Decision maker's preferences modeling for multiple objective stochastic linear programming problems

• Autorzy: Bellahcene Fatima

Identyfikatory

DOI

10.5277/ord190301

• Języki publikacji: EN

Abstrakty

EN

A method has been suggested which solves a multiobjective stochastic linear programming problem with normal multivariate distributions in accordance with the minimum-risk criterion. The approach to the problem uses the concept of satisfaction functions for the explicit integration of the preferences of the decision-maker for different achievement level of each objective. Thereafter, a nonlinear deterministic equivalent problem is formulated and solved by the bisection method. Numerical examples with two and three objectives are given for illustration. The solutions obtained by this method are compared with the solutions given by other approaches.

Słowa kluczowe

EN

multiobjective programming; stochastic programming; nonlinear programming; satisfaction function

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2019
• Tom: Vol. 29, No. 3
• Strony: 5--16
• Opis fizyczny: Bibliogr. 36 poz., rys.

Twórcy

autor

Bellahcene Fatima

• LAROMAD Laboratory, Faculty of Sciences, Mouloud Mammeri University, BP 17 RP, 15000 Tizi-Ouzou, Algeria

Bibliografia

• [1] ABBAS M., BELLAHCENE F., Cutting plane method for multiple objective stochastic integer linear programming, Eur. J. Oper. Res., 2006, 168, 967–984.
• [2] ADEYEFA A., LUHANDJULA M., Multiobjective stochastic linear programming: an overview, Amer. J. Oper. Res., 2011, 1 (4), 203–213.
• [3] AMROUCHE S., MOULAÏ M., Multi-objective stochastic integer linear programming with fixed recourse, Int. J. Multicr. Dec. Making, 2012, 2 (4), 355–378.
• [4] AOUNI B., COLAPINTO C., LA TORRE D., Solving stochastic multi-attribute portfolio selection through the goal programming model, J. Fin. Dec. Making, 2010, 6 (2), 17–30.
• [5] BAZARAA M., SHERALI H., SHETTY C., Theory and Algorithms, 2nd Ed., Wiley, New York 1993.
• [6] BELLAHCENE F., MARTHON P., A compromise solution method for the multiobjective minimum risk problem, Oper. Res., May 2019, DOI 10.1007/ s12351-019-00493-1.
• [7] BEN ABDELAZIZ F., L’efficacité en programmation multi-objectifs stochastique, Ph.D. Thesis, Université de Laval, Québec 1992.
• [8] BEN ABDELAZIZ F., LAND P., NADEAU R., Distributional unanimity multiobjective stochastic linear programming, [In:] J. Climaco (Ed.), Multicriteria Analysis, Proc. 11th Int. Conf. MCDM, Springer-Verlag, Berlin 1997, 225–236.
• [9] BEN ABDELAZIZ F., LANG P., NADEAU R., Dominance and efficiency in multicriteria decision under uncertainty, Theory Dec., 1999, 47 (3), 191–211.
• [10] BEN ABDELAZIZ F., MEJRI S., Application of goal programming in a multi-objective reservoir operation model in Tunisia, Eur. J. Oper. Res., 2001, 133, 352–361.
• [11] BEN ABDELAZIZ F., AOUNI B., EL FAYEDH R., Multi-objective stochastic programming for portfolio selection, Eur. J. Oper. Res., 2007, 177 (3), 1811–1823.
• [12] BOSWARVA I., AOUNI B., Different probability distributions for portfolio selection in the chance constrained compromise programming model, Inf. Syst. Oper. Res. J., 2012, 50 (3), 140–146.
• [13] BRAVO M., GONZALEZ I., Applying stochastic goal programming. A case study on water use planning, Eur. J. Oper. Res., 2009, 196 (39), 1123–1129.
• [14] CABALLERO R., CERDA E., MUÑOZ M.M., REY L., Relations among several efficiency concepts in stochastic multiple objective programming, [In:] Y.Y. Haimes, R. Steuer (Eds.), Research and Practice in Multiple Criteria Decision Making, Lecture Notes in Economics and Mathematical Systems, 487, Springer-Verlag/Kluwer, 2000, 57, 58.
• [15] CABALLERO R., CERDA E., DEL MAR M., REY L., Efficient solution concepts and their relations in stochastic multiobjective programming, J. Opt. Theory Appl., 2001, 110 (1), 53–74.
• [16] CABALLERO R., CERDA E., MUÑOZ M.M., REY L., Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems, Eur. J. Oper. Res., 2004, 158, 633–638.
• [17] CHAABANE D., MEBREK F., Optimization of a linear function over the set of stochastic efficient solutions, Comp. Manage. Sci., 2014, 11 (1), 157–178.
• [18] FAZLOLLAHTABAR H., MAHDAVI I., Applying stochastic programming for optimizing production time and cost in an automated manufacturing system, Int. Conf. Computers and Industrial Engineering, Troyes 2009, 1226–1230.
• [19] GOICOECHEA A., DUKSTEIN L., BULFIN R.L., Multiobjective stochastic programming, the PROTRADE method, Oper. Res. Soc. Amer., Miami Beach 1976.
• [20] KLEIN G., MOSKOWITZ H., RAVINDRAN A., Interactive multiobjective optimization under uncertainty, Manage. Sci., 1990, 36 (1), 58–75.
• [21] KUMRAL M., Application of chance-constrained programming based on multiobjective simulated annealing to solve mineral blending problem, Eng. Opt., 2003, 35 (6), 661–673.
• [22] LUQUE M., RUIZ F., CABELLO J.M., A synchronous reference point-based interactive method for stochastic multiobjective programming, OR Spectrum, 2012, 34, 763–784.
• [23] MARTEL J.M., AOUNI B., Incorporating the decision-makers preferences in the goal-programming model, Journal of the Operational Research Society, 1990, 41 (12), 1121–1132.
• [24] MIETTINEN K.M., Nonlinear Multiobjective Optimization, Kluwer’s International Series, 1999.
• [25] MUÑOZ M.M., RUIZ F., ISTMO, an interval reference point-based method for stochastic multiobjective programming problems, Eur. J. Oper. Res., 2009, 197, 25–35.
• [26] OGRYCZAK W., Multiple criteria linear programming model for portfolio selection, Ann. Oper. Res., 2000, 97, 143–162.
• [27] SHING C., NAGASAWA H., Interactive decision system in stochastic multi-objective portfolio selection, Int. J. Prod. Econ., 1999, 60, 187–193.
• [28] SLOWINSKI R., TEGHEM T., Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, Kluwer, Boston 1990.
• [29] STANCU-MINASIAN I.M., On the problem of multiple minimum risk. I. The case of two objective functions, II. The case of r (r > 2) objective functions, Stud. Cerc. Mat., 1976, 28 (5), 617–623, ibidem 28 (6), 723–734 (in Romanian).
• [30] STANCU-MINASIAN I.M., TIGAN S., The vectorial minimum risk problem, Proc. Coll. Approximation and Optimization, Cluj-Napoca, 1984, 321–328.
• [31] TEGHEM J., KUNSCH P., Application of multiobjective stochastic linear programming to power systems planning, Eng. Costs Prod. Econ., 1985, 9 (13), 83–89.
• [32] TEGHEM J., DUFRANE D., THAUVOYE M., KUNSCH P.L., STRANGE, an interactive method for multiobjective stochastic linear programming under uncertainty, Eur. J. Oper. Res., 1986, 26 (1), 65–82.
• [33] TEGHEM J., STRANGE-MOMIX. An interactive method for mixed integer linear programming, [In:] R. Slowinski, J. Teghem (Eds.), Stochastic Versus Fuzzy Apprroaches to Multiobjective Mathematical Programming Under Uncertainty, Kluwer, Dordrecht 1990, 101–115.
• [34] URLI B., NADEAU R., PROMISE/scenarios: An interactive method for multiobjective stochastic linear programming under partial uncertainty, Eur. J. Oper. Res., 2004, 155, 361–372.
• [35] VAHIDINASAB V., JADID S., Stochastic multiobjective self-scheduling of a power producer in joint Energy and reserves markets, Elect. Power Syst. Res., 2010, 80 (7), 760–769.
• [36] WANG Z., JIA X.P., SHI L., Optimization of multi-product batch plant design under uncertainty with environmental considerations, Clean Techn. Environ. Pol., 2009, 12 (3), 273–282.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).