A discontinuous derivative-free optimization framework for multi-enterprise supply chain. (English) Zbl 1444.90118

Summary: 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 a 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.


90C56 Derivative-free methods and methods using generalized derivatives
90C90 Applications of mathematical programming
Full Text: DOI


[1] Grossmann, I., Enterprise-wide optimization: a new frontier in process systems engineering, AIChE J., 51, 1846-1857 (2005)
[2] Garcia, DJ; You, F., Supply chain design and optimization: challenges and opportunities, Comput. Chem. Eng., 81, 153-170 (2015)
[3] Ryu, JH; Dua, V.; Pistikopoulos, EN, A bilevel programming framework for enterprise-wide process networks under uncertainty, Comput. Chem. Eng., 28, 1121-1129 (2004)
[4] Zamarripa, MA; Aguirre, AM; Méndez, CA; 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)
[5] Yeh, K.; Whittaker, C.; Realff, MJ; Lee, JH, Two stage stochastic bilevel programming model of a pre-established timberlands supply chain with biorefinery investment interests, Comput. Chem. Eng., 73, 141-153 (2015)
[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)
[7] Florensa, C.; Garcia-Herreros, P.; Misra, P.; Arslan, E.; Mehta, S.; Grossmann, IE, Capacity planning with competitive decision-makers: trilevel MILP formulation, degeneracy, and solution approaches, Eur. J. Oper. Res., 262, 449-463 (2017) · Zbl 1375.90149
[8] Köchel, P.; Nieländer, U., Simulation-based optimisation of multi-echelon inventory systems, Int. J. Prod. Econ., 93-94, 505-513 (2005)
[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)
[10] Sahay, N.; Ierapetritou, M., Supply chain management using an optimization driven simulation approach, AIChE J., 59, 4612-4626 (2013)
[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.; Demazeau, Y.; Dignum, F.; Corchado, JM; Bajo, J.; Corchuelo, R.; Corchado, E.; Fernández-Riverola, F.; Julián, VJ; Pawlewski, P.; Campbell, A., Towards improving supply chain coordination through agent-based simulation, Trends in Practical Applications of Agents and Multiagent Systems, 217-224 (2010), Berlin: Springer, Berlin
[13] Swaminathan, J.; Smith, SF; Sadeh, NM, Modeling supply chain dynamics : a multiagent approach, Decis. Sci., 29, 607-632 (1998)
[14] Lee, JH; Kim, CO, Multi-agent systems applications in manufacturing systems and supply chain management: a review paper, Int. J. Prod. Res., 46, 233-265 (2008) · Zbl 1128.90406
[15] García-Flores, R.; Wang, XZ, A multi-agent system for chemical supply chain simulation and management support, OR Spectr., 24, 343-370 (2002) · Zbl 1007.90501
[16] Julka, N.; Srinivasan, R.; Karimi, I.; Srinivasan, R., Agent-based supply chain management*/1: framework, Comput. Chem. Eng., 26, 1755-1769 (2002)
[17] Julka, N.; Karimi, I.; Srinivasan, R., Agent-based supply chain management—2: a refinery application, Comput. Chem. Eng., 26, 1771-1781 (2002)
[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)
[19] Sahay, N.; Ierapetritou, M., Multienterprise supply chain: simulation and optimization, AIChE J., 62, 3392-3403 (2016)
[20] Bhosekar, A.; Ierapetritou, M., Advances in surrogate based modeling, feasibility analysis, and optimization: a review, Comput. Chem. Eng., 108, 250-267 (2018)
[21] Anderson, J.M.: Modelling step discontinuous functions using Bayesian emulation (2017)
[22] Gorodetsky, AA; Marzouk, YM, Efficient Localization of Discontinuities in Complex Computational Simulations, SIAM J. Sci. Comput., 36, A2584-A2610 (2014) · Zbl 1310.65016
[23] Jakeman, JD; Archibald, R.; Xiu, D., Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids, J. Comput. Phys., 230, 3977-3997 (2011) · Zbl 1218.65010
[24] Jakeman, JD; Narayan, A.; Xiu, D., Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions, J. Comput. Phys., 242, 790-808 (2013) · Zbl 1311.65158
[25] Archibald, R.; Gelb, A.; Saxena, R.; Xiu, D., Discontinuity detection in multivariate space for stochastic simulations, J. Comput. Phys., 228, 2676-2689 (2009) · Zbl 1161.65307
[26] Caiado, CCS; 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) · Zbl 1440.62393
[27] Moreau, L.; Aeyels, D., Optimization of discontinuous functions: a generalized theory of differentiation, SIAM J. Control Optim., 11, 53-69 (2000) · Zbl 1035.49017
[28] Vicente, LN; Custódio, AL, Analysis of direct searches for discontinuous functions, Math. Program., 133, 299-325 (2012) · Zbl 1245.90127
[29] Boursier Niutta, C.; Wehrle, EJ; Duddeck, F.; Belingardi, G., Surrogate modeling in design optimization of structures with discontinuous responses, Struct. Multidiscip. Optim., 57, 1857-1869 (2018)
[30] Sahay, N.; Ierapetritou, M., Multienterprise supply chain: simulation and optimization, AIChE J., 62, 3392-3403 (2016)
[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). 10.1109/icect.2005.61
[32] Steiglitz, K.; Honig, ML; Cohen, LM, A computational market model based on individual action, Market-based Control., 1-27 (1996), River Edge, NJ, USA: World Scientific Publishing Co., Inc., River Edge, NJ, USA
[33] Morris, MD; Mitchell, TJ, Exploratory designs for computational experiments, J. Stat. Plan. Inference, 43, 381-402 (1995) · Zbl 0813.62065
[34] Gerstner, T.; Griebel, M., Numerical integration using sparse grids, Numer. Algorithms, 18, 209-232 (1998) · Zbl 0921.65022
[35] Barthelmann, V.; Novak, E.; Ritter, K., High dimensional polynomial interpolation on sparse grids, Adv. Comput. Math., 12, 273-288 (2000) · Zbl 0944.41001
[36] Kieslich, CA; Boukouvala, F.; Floudas, CA, Optimization of black-box problems using Smolyak grids and polynomial approximations, J. Glob. Optim., 71, 845-869 (2018) · Zbl 1405.90107
[37] Vapnik, VN, The Nature of Statistical Learning Theory (1995), Berlin: Springer, Berlin
[38] Cristianini, N.; Shawe-Taylor, J., An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods (2000), New York: Cambridge University Press, New York
[39] Hastie, T.; Tibshirani, R.; Friedman, J., The elements of statistical learning, Elements, 1, 337-387 (2009)
[40] Knerr, S.; Personnaz, L.; Dreyfus, G., Single-layer learning revisited: a stepwise procedure for building and training a neural network, Neurocomputing, 41-50 (1996), Berlin, Heidelberg: Springer, Berlin, Heidelberg
[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) · Zbl 1280.68189
[42] Le Digabel, S., Algorithm 909: NOMAD: nonlinear optimization with the MADS algorithm, ACM Trans. Math. Softw., 37, 44:1-44:15 (2011) · Zbl 1365.65172
[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, DI, OPTI: Lowering the barrier between open source optimizers and the industrial MATLAB user, Foundations of Computer-Aided Process Operations (2012), Georgia, USA: Savannah, Georgia, USA
[45] Runarsson, TP; Yao, X., Search biases in constrained evolutionary optimization, IEEE Trans. Syst. Man Cybern. Part C Appl. Rev., 35, 233-243 (2005)
[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, DR; Schonlau, M.; Welch, WJ, Efficient global optimization of expensive black-box functions, J. Glob. Optim., 13, 455-492 (1998) · Zbl 0917.90270
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.