Dynamic Supernetworks for the Integration of Social Networks and Supply Chains with Electronic Commerce: Modeling and Analysis of Buyer-Seller Relationships with Computations

In this paper, we develop a dynamic supernetwork framework for the modeling and analysis of supply chains with electronic commerce that also includes the role that relationships play. Manufacturers are assumed to produce a homogeneous product and to sell it either through physical or electronic links to retailers and/or directly to consumers through electronic links. Retailers, in turn, can sell the product through physical links to consumers. Increasing relationship levels in our framework are assumed to reduce transaction costs as well as risk and to have some additional value for both sellers and buyers. Establishing those relationship levels incurs some costs that have to be borne by the decision-makers in the supernetwork, which is multilevel in structure and consists of the supply chain and the social network. The decision-makers, who are located at distinct tiers in the supernetwork, try to optimize their objective functions and are faced with multiple criteria including relationshiprelated ones and weight them according to their preferences. We establish the optimality conditions for the manufacturers, retailers, and consumers, derive the equilibrium conditions, and provide the variational inequality formulation. We then present the projected dynamical system, which describes the disequilibrium dynamics of the product transactions, relationship levels, and prices on the supernetwork, and whose set of stationary points coincides with the set of solutions of the variational inequality problem. We also illustrate the dynamic supernetwork model through several numerical examples, for which the explicit equilibrium patterns are computed.