Abstract
Supply chain networks represent economic entities in tiers such as manufacturers, distributors and demand markets. To study how the market share among the commodities is determined under the assumption of profit maximization, we formulate the supply chain network equilibrium problem with logit demand functions using the variational inequality approach. A nested diagonalization method, along with the specially designed supernetwork representation, is then proposed for the solution. The test example shows that the obtained results comply with the generalized Wardrop second principle in that: the market share of the two commodities is determined according to the binary logit formula and for each origin-destination pair, the same commodity at the destination is charged with the same price no matter which transport route is used. In addition, a sensitivity analysis shows that the larger of price difference of the two commodities, the more deviation of their market share, which is consistent with our intuition.
