In this article we analyze the interactions among the assembler and two component suppliers in their procurement decisions under a Vendor-Managed Inventory (VMI) contract. Under the VMI contract, the assembler first offers a unit price for each component and will pay component suppliers only for the amounts used to meet the actual demand. The two independent component suppliers then decide on the production quantities of their individual components before the actual demand is realized. We assume that one of the component suppliers has uncertainty in the supply process, in which the actual number of components available for assembly is equal to a random fraction of the production quantity. Under the assembly structure, both component suppliers need to take into account the underlying supply uncertainty in deciding their individual production quantities, as both components are required for the assembly of the final product. We first analyze the special case under deterministic demand and then extend our analysis to the general case under stochastic demand. We derive the optimal component prices offered by the assembler and the corresponding equilibrium production quantities of the component suppliers.