review
Computers and Industrial Engineering
Soft-computing based heuristics for location on networks: the p-median problem
Applied Soft Computing
A bi-objective model to optimize reliability and cost of system with a choice of redundancy strategies
Computers and Industrial Engineering
Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: a harmony search algorithm
Applied Mathematics and Computation
A new structural optimization method based on the harmony search algorithm
Computers and Structures
Multi-objective harmony search algorithm for optimal power flow problem
Electrical Power and Energy Systems
A novel meta-heuristic optimization methodology for solving various types of economic dispatch problem
Energy
Location-allocation problems
Operations Research
Discrete network location models
Solving conflicting bi-objective facility location problem by NSGA-II evolutionary algorithm
The International Journal of Advanced Manufacturing Technology
Optimal 2-facility network districting in the presence of queuing
Transportation Science
Algorithms for a facility location problem with stochastic customer demand and immobile servers
Annals of Operations Research
Cited by (0)
- 1
Tel.: +98 281 3665275; fax: +98 281 3665277.