Abstract
Production system optimization still remains a difficult problem even if fast analytical methods are used to estimate their mean performance measures. This paper addresses optimization problems in which the system performance measures are obtained from analytical methods implemented in computer codes that are usually time expensive. A global search algorithm is proposed to solve the addressed optimization problem. A Kriging metamodel is built to approximate the system performance function on the basis of the deterministic output values provided by the analytical model. Then a standard optimization method is applied on the explicit metamodel expression. The main advantages of the proposed method are its generality and ease of use. Indeed, the algorithm can be applied to optimize any production system assessable by an analytical method. Also, the Kriging technique allows contemporarily building the approximation of the unknown function and assessing its quality. Numerical results are satisfactory and prove the applicability of the method to real problems.
Similar content being viewed by others
References
Alexandrov N. M., Dennis J. E. J., Lewis R. M., Torczon V. (1998) A trust-region framework for managing the use of approximation models in optimization. Structural and Multidisciplinary Optimization 15(1): 16–23
Balsamo S. (1993) Properties and analysis of queueing network models with finite capacities. Lecture Notes in Computer Science 729: 21–52
Buzacott J. A., Shantikumar J. G. (1993) Stochastic models of manufacturing systems. Prentice Hall, Englewood Cliffs, NJ
Dallery Y., Gershwin S. B. (1992) Manufacturing flow line systems: A review of models and analytical results. Queueing Systems Theory and Applications, Special Issue on Queueing Models of Manufacturing Systems 12(1–2): 3–94
Den Hertog D., Kleijnen J. P. C., Siem A. Y. D. (2006) The correct kriging variance estimated by bootstrapping. Journal of the Operational Research Society 57(4): 400–409
Di Mascolo M., Frein Y., Dallery Y. (1996) An analytical method for performance evaluation of kanban controlled production systems. Operations Research 44(1): 50–64
Duri C., Frein Y., Di Mascolo M. (2000) Comparison among three pull control policies: Kanban, base stock, and generalized kanban. Annals of Operations Research 44: 41–69
Fang, K.-T., Li, R., & Sudjianto, A. (2006). Design and modeling for computer experiments. Computer Science and Data Analysis Series.
Gershwin S. B. (1987) An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking. Operations Research 35(2): 291–305
Gershwin S. B. (1994) Manufacturing systems engineering. Prentice Hall, Englewood Cliffs, NJ
Gershwin S. B., Schor J. E. (2000) Efficient algorithms for buffer space allocation. Annals of Operational Research 93(1–4): 117–144
Gill P. E., Murray W., Wright M. H. (2007) Practical optimization. Emerald, England
Jin R., Chen W., Simpson T. W. (2001) Comparative studies of metamodeling techniques under multiple modeling criteria. Structure of Multidisciplinary Optimization 23(1): 1–13
Jones D. R. (2001) A taxonomy of global optimization methods based on response surfaces. Journal of Global Optimization 21(4): 345–383
Jones D. R., Schonlau M., Welch W. J. (1998) Efficient global optimization of expensive black box functions. Journal of Global Optimization 13(4): 455–492
Kleijnen J. P. C. (2008) Design and analysis of simulation experiments, volume 111 of International Series in Operations Research & Management science. Springer, New York
Koehler, J. R., & Owen, A. B. (1996). Computer experiments. In Handbook of statistics (Vol. 13, pp. 261–308). New York: Elsevier.
Levantesi R., Matta A., Tolio T. (2003) Performance evaluation of continuous production lines with machines having different processing times and multiple failure modes. Performance Evaluation 51(2–4): 247–268
Locatelli M. (1997) Bayesian algorithms for one-dimensional global optimization. Journal of Global Optimization 10(1): 57–76
Lophaven, S. N., Nielsen, H. B., & Søndergaard, J. (2002). DACE, a matlab kriging toolbox. Technical report, Informatics and Mathematical Modelling, Technical University of Denmark, DTU.
Martin J. D., Simpson T. W. (2005) Use of kriging models to approximate deterministic computer models. AIAA Journal 43(4): 853–863
Matheron G. (1963) Principles of geostatistics. Economic Geology 58(8): 1246–1266
Mckay M. D., Beckman R. J., Conover W. J. (2000) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1): 55–61
Myers R. H., Montgomery D. C. (1995) Response surface methodology: Process and product in optimization using designed experiments (1st ed.). Wiley, New York, USA
Nocedal J., Wright S. J. (1999) Numerical optimization. In: Glynn P., Robinson S. M. (eds) Springer series in operations research. Springer, New York, USA
Papadopoulos C. T., O’Kelly M. E. J., Vidalis M. J., Spinellis D. (2009) Analysis and design of discrete part production lines. Springer, New York
Park J. S. (1994) Optimal latin-hypercube designs for computer experiments. Journal of Statistical Planing Inference 39: 95–111
Sacks J., Welch W. J., Mitchell T. J., Wynn H. P. (1989) Design and analysis of computer experiments. Statistical Science 4(4): 409–423
Santner T. J., Williams B. J., Notz W. I. (2003) The design and analysis of computer experiments. Springer Series in Statistics, New York
Schonlau M., Welch W. J., Jones D. R. (1998) Global versus local search in constrained optimization of computer models. In: Flournoy N., Rosenberger W. F., Wong W. K. (eds) New development and applications in experimental design. Institute of Mathematical Statistics, Hayward, CA, pp 11–25
Spinellis D. D., Papadopoulos C. T. (2000) A simulated annealing approach for buffer allocation in reliable production lines. Annals of Operations Research 93(1–4): 373–384
Tempelmeier H., Kuhn H. (1993) Flexible manufacturing systems—decision support for design and operation. Wiley, New York
Tolio T., Matta A., Gershwin S. B. (2002) Analysis of two-machine lines with multiple failure modes. IIE Transactions 34(1): 51–62
Vazquez, E., & Bect, J. (2007). On the convergence of the expected improvement algorithm. eprint arXiv:0712.3744.
Wang G. G. (2003) Adaptive response surface method using inherited latin hypercube design points. Transactions of ASME, Journal of Mechanical Design 125: 210–220
Wang, G. G., & Simpson, T. W. (2002). Fuzzy clustering based hierarchical metamodeling for design optimization. In 9th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta, Georgia.
Wang L., Shan S., Wang G. G. (2004) Mode-pursuing sampling method for global optimization on expensive black-box functions. Engineering Optimization 36(4): 419–438
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Matta, A., Pezzoni, M. & Semeraro, Q. A Kriging-based algorithm to optimize production systems approximated by analytical models. J Intell Manuf 23, 587–597 (2012). https://doi.org/10.1007/s10845-010-0397-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10845-010-0397-0