An Optimization Model for Supply Chain Networks with co-creation

In this paper we study a supply chain network with innovation determined by the co-creation of some users that has an impact on the global market. We consider a three-tier network where the upper level is represented by manufacturers, the middle level by retailers and the bottom one by consumers at the demand markets. In the first scenario, manufacturers produce a non co-created commodity which is sold to retailers and demand markets, and we find the optimization problem for manufacturers who wish to maximize their own profit under some constraints. In the second scenario, some consumers decide to collaborate with a manufacturer in the co-creation of the commodity and they receive a reward in exchange for their suggestions. So, manufacturers can sell the new co-created commodity to retailers and consumers and, at the same time, they can sell the old non cocreated merchandise, which is left in stock, directly to consumers via e-commerce at a discounted price. Also in this case, where the presence of co-creation has globally modified the transactions among the various decision-makers, we derive the criterion of profit maximization for the manufacturers and the associated variational inequality formulation. Some existence results for the solution of the variational inequalities is recalled together with a comparison between the total profits in the two cases. The computational procedure is applied to some numerical examples to determine the equilibrium flows and prices.