A Multiproduct, Multicriterion Supply-Demand Network Equilibrium Model

Abstract

We consider a multiproduct supply-demand network equilibrium model on the basis of Wardrop’s equilibrium principle. We prove that such a network equilibrium model with both a single criterion and multiple criteria are each equivalent to a vector variational inequality. For the case with multiple criteria, we derive the necessary and sufficient conditions for network equilibrium in terms of a vector variational inequality by Gerstewitz’s function when the cost function is vector valued. This result is derived based on conditions that are weaker than those for many existing results. We follow with an example to illustrate the application of the theoretical results.

Optimal decision making process of transportation service providers in maritime freight networks

“…A few papers (Dafermos and Narguney, 1987;Harker, 1988;Miller et al, 1991;Cheng and Wu, 2006) focused on the shipper problem, determining the optimal production, consumption and delivery routes. On the other hand, lots of models (Harker and Freisz, 1986a, 1986b, 1986cFriesz et al, 1986;Hurley and Peterson, 1994;Fernandez et al, 2003;Agrawal and Ziliaskopoulos, 2006;Yang et al, 2007;Xu and Holguin-Veras, 2009) captured interactions between shippers and carriers.…”

“…Xiao and Yang (2007) initially proposed sequential games among three stakeholder groups of one shipper, multiple carriers and infrastructure companies. The developed models commonly applied freight network equilibrium (Friesz et al, 1986;Harker, 1988;Guelat et al, 1990;Hurley and Petersen, 1994;Zan, 1999;Fernandez et al, 2003;Kuroda et al, 2005;Agrawal and Ziliaskopoulos, 2006;Cheng and Wu, 2006;Ziliaskopoulos, 2006;Xiao and Yang, 2007), spatial price equilibrium (Dafermos and Narguney, 1987;Xu and HolguinVeras, 2009) and integrated network equilibrium (Harker and Friesz, 1986a, 1986b, 1986c. Some interesting works have been conducted to propose the improved network analyses.…”

The system optimization perspective for multiproduct supply chain network

“…Nagurney, [6] subsequently, proved that supply chain network equilibrium problems, in which there is cooperation between tiers, but competition among decision-makers within a tier, can be reformulated and solved as transportation network equilibrium problems. Cheng and Wu [2] proposed a multiproduct, and multi criterion, supply-demand network equilibrium model. Davis and Wilson [4], in turn, studied differentiated product competition in an equilibrium framework.…”

Multi‐product supply chain horizontal network integration: models, theory, and computational results

“…Nagurney (2006b) subsequently proved that supply chain network equilibrium problems, in which there is cooperation between tiers, but competition among decision‐makers within a tier, can be reformulated and solved as transportation network equilibrium problems. Cheng and Wu (2006) proposed a multi‐product, and multi‐criterion, supply‐demand network equilibrium model. Davis and Wilson (2006), in turn, studied differentiated product competition in an equilibrium framework.…”