Mathematical Model and Stochastic Multi-Criteria Acceptability Analysis for Facility Location Problem

This paper studies a real-life public sector facility location problem. The problem fundamentally originated from the idea of downsizing the number of service centres. However, opening of new facilities is also considered in case the current facilities fail to fulfil general management demands. Two operation research methodologies are used to solve the problem and the obtained results are compared. First, a mathematical programming model is introduced to determine where the new facilities will be located, and which districts get service from which facilities, as if there were currently no existing facilities. Second, the Stochastic Multi-criteria Acceptability Analysis-TRI (SMAA-TRI) method is used to select the best suitable places for service centres among the existing facilities. It is noted that the application of mathematical programming model and SMAA-TRI integration approach on facility location problem is the first study in literature. Compression of outcomes shows that mixed integer linear programming (MILP) model tries to open facilities in districts which are favoured by SMAA-TRI solution.

[1]  Alfred A. Kuehn,et al.  A Heuristic Program for Locating Warehouses , 1963 .

[2]  Tzu-Liang Tseng,et al.  A hybrid algorithm for capacitated plant location problem , 2010, Expert Syst. Appl..

[3]  Paula Camelia Trandafir,et al.  Some heuristic methods for solving p-median problems with a coverage constraint , 2012, Eur. J. Oper. Res..

[4]  J. Figueira,et al.  A survey on stochastic multicriteria acceptability analysis methods , 2008 .

[5]  Risto Lahdelma,et al.  Stochastic multicriteria acceptability analysis using the data envelopment model , 2006, Eur. J. Oper. Res..

[6]  Charles S. ReVelle,et al.  The Location of Emergency Service Facilities , 1971, Oper. Res..

[7]  Numan Çelebi,et al.  Comparative analysis of multi-criteria decision making methodologies and implementation of a warehouse location selection problem , 2011, Expert Syst. Appl..

[8]  Maria João Cortinhal,et al.  Upper and lower bounds for the single source capacitated location problem , 2003, Eur. J. Oper. Res..

[9]  Horst A. Eiselt,et al.  Location analysis: A synthesis and survey , 2005, Eur. J. Oper. Res..

[10]  J. Reese,et al.  Fast and robust techniques for the euclidean p-median problem with uniform weights , 2009, Comput. Ind. Eng..

[11]  Juscelino Almeida Dias,et al.  A stochastic method for robustness analysis in sorting problems , 2009, Eur. J. Oper. Res..

[12]  Gilbert Laporte,et al.  LOCATION OF A NEW FACILITY ON A LINEAR MARKET IN THE PRESCENCE OF WEIGHTS , 1987 .

[13]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[14]  J A Díaz,et al.  A Branch-and-Price algorithm for the Single Source Capacitated Plant Location Problem , 2002, J. Oper. Res. Soc..

[15]  Xiaodong Liu,et al.  Selection of logistics center location using Axiomatic Fuzzy Set and TOPSIS methodology in logistics management , 2011, Expert Syst. Appl..

[16]  K S Hindi,et al.  Efficient solution of large scale, single-source, capacitated plant location problems , 1999, J. Oper. Res. Soc..

[17]  Ju-Liang Zhang,et al.  Capacitated facility location problem with general setup cost , 2006, Comput. Oper. Res..

[18]  Thomas L. Magnanti,et al.  Decomposition methods for facility location problems , 1986 .

[19]  Sibel A. Alumur,et al.  Network hub location problems: The state of the art , 2008, Eur. J. Oper. Res..

[20]  Kaisa Miettinen,et al.  Determining the implementation order of a general plan by using a multicriteria method , 1998 .

[21]  Andreas Drexl,et al.  Facility location models for distribution system design , 2005, Eur. J. Oper. Res..

[22]  Kaisa Miettinen,et al.  Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA) , 2003, Eur. J. Oper. Res..

[23]  Kaisa Miettinen,et al.  Reference point approach for multiple decision makers , 2005, Eur. J. Oper. Res..

[24]  Risto Lahdelma,et al.  A multiple criteria decision model for analyzing and choosing among different development patterns for the Helsinki cargo harbor , 1999 .

[25]  K. Ravindranath,et al.  A Multi-Criteria Procedure for the User Interface Components Layout Problem , 2009, Asia Pac. J. Oper. Res..

[26]  Risto Lahdelma,et al.  SMAA-2: Stochastic Multicriteria Acceptability Analysis for Group Decision Making , 2001, Oper. Res..

[27]  Ali Fuat Guneri,et al.  A fuzzy ANP approach to shipyard location selection , 2009, Expert Syst. Appl..

[28]  Maria Paola Scaparra,et al.  Sloan School of Management Working Paper 4387-02 October 2002 A MULTI-EXCHANGE HEURISTIC FOR THE SINGLE SOURCE CAPACITATED FACILITY LOCATION PROBLEM , 2002 .

[29]  Michel Balinski,et al.  Integer Programming: Methods, Uses, Computation , 2010, 50 Years of Integer Programming.

[30]  Tony J. Van Roy,et al.  A Cross Decomposition Algorithm for Capacitated Facility Location , 1986, Oper. Res..

[31]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[32]  Mark S. Daskin,et al.  Capacitated facility location/network design problems , 2001, Eur. J. Oper. Res..

[33]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[34]  Rua Antero de Quental,et al.  SMAA-TRI: A Parameter Stability Analysis Method for ELECTRE TRI , 2005 .

[35]  Iván A. Contreras,et al.  Scatter search for the single source capacitated facility location problem , 2007, Ann. Oper. Res..

[36]  Roberto Baldacci,et al.  A new method for solving capacitated location problems based on a set partitioning approach , 2002, Comput. Oper. Res..

[37]  Justo Puerto,et al.  A multiperiod two-echelon multicommodity capacitated plant location problem , 2000, Eur. J. Oper. Res..

[38]  P. S. Davis,et al.  A branch‐bound algorithm for the capacitated facilities location problem , 1969 .

[39]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[40]  Simon Görtz,et al.  A branch-and-price algorithm for the capacitated facility location problem , 2007, Eur. J. Oper. Res..

[41]  Ching-Jung Ting,et al.  Combining Lagrangian heuristic and Ant Colony System to solve the Single Source Capacitated Facility Location Problem , 2008 .

[42]  Roberto Musmanno,et al.  The capacitated plant location problem with multiple facilities in the same site , 2002, Comput. Oper. Res..

[43]  J. Reese,et al.  Solution methods for the p-median problem: An annotated bibliography , 2006 .

[44]  S. Hakimi.  Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems , 1965 .

[45]  S Salhi,et al.  Lagrangean heuristics applied to a variety of large capacitated plant location problems , 1998, J. Oper. Res. Soc..

[46]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[47]  Risto Lahdelma,et al.  Decision support for centralizing cargo at a Moroccan airport hub using stochastic multicriteria acceptability analysis , 2010, Eur. J. Oper. Res..

[48]  Søren Kruse Jacobsen,et al.  Heuristics for the capacitated plant location model , 1983 .

[49]  Risto Lahdelma,et al.  Locating a waste treatment facility by using stochastic multicriteria acceptability analysis with ordinal criteria , 2002, Eur. J. Oper. Res..

[50]  J. Beasley.  An algorithm for solving large capacitated warehouse location problems , 1988 .

[51]  Arianna Alfieri,et al.  LP-based heuristics for the capacitated lot-sizing problem: The interaction of model formulation and solution algorithm , 2002 .

[52]  Hugues Delmaire,et al.  REACTIVE GRASP AND TABU SEARCH BASED HEURISTICS FOR THE SINGLE SOURCE CAPACITATED PLANT LOCATION PROBLEM , 1999 .

[53]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[54]  Charles ReVelle,et al.  Central Facilities Location , 2010 .

[55]  B. M. Khumawala,et al.  An Efficient Branch and Bound Algorithm for the Capacitated Warehouse Location Problem , 1977 .

[56]  Donald Erlenkotter,et al.  A comparative study of approaches to dynamic location problems , 1981 .

[57]  Tommi Tervonen,et al.  JSMAA: open source software for SMAA computations , 2014, Int. J. Syst. Sci..

[58]  Risto Lahdelma,et al.  SMAA - Stochastic multiobjective acceptability analysis , 1998, Eur. J. Oper. Res..