Integral analysis method - IAM

This paper presents the theoretical foundations of the new integral analysis method (IAM), and its application to a facility location problem. This methodology integrates the cardinal and ordinal criteria of combinatorial stochastic optimization problems in four stages: definition of the problem, cardinal analysis, ordinal analysis and integration analysis. The method uses the concepts of stochastic multicriteria acceptability analysis (SMAA), Monte Carlo simulation, optimization techniques and elements of probability. The proposed method (IAM) was used to determine optimal locations for the retail stores of a Colombian coffee marketing company.

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

[2]  Graham Kendall,et al.  Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques , 2013 .

[3]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[4]  Rafael Guillermo García Cáceres,et al.  FORMAS DE CONTRATACIÓN DE LOS SERVICIOS DE URGENCIAS: UNA APROXIMACIÓN DESDE LA ECONOMÍA DE LOS COSTOS DE TRANSACCIÓN , 2005 .

[5]  B. M. Khumawala An Efficient Branch and Bound Algorithm for the Warehouse Location Problem , 1972 .

[6]  S. R. Watson,et al.  Decision Synthesis: The Principles and Practice of Decision Analysis@@@Strategic and Tactical Decisions , 1989 .

[7]  Ian N. Durbach,et al.  A simulation-based test of stochastic multicriteria acceptability analysis using achievement functions , 2006, Eur. J. Oper. Res..

[8]  B. Beamon Supply chain design and analysis:: Models and methods , 1998 .

[9]  Peter Kall,et al.  Stochastic Programming , 1995 .

[10]  S. Greco,et al.  Decision Rule Approach , 2005 .

[11]  C. B. E. Costa A multicriteria decision aid methodology to deal with conflicting situations on the weights , 1986 .

[12]  Douglas P. Woodward,et al.  A Tractable Approach to the Firm Location Decision Problem , 2003, Review of Economics and Statistics.

[13]  Marc Goetschalckx,et al.  Strategic production-distribution models: A critical review with emphasis on global supply chain models , 1997 .

[14]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[15]  Arthur M. Geoffrion,et al.  Twenty Years of Strategic Distribution System Design: An Evolutionary Perspective , 1995 .

[16]  Piet Rietveld,et al.  Ordinal data in multicriteria decision making, a stochastic dominance approach to siting nuclear power plants , 1992 .

[17]  Salvatore Greco,et al.  Rough Set Based Decision Support , 2005 .

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

[19]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[20]  M. Goetschalckx,et al.  MODELING THE EFFECT OF UNCERTAINTIES ON GLOBAL LOGISTICS SYSTEMS. , 2000 .

[21]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[22]  R. Kipp Martin,et al.  Large scale linear and integer optimization - a unified approach , 1998 .

[23]  Risto Lahdelma,et al.  Classifying Alternatives in SMAA Using Cross Confidence Factors , 2002 .

[24]  Carlos A. Bana e Costa,et al.  A methodology for sensitivity analysis in three-criteria problems: A case study in municipal management , 1988 .

[25]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[26]  Risto Lahdelma,et al.  Multivariate Gaussian criteria in SMAA , 2006, Eur. J. Oper. Res..

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

[28]  Kaisa Miettinen,et al.  Decision-aid for discrete multiple criteria decision making problems with imprecise data , 1999, Eur. J. Oper. Res..

[29]  Tommi Tervonen,et al.  Implementing stochastic multicriteria acceptability analysis , 2007, Eur. J. Oper. Res..

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

[31]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

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

[33]  Martha Patricia Caro Gutiérrez,et al.  Metodología marco de referencia para localización de instalaciones , 2004 .

[34]  Mark S. Daskin,et al.  Strategic facility location: A review , 1998, Eur. J. Oper. Res..

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

[36]  D. F. Gibson,et al.  A Quantified Model for Facility Site Selection-Application to a Multiplant Location Problem , 1972 .

[37]  Thomas L. Saaty,et al.  Marketing Applications of the Analytic Hierarchy Process , 1980 .

[38]  Gilbert A. Churchill A Paradigm for Developing Better Measures of Marketing Constructs , 1979 .

[39]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[40]  Risto Lahdelma,et al.  Classifying efficient alternatives in SMAA using cross confidence factors , 2006, Eur. J. Oper. Res..

[41]  Philippe Vincke,et al.  Multicriteria Decision-Aid , 1992 .

[42]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..