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Increasing the efficiency in integer simulation optimization: reducing the search space through data envelopment analysis and orthogonal arrays. (English) Zbl 1375.90336
Summary: The development of various heuristics has enabled optimization in simulation environments. Nevertheless, this research area remains underexplored, primarily with respect to the time required for convergence of these heuristics. In this sense, simulation optimization is influenced by the complexity of the simulation model, the number of variables, and by their ranges of variation. Within this context, this paper proposes a method capable of identifying the best ranges for each integer decision variable within the simulation optimization problem, thereby providing a reduction in computational cost without loss of the quality in the response. The proposed method combines experimental design techniques, discrete event simulation, and data envelopment analysis. The experimental designs called orthogonal arrays are used to generate the input scenarios to be simulated, and super-efficiency analysis is applied in a data envelopment analysis model with variable returns to scale to rank the input scenarios. The use of the super-efficiency concept enables to distinguish the most efficient input scenarios, which allows for the ranking of all the orthogonal array scenarios used. The values of the variables of the two input scenarios that present the highest values of super-efficiency are adopted as the new range of the optimization problem. To illustrate this method’s use and advantages, it was applied to real cases associated with integer simulation optimization problems. Based on the results, the effectiveness of this approach is verified because it delivered considerable reductions in the search space and in the computational time required to obtain a solution without affecting the quality.
MSC:
90C90 Applications of mathematical programming
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90C59 Approximation methods and heuristics in mathematical programming
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[1] Ahuja, R. K.; Magnanti, T. L.; Orlin, J. B., Network flows, (1993), Prentice Hall New Jersey · Zbl 1201.90001
[2] Alrabghi, A.; Tiwari, A., State of the art in simulation-based optimisation for maintenance systems, Computers & Industrial Engineering, 82, 167-182, (2015)
[3] Andersen, P.; Petersen, N. C., A procedure for ranking efficient units in data envelopment analysis, Management Science, 39, 1261-1264, (1993) · Zbl 0800.90096
[4] Antony, J., Taguchi or classical design of experiments: A perspective from a practitioner, Sensor Review, 26, 227-230, (2006)
[5] Azadeh, A.; Moghaddam, M.; Asadzadeh, S. M.; Negahban, A., An integrated fuzzy simulation-fuzzy data envelopment analysis algorithm for job-shop layout optimization: the case of injection process with ambiguous data, European Journal of Operational Research, 214, 768-779, (2011) · Zbl 1219.90055
[6] Bachelet, B.; Yon, L., Model enhancement: improving theoretical optimization with simulation, Simulation Modelling Practice and Theory, 15, 703-715, (2007)
[7] Bal, H.; Örkcü, H.; Çelebioglu, S., Improving the discrimination power and weights dispersion in the data envelopment analysis, Computers & Industrial Engineering, 37, 99-107, (2010) · Zbl 1171.90418
[8] Ballantyne, K. N.; Van Oorschot, R. A.; Mitchell, R. J., Reduce optimization time and effort: Taguchi experimental design methods, Forensic Science International: Genetics, 1, 7-8, (2008)
[9] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30, 1078-1092, (1984) · Zbl 0552.90055
[10] Banker, R. D.; Charnes, A.; Cooper, W. W.; Swarts, J.; Thomas, D. A., An introduction to data envelopment analysis with some of its models and their uses, Research in Governmental and Nonprofit Accounting, 5, 125-163, (1989)
[11] Banks, J.; Carson II, J. S.; Nelson, B. L.; Nicol, D. M., Discrete-event system simulation, (2009), Pearson Upper Saddle River
[12] Besseris, G. J., Profiling effects in industrial data mining by non-parametric DOE methods: an application on screening check weighing systems in packaging operations, European Journal of Operational Research, 220, 147-161, (2012) · Zbl 1253.90226
[13] Better, M.; Glover, F.; Kochenberger, G., Simulation optimization: improving decisions under uncertainty, (L. A., Cox, Breakthroughs in decision science and risk analysis, (2015), John Wiley & Sons New Jersey), 59-82
[14] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429-444, (1978) · Zbl 0416.90080
[15] Cook, W. D.; Seiford, L. M., Data envelopment analysis (DEA) - thirty years on, European Journal of Operational Research, 192, 1-17, (2009) · Zbl 1180.90151
[16] Cooper, W. W.; Sieford, L. M.; Tone, K., Data envelopment analysis: A comprehensive text with models, application, references and DEA-solver software, (2007), Springer Science+Business Media New York · Zbl 1111.90001
[17] Dellino, G.; Kleijnen, J. P.C.; Meloni, C., Robust optimization in simulation: Taguchi and response surface methodology, International Journal of Production Economics, 125, 52-59, (2010)
[18] Figueira, G.; Almada-Lobo, B., Hybrid simulation-optimization methods: a taxonomy and discussion, Simulation Modelling Practice and Theory, 46, 118-134, (2014)
[19] Fu, M. C., Optimization via simulation: a review, Annals of Operations Research, 53, 199-247, (1994) · Zbl 0833.90089
[20] Fu, M. C., Optimization for simulation: theory vs. practice, Journal on Computing, 14, 192-215, (2002) · Zbl 1238.90001
[21] Fu, M. C., Handbook of simulation optimization, (2015), Springer New York · Zbl 1303.90004
[22] Fu, M. C.; Andradóttir, S.; Carson, J. S.; Glover, F.; Harrel, C. R.; Ho, Y. C.; Kelly, J. P.; Robinson, S. M., Integrating optimization and simulation: research and practice, (Joines, J. A.; Barton, R. R.; Kang, K.; Fishwick, P. A., Proceedings of the 2000 Winter Simulation Conference, (2000)), 610-616
[23] Fu, M. C.; Bayraksan, G.; Henderson, S. G.; Nelson, B. L.; Powell, W. B.; Ryzhov, I. O.; Thengvall, B., Simulation optimization: a panel on the state of the art in research and practice, (Tolk, A.; Diallo, S. Y.; Ryzhov, I. O.; Yilmaz, L.; Buckley, S.; Miller, J. A., Proceedings of the 2014 Winter Simulation Conference, (2014)), 3696-3706
[24] GAMS. The General Algebraic Modeling. (2015). http://www.gams.com/ Accessed 11.11.15.
[25] Ghasemi, M. R.; Ignatius, J.; Emrouznejad, A., A bi-objective weighted model for improving the discrimination power in MCDEA, European Journal of Operational Research, 233, 3, 640-650, (2014) · Zbl 1339.90297
[26] Harrel, C. R.; Ghosh, B. K.; Bowden, R., Simulation using promodel, (2004), McGraw-Hill New York
[27] Hillier, F. S.; Lieberman, G. J., Introduction to operations research, (2010), McGraw-Hill New York · Zbl 0155.28202
[28] Jahangirian, M.; Eldabi, T.; Naseer, A.; Stergioulas, L. K.; Young, T., Simulation in manufacturing and business: a review, European Journal of Operational Research, 203, 1-13, (2010)
[29] Kleijnen, J. P.C., Experimental design for sensitivity analysis, optimization, and validation of simulation models, (Banks, J., Handbook of simulation, (1998), Wiley New-York), 173-223
[30] Kleijnen, J. P.C., Regression and Kriging metamodels with their experimental designs in simulation: a review, European Journal of Operational Research, 256, 1-16, (2017) · Zbl 1394.90004
[31] Kleijnen, J. P.C., Design and analysis of simulation experiments, (2015), Springer New York · Zbl 1321.62006
[32] Kleijnen, J. P.C.; Van Beers, W.; Van Nieuwenhuyse, I., Constrained optimization in simulation: a novel approach, European Journal of Operational Research, 202, 164-174, (2010) · Zbl 1189.90156
[33] Law, A. M., Simulation modeling and analysis, (2015), McGraw-Hill Boston
[34] Law, A. M.; McComas, M. G., Simulation-based optimization, (Farrington, P. A.; Nembhard, H. B.; Sturrock, D. T.; Evans, G. W., Proceedings of the 1999 Winter Simulation Conference, (2002)), 56-59
[35] Lee, L. H.; Chew, E. P.; Teng, S.; Chen, Y., Multi-objective simulation-based evolutionary algorithm for an aircraft spare parts allocation problem, European Journal of Operational Research, 189, 476-491, (2008) · Zbl 1149.90355
[36] Lin, R. C.; Sir, M. Y.; Pasupathy, K. S., Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: specific application to determining optimal resource levels in surgical services, Omega - The International Journal of Management Science, 41, 881-892, (2013)
[37] Martins, M. S.R.; Fuchs, S. C.; Pando, L. U.; Lüders, R.; Delgado, M. R., PSO with path relinking for resource allocation using simulation optimization, Computers & Industrial Engineering, 65, 322-330, (2013)
[38] Miranda, R. C.; Montevechi, J. A.B.; Silva, A. F.; Marins, F. A.S., A new approach to reducing search space and increasing efficiency in simulation optimization problems via the fuzzy-DEA-BCC, Mathematical Problems in Engineering, 2014, 1-15, (2014) · Zbl 1407.90382
[39] Montevechi, J. A.B.; Miranda, R. C.; Friend, J. D., Sensitivity analysis in discrete event simulation using design of experiments, (Lim, E. W.C., Discrete event simulations - development and applications, (2012), Rijeka), 63-102, InTech
[40] Montgomery, D. C., Design and analysis of experiments, (2009), Wiley Hoboken
[41] Nelson, B. L., Optimization via simulation over discrete decision variables, (Hasenbein, J. J., Tutorials in operations research: Risk and optimization in an uncertain world, (2010), INFORMS Hanover), 193-207
[42] Pasupathy, R.; Ghosh, S., Simulation optimization: a concise overview and implementation guide, (Topaloglu, H., Tutorials in operations research: Theory driven by influential applications, (2014), Informs Catonsville), 122-150
[43] ProModel. ProModel Corporation. (2016). https://www.promodel.com/ Accessed 12.12.16.
[44] Ross, P. J., Taguchi techniques for quality engineering, 329, (1996), McGraw-Hill New York
[45] Roy, R. K., A primer on the Taguchi method, (2010), Society of Manufacturing Engineers Dearborn
[46] Shen, H.; Wan, H., Controlled sequential factorial design for simulation factor screening, European Journal of Operational Research, 198, 511-519, (2009) · Zbl 1163.90637
[47] Siegmund, F.; Bernedixen, J.; Pehrsson, L.; Ng, A. H.C.; Deb, K., Reference point-based evolutionary multi-objective optimization for industrial systems simulation, (Laroque, C.; Himmelspach, J.; Pasupathy, R.; Rose, O.; Uhrmacher, A. M., Proceedings of the 2012 Winter Simulation Conference, (2012)), 1-11
[48] Simrunner User Guide. (2002). ProModel Corporation. Orem: ProModel.
[49] Swisher, J. R.; Hyden, P. D.; Jacobson, S. H.; Schruben, L. W., A survey of simulation optimization techniques and procedures, (Joines, J. A.; Barton, R. R.; Kang, K.; Fishwick, P. A., Proceedings of the 2000 Winter Simulation Conference, (2000)), 119-128
[50] Taguchi, G., System of experimental design: engineering methods to optimize quality and minimize costs, (1987), UNIPUB/Kraus International Publications Dearborn
[51] Taguchi, G.; Chowdhury, S.; Wu, Y., Taguchi’s quality engineering handbook, (2005), John Wiley & Sons, Inc New Jersey · Zbl 1121.62115
[52] Tamiz, M.; Jones, D. F.; El-Darzi, E., A review of goal programming and its applications, Annals of Operations Research, 58, 1, 39-53, (1995) · Zbl 0836.90106
[53] Tenne, Y.; Goh, C-K., Computational intelligence in expensive optimization problems, (2010), Springer Berlin · Zbl 1187.90020
[54] Willis, K. O.; Jones, D. F., Multi-objective simulation optimization through search heuristics and relational database analysis, Decision Support Systems, 46, 277-286, (2008)
[55] Xu, J.; Huang, E.; Chen, C-H.; Lee, L. H., Simulation optimization: A review and exploration in the new era of cloud computing and big data, Asia-Pacific Journal of Operational Research, 32, 3, 1-34, (2015) · Zbl 1318.68186
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