Elsevier

Applied Soft Computing

Volume 13, Issue 4, April 2013, Pages 1728-1740
Applied Soft Computing

A soft-computing Pareto-based meta-heuristic algorithm for a multi-objective multi-server facility location problem

https://doi.org/10.1016/j.asoc.2012.12.016Get rights and content

Abstract

In this paper, a novel multi-objective location model within multi-server queuing framework is proposed, in which facilities behave as M/M/m queues. In the developed model of the problem, the constraints of selecting the nearest-facility along with the service level restriction are considered to bring the model closer to reality. Three objective functions are also considered including minimizing (I) sum of the aggregate travel and waiting times, (II) maximum idle time of all facilities, and (III) the budget required to cover the costs of establishing the selected facilities plus server staffing costs. Since the developed model of the problem is of an NP-hard type and inexact solutions are more probable to be obtained, soft computing techniques, specifically evolutionary computations, are generally used to cope with the lack of precision. From different terms of evolutionary computations, this paper proposes a Pareto-based meta-heuristic algorithm called multi-objective harmony search (MOHS) to solve the problem. To validate the results obtained, two popular algorithms including non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are utilized as well. In order to demonstrate the proposed methodology and to compare the performances in terms of Pareto-based solution measures, the Taguchi approach is first utilized to tune the parameters of the proposed algorithms, where a new response metric named multi-objective coefficient of variation (MOCV) is introduced. Then, the results of implementing the algorithms on some test problems show that the proposed MOHS outperforms the other two algorithms in terms of computational time.

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.

    Indices

    i

    an index for a customer i = 1, 2,…, I

    j

    an index for a facility containing multiple servers j = 1, 2,…, J

    Parameters

    P

    maximum number of on-duty servers

    λi

    demand rate of service requested from customer i

    μj

    service rate of the servers in facility j

    ψj

    demand rate at facility node j

    cj,1

    fixed cost of establishing a facility at potential node j

    cj,2

    staffing cost for a server at potential node j

    tij

    traveling time

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.

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