A note on supply chain network equilibrium models |
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| Institution: | 1. Department of Behavioral Sciences, Arkansas Tech University, Russellville, AR, USA;2. Department of Psychology, University of Southern Mississippi, Long Beach, MS 39560, USA;2. Department of Internal Medicine, University of Michigan, Ann Arbor, Michigan;3. Department of Translational Molecular Pathology, The University of Texas M. D. Anderson Cancer Center, Houston, Texas;4. Département de Pathologie et de Biopathologie, Centre Jean Perrin, Clermont-Ferrand, France; and EA 4766, ERTICa, Université d’Auvergne, Clermont-Ferrand, France;6. Inserm Unit 1030, DHU TORINO, Gustave Roussy and University Paris Sud, France;1. Department of Industrial Engineering, Tsinghua University, Beijing 100084, China;2. Operations Research and Logistics, Wageningen University, Hol landseweg 1, 6706KN Wageningen, The Netherlands;1. Ecole Nationale Supérieure des Mines de Saint Etienne, Henri Fayol Institute, 42100 Saint –Etienne, France;2. Centre Technique des Industries Mécaniques, 42000 Saint –Etienne, France |
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| Abstract: | This paper is concerned with the supply chain network equilibrium models proposed by Nagurney et al. Nagurney, A., Dong, J., Zhang, D., 2002. A supply chain network equilibrium model. Transportation Research 38E, 281–303] and Dong et al. Dong, J., Zhang, D., Nagurney, A., 2004. A supply chain network equilibrium model with random demands. European Journal of Operational Research 156, 194–212]. It demonstrates that these models possess the unconstrained continuously differentiable minimization formulations, whose any stationary point is the solution of the corresponding model. Accordingly, not only is the Quasi-Newton algorithm capable of finding a solution of the model, but also it can overcome the difficulty experienced by the modified projection method in choosing an appropriate predetermined step size. In addition, 11 benchmark examples are employed to show the advantage of the unconstrained minimization formulation. |
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