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A discontinuous derivative-free optimization framework for multi-enterprise supply chain

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Abstract

Supply chain simulation models are widely used for assessing supply chain performance and analyzing supply chain decisions. In combination with derivative-free optimization algorithms, simulation models have shown great potential in effective decision-making. Most of the derivative-free optimization algorithms, however, assume continuity of the response, which may not be true in some practical applications. In this work, a supply chain inventory optimization problem is addressed that results in a discontinuous objective function. A derivative-free optimization framework is proposed that addresses the discontinuities in the objective function. The framework employs a sparse grid sampling and support vector machines for identification of discontinuities. Computational comparisons presented show that addressing discontinuity leads to more cost-effective decisions over existing approaches.

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References

  1. Grossmann, I.: Enterprise-wide optimization: a new frontier in process systems engineering. AIChE J. 51, 1846–1857 (2005). https://doi.org/10.1002/aic.10617

    Article  Google Scholar 

  2. Garcia, D.J., You, F.: Supply chain design and optimization: challenges and opportunities. Comput. Chem. Eng. 81, 153–170 (2015). https://doi.org/10.1016/j.compchemeng.2015.03.015

    Article  Google Scholar 

  3. Ryu, J.H., Dua, V., Pistikopoulos, E.N.: A bilevel programming framework for enterprise-wide process networks under uncertainty. Comput. Chem. Eng. 28, 1121–1129 (2004). https://doi.org/10.1016/j.compchemeng.2003.09.021

    Article  Google Scholar 

  4. Zamarripa, M.A., Aguirre, A.M., Méndez, C.A., Espu, A.: Mathematical programming and game theory optimization-based tool for supply chain planning in cooperative/competitive environments. Chem. Eng. Res. Des. 1, 1588–1600 (2013). https://doi.org/10.1016/j.cherd.2013.06.008

    Article  Google Scholar 

  5. Yeh, K., Whittaker, C., Realff, M.J., Lee, J.H.: Two stage stochastic bilevel programming model of a pre-established timberlands supply chain with biorefinery investment interests. Comput. Chem. Eng. 73, 141–153 (2015). https://doi.org/10.1016/j.compchemeng.2014.11.005

    Article  Google Scholar 

  6. Yue, D., You, F.: Stackelberg-game-based modeling and optimization for supply chain design and operations: a mixed integer bilevel programming framework. Comput. Chem. Eng. 102, 81–95 (2017). https://doi.org/10.1016/j.compchemeng.2016.07.026

    Article  Google Scholar 

  7. Florensa, C., Garcia-Herreros, P., Misra, P., Arslan, E., Mehta, S., Grossmann, I.E.: Capacity planning with competitive decision-makers: trilevel MILP formulation, degeneracy, and solution approaches. Eur. J. Oper. Res. 262, 449–463 (2017). https://doi.org/10.1016/j.ejor.2017.04.013

    Article  MathSciNet  MATH  Google Scholar 

  8. Köchel, P., Nieländer, U.: Simulation-based optimisation of multi-echelon inventory systems. Int. J. Prod. Econ. 93–94, 505–513 (2005). https://doi.org/10.1016/j.ijpe.2004.06.046

    Article  Google Scholar 

  9. Ye, W., You, F.: A computationally efficient simulation-based optimization method with region-wise surrogate modeling for stochastic inventory management of supply chains with general network structures. Comput. Chem. Eng. 87, 164–179 (2016). https://doi.org/10.1016/j.compchemeng.2016.01.015

    Article  Google Scholar 

  10. Sahay, N., Ierapetritou, M.: Supply chain management using an optimization driven simulation approach. AIChE J. 59, 4612–4626 (2013). https://doi.org/10.1002/aic.14226

    Article  Google Scholar 

  11. Hicks, C., Hines, S.A., Harvey, D., McLeay, F.J., Christensen, K.: An agent based model of supply chains. In: Proceedings of the 12th European Simulation Multiconference on Simulation—Past, Present and Future, pp. 609–613. SCS Europe (1998)

  12. Manataki, A., Chen-Burger, Y.-H., Rovatsos, M.: Towards improving supply chain coordination through agent-based simulation. In: Demazeau, Y., Dignum, F., Corchado, J.M., Bajo, J., Corchuelo, R., Corchado, E., Fernández-Riverola, F., Julián, V.J., Pawlewski, P., Campbell, A. (eds.) Trends in Practical Applications of Agents and Multiagent Systems, pp. 217–224. Springer, Berlin (2010)

    Chapter  Google Scholar 

  13. Swaminathan, J., Smith, S.F., Sadeh, N.M.: Modeling supply chain dynamics : a multiagent approach. Decis. Sci. 29, 607–632 (1998). https://doi.org/10.1111/j.1540-5915.1998.tb01356.x

    Article  Google Scholar 

  14. Lee, J.H., Kim, C.O.: Multi-agent systems applications in manufacturing systems and supply chain management: a review paper. Int. J. Prod. Res. 46, 233–265 (2008). https://doi.org/10.1080/00207540701441921

    Article  MATH  Google Scholar 

  15. García-Flores, R., Wang, X.Z.: A multi-agent system for chemical supply chain simulation and management support. OR Spectr. 24, 343–370 (2002). https://doi.org/10.1007/s00291-002-0099-x

    Article  MathSciNet  MATH  Google Scholar 

  16. Julka, N., Srinivasan, R., Karimi, I., Srinivasan, R.: Agent-based supply chain management*/1: framework. Comput. Chem. Eng. 26, 1755–1769 (2002). https://doi.org/10.1016/S0098-1354(02)00150-3

    Article  Google Scholar 

  17. Julka, N., Karimi, I., Srinivasan, R.: Agent-based supply chain management—2: a refinery application. Comput. Chem. Eng. 26, 1771–1781 (2002). https://doi.org/10.1016/S0098-1354(02)00151-5

    Article  Google Scholar 

  18. Singh, A., Chu, Y., You, F.: Biorefinery supply chain network design under competitive feedstock markets: an agent-based simulation and optimization approach. Ind. Eng. Chem. Res. 53, 15111–15126 (2014). https://doi.org/10.1021/ie5020519

    Article  Google Scholar 

  19. Sahay, N., Ierapetritou, M.: Multienterprise supply chain: simulation and optimization. AIChE J. 62, 3392–3403 (2016). https://doi.org/10.1002/aic.15399

    Article  Google Scholar 

  20. Bhosekar, A., Ierapetritou, M.: Advances in surrogate based modeling, feasibility analysis, and optimization: a review. Comput. Chem. Eng. 108, 250–267 (2018). https://doi.org/10.1016/j.compchemeng.2017.09.017

    Article  Google Scholar 

  21. Anderson, J.M.: Modelling step discontinuous functions using Bayesian emulation (2017)

  22. Gorodetsky, A.A., Marzouk, Y.M.: Efficient Localization of Discontinuities in Complex Computational Simulations. SIAM J. Sci. Comput. 36, A2584–A2610 (2014). https://doi.org/10.1137/140953137

    Article  MathSciNet  MATH  Google Scholar 

  23. Jakeman, J.D., Archibald, R., Xiu, D.: Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids. J. Comput. Phys. 230, 3977–3997 (2011). https://doi.org/10.1016/j.jcp.2011.02.022

    Article  MathSciNet  MATH  Google Scholar 

  24. Jakeman, J.D., Narayan, A., Xiu, D.: Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions. J. Comput. Phys. 242, 790–808 (2013). https://doi.org/10.1016/j.jcp.2013.02.035

    Article  MathSciNet  MATH  Google Scholar 

  25. Archibald, R., Gelb, A., Saxena, R., Xiu, D.: Discontinuity detection in multivariate space for stochastic simulations. J. Comput. Phys. 228, 2676–2689 (2009). https://doi.org/10.1016/j.jcp.2009.01.001

    Article  MathSciNet  MATH  Google Scholar 

  26. Caiado, C.C.S., Goldstein, M.: Bayesian uncertainty analysis for complex physical systems modelled by computer simulators with applications to tipping points. Commun. Nonlinear Sci. Numer. Simul. 26, 123–136 (2015). https://doi.org/10.1016/j.cnsns.2015.02.006

    Article  MATH  Google Scholar 

  27. Moreau, L., Aeyels, D.: Optimization of discontinuous functions: a generalized theory of differentiation. SIAM J. Control Optim. 11, 53–69 (2000). https://doi.org/10.1137/S1052623499354679

    Article  MathSciNet  MATH  Google Scholar 

  28. Vicente, L.N., Custódio, A.L.: Analysis of direct searches for discontinuous functions. Math. Program. 133, 299–325 (2012). https://doi.org/10.1007/s10107-010-0429-8

    Article  MathSciNet  MATH  Google Scholar 

  29. Boursier Niutta, C., Wehrle, E.J., Duddeck, F., Belingardi, G.: Surrogate modeling in design optimization of structures with discontinuous responses. Struct. Multidiscip. Optim. 57, 1857–1869 (2018). https://doi.org/10.1007/s00158-018-1958-7

    Article  MathSciNet  Google Scholar 

  30. Sahay, N., Ierapetritou, M.: Multienterprise supply chain: simulation and optimization. AIChE J. 62, 3392–3403 (2016). https://doi.org/10.1002/aic.15399

    Article  Google Scholar 

  31. Gimpel, H., Mäkiö, J., Weinhardt, C.: Multi-attribute double auctions in financial trading. In: Proceedings of 7th IEEE International Conference on E-Commerce Technol. CEC 2005, pp. 366–369 (2005). https://doi.org/10.1109/icect.2005.61

  32. Steiglitz, K., Honig, M.L., Cohen, L.M.: A computational market model based on individual action. In: Market-based Control. pp. 1–27. World Scientific Publishing Co., Inc., River Edge, NJ, USA (1996)

    Google Scholar 

  33. Morris, M.D., Mitchell, T.J.: Exploratory designs for computational experiments. J. Stat. Plan. Inference 43, 381–402 (1995). https://doi.org/10.1016/0378-3758(94)00035-T

    Article  MATH  Google Scholar 

  34. Gerstner, T., Griebel, M.: Numerical integration using sparse grids. Numer. Algorithms 18, 209–232 (1998). https://doi.org/10.1023/A:1019129717644

    Article  MathSciNet  MATH  Google Scholar 

  35. Barthelmann, V., Novak, E., Ritter, K.: High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math. 12, 273–288 (2000). https://doi.org/10.1023/A:1018977404843

    Article  MathSciNet  MATH  Google Scholar 

  36. Kieslich, C.A., Boukouvala, F., Floudas, C.A.: Optimization of black-box problems using Smolyak grids and polynomial approximations. J. Glob. Optim. 71, 845–869 (2018). https://doi.org/10.1007/s10898-018-0643-0

    Article  MathSciNet  MATH  Google Scholar 

  37. Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, Berlin (1995)

    Book  Google Scholar 

  38. Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge University Press, New York (2000)

    Book  Google Scholar 

  39. Hastie, T., Tibshirani, R., Friedman, J.: The elements of statistical learning. Elements 1, 337–387 (2009). https://doi.org/10.1007/b94608

    Article  MATH  Google Scholar 

  40. Knerr, S., Personnaz, L., Dreyfus, G.: Single-layer learning revisited: a stepwise procedure for building and training a neural network. In: Neurocomputing. pp. 41–50. Springer, Berlin, Heidelberg (1990)

    Google Scholar 

  41. Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., Duchesnay, E.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)

    MathSciNet  MATH  Google Scholar 

  42. Le Digabel, S.: Algorithm 909: NOMAD: nonlinear optimization with the MADS algorithm. ACM Trans. Math. Softw. 37, 44:1–44:15 (2011). https://doi.org/10.1145/1916461.1916468

    Article  MathSciNet  MATH  Google Scholar 

  43. Abramson, M.A., Audet, C., Couture, G., Dennis, J.E., Digabel, S. Le: The Nomad project (2009). http://www.gerad.ca/nomad. Accessed 8 Nov 2018

  44. Currie, J., Wilson, D.I.: OPTI: Lowering the barrier between open source optimizers and the industrial MATLAB user. In: Foundations of Computer-Aided Process Operations. Savannah, Georgia, USA (2012)

    Google Scholar 

  45. Runarsson, T.P., Yao, X.: Search biases in constrained evolutionary optimization. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 35, 233–243 (2005). https://doi.org/10.1109/tsmcc.2004.841906

    Article  Google Scholar 

  46. Johnson, S.G.: The NLopt nonlinear-optimization package (2015). http://github.com/stevengj/nlopt. Accessed 8 Nov 2018

  47. Viana, F.A.C.: SURROGATES Toolbox User’s Guide, version 2.1 (2010)

  48. Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13, 455–492 (1998). https://doi.org/10.1023/A:1008306431147

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Financial support from National Science Foundation under Grant 1839007 is gratefully acknowledged. Authors thank the anonymous reviewers whose suggestions helped improve and clarify the manuscript.

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  1. Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, 08901, USA

    Atharv Bhosekar & Marianthi Ierapetritou

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  1. Atharv Bhosekar
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Correspondence to Marianthi Ierapetritou.

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Bhosekar, A., Ierapetritou, M. A discontinuous derivative-free optimization framework for multi-enterprise supply chain. Optim Lett 14, 959–988 (2020). https://doi.org/10.1007/s11590-019-01446-5

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