In this paper, we develop a new supply chain network model with multiple decision-makers associated at different tiers and with multiple transportation modes for shipment of the good between tiers. The model formulation captures supply side risk as well as demand-side risk, along with uncertainty in transportation and other costs. The model also incorporates the individual attitudes towards disruption risks among the manufacturers and the retailers, with the demands for the product associated with the retailers being random. We present the behavior of the various decision-makers, derive the governing equilibrium conditions, and establish the finite dimensional variational inequality formulation. We also propose a weighted supply chain performance and robustness measure based on our recently derived network performance/efficiency measure and provide supply chain examples for which the equilibrium solutions are determined along with the robustness analyzes. This paper extends previous supply chain research by capturing supply-side disruption risks, transportation and other cost risks, and demand-side uncertainty within an integrated modeling and robustness analysis framework.