An algorithm for the supply chain networks with random demands

The supply chain network equilibrium problem with random demands (SCNE-R) was recently formulated using the variational inequality (VI) approach and solved with the modified projection method (Dong et al., 2004a; 2004b). The significance of the problem stems from the fact that retailers may not know the demands for a product with certainty but may, nevertheless, possess some information such as the density function based on historical or forecasted data. By relaxing the assumption of fixed demands at the level of retailers, real situations can be better approximated. In this paper, the SCNE-R problem is revisited by formulating a "simpler" VI model and proposing a two loop algorithm. The first loop deals with a fixed demand traffic assignment problem. The second loop computes the product price and, hence, product demands based on a prespecified probability distribution function. A numerical example is provided for demonstration and a few remarks conclude the paper.