Spatial economic networks with multicriteria producers and consumers: Statics and dynamics

In this paper, we develop a framework for the formulation, analysis, and computation of solutions to spatial network problems in which the firms are multicriteria decision-makers and the consumers are as well. In particular, the firms, which are involved in the production of a homogeneous commodity, are spatially separated and weight the two criteria of profit maximization and total output maximization in distinct fashion. They are faced with the selection of modes/routes (which are modeled in an aggregated manner) to transport the commodity to the demand markets where consumers, consisting of different classes, consider the price charged by the producers and weight the transportation cost and the transportation time of the product on the links in an individual manner. We derive the governing equilibrium conditions and present the variational inequality formulation. We provide qualitative properties of the equilibrium commodity shipment and generalized price pattern and then propose a tatonnement process, which we formulate as a projected dynamical system. We give an algorithm for computational purposes and apply it to several numerical examples for illustration purposes. This paper is the first to integrate multicriteria decision-making on the production side and on the consumption side in a basic network context.