A supply chain network equilibrium model with a smoothing newton solution scheme

ABSTRACT Considering that a supply chain comprises several independent decision makers, a supply chain network equilibrium model that consists of manufacturers, retailers and consumers is developed. After analysing the optimal conditions of various decision makers in the model, the equilibrium condition is established as an equivalent, finite-dimensional variational inequality formulation and is solved by a smoothing Newton method. The global and quadratic convergence of the method is established. The numerical results show the rapid convergence of the method. Additionally, the rapid convergence of the smoothing Newton method is beneficial when solving a complicated network model in the real world.

[1]  Elise Miller-Hooks,et al.  Equilibrium network design of shared-vehicle systems , 2014, Eur. J. Oper. Res..

[2]  Yang Hai.  Sensitivity analysis for queuing equilibrium network flow and its application to traffic control , 1995 .

[3]  Anna Nagurney.  Economic equilibrium and financial networks , 1999 .

[4]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[5]  Francisco Facchinei,et al.  A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm , 1997, SIAM J. Optim..

[6]  A. Nagurney,et al.  A supply chain network equilibrium model , 2002 .

[7]  Xiaojun Chen,et al.  A Global and Local Superlinear Continuation-Smoothing Method for P0 and R0 NCP or Monotone NCP , 1999, SIAM J. Optim..

[8]  Qian Yu,et al.  Solving the logit-based stochastic user equilibrium problem with elastic demand based on the extended traffic network model , 2014, Eur. J. Oper. Res..

[9]  F. J. García-Rodríguez,et al.  Implementation of reverse logistics as a sustainable tool for raw material purchasing in developing countries: The case of Venezuela , 2013 .

[10]  Hai Yang,et al.  The multi-class, multi-criteria traffic network equilibrium and systems optimum problem , 2004 .

[11]  A. Goldstein.  Convex programming in Hilbert space , 1964 .

[12]  Anna Nagurney,et al.  Reverse supply chain management and electronic waste recycling: a multitiered network equilibrium framework for e-cycling , 2005 .

[13]  Liqun Qi,et al.  A nonsmooth version of Newton's method , 1993, Math. Program..

[14]  Lei Rao,et al.  A simultaneous route and departure time choice equilibrium model on dynamic networks , 1999 .

[15]  A Min Tjoa,et al.  Information technology for sustainable supply chain management: a literature survey , 2017, Enterp. Inf. Syst..

[16]  Patrick T. Harker,et al.  Smooth Approximations to Nonlinear Complementarity Problems , 1997, SIAM J. Optim..

[17]  Boris Polyak,et al.  Constrained minimization methods , 1966 .

[18]  Helmut Kleinmichel,et al.  A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems , 1998, Comput. Optim. Appl..

[19]  Hai Yang,et al.  DEMAND-SUPPLY EQUILIBRIUM OF TAXI SERVICES IN A NETWORK UNDER COMPETITION AND REGULATION , 2002 .

[20]  Anna Nagurney,et al.  A supply chain network equilibrium model with random demands , 2004, Eur. J. Oper. Res..

[21]  Yafeng Yin,et al.  Network equilibrium models with battery electric vehicles , 2014 .

[22]  Ángel Marín,et al.  Network equilibrium with combined modes: models and solution algorithms , 2005 .

[23]  Olvi L. Mangasarian,et al.  A class of smoothing functions for nonlinear and mixed complementarity problems , 1996, Comput. Optim. Appl..

[24]  Michael G.H. Bell,et al.  Genetic algorithm solution for the stochastic equilibrium transportation networks under congestion , 2005 .

[25]  Xiaojun Chen,et al.  Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities , 1998, Math. Comput..

[26]  Michael C. Ferris,et al.  Engineering and Economic Applications of Complementarity Problems , 1997, SIAM Rev..

[27]  C. SIAMJ..  A NEW NONSMOOTH EQUATIONS APPROACH TO NONLINEAR COMPLEMENTARITY PROBLEMS∗ , 1997 .

[28]  Lourdes Zubieta,et al.  A network equilibrium model for oligopolistic competition in city bus services 1 1 This work was par , 1998 .

[29]  Defeng Sun,et al.  A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities , 2000, Math. Program..

[30]  Christian Kanzow,et al.  Jacobian Smoothing Methods for Nonlinear Complementarity Problems , 1999, SIAM J. Optim..

[31]  A. Nagurney,et al.  Supply Chain Networks and Electronic Commerce: A Theoretical Perspective , 2002 .

[32]  Yuan Zhou,et al.  A new approach to supply chain network equilibrium models , 2012, Comput. Ind. Eng..

[33]  Mike Smith,et al.  A new dynamic traffic model and the existence and calculation of dynamic user equilibria on congested capacity-constrained road networks , 1993 .

[34]  Steven H. Low,et al.  Equilibrium Allocation and Pricing of Variable Resources Among User-Suppliers , 1998, Perform. Evaluation.

[35]  Uday S. Karmarkar,et al.  Competition and Structure in Serial Supply Chains with Deterministic Demand , 2001, Manag. Sci..

[36]  Xiaojun ChenyMay.  A Global and Local Superlinear Continuation-Smoothing Method for P0 +R0 and Monotone NCP , 1997 .

[37]  Piet A Slats,et al.  Logistic chain modelling , 1995 .

[38]  James V. Burke,et al.  The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems , 1998, Math. Oper. Res..

[39]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .

[40]  Christian Kanzow,et al.  Some Noninterior Continuation Methods for Linear Complementarity Problems , 1996, SIAM J. Matrix Anal. Appl..

[41]  Antonino Maugeri,et al.  Variational inequalities and discrete and continuum models of network equilibrium problems , 2002 .

[42]  Qiang Meng,et al.  A note on supply chain network equilibrium models , 2007 .

[43]  Bingsheng He,et al.  A projection and contraction method for a class of linear complementarity problems and its application in convex quadratic programming , 1992 .

[44]  Phillip J. Lederer,et al.  Pricing, Production, Scheduling, and Delivery-Time Competition , 1997, Oper. Res..

[45]  Phillip J. Lederer.  A Competitive Network Design Problem with Pricing , 1993, Transp. Sci..