Optimal Product Pricing and Component Production Quantities for an Assembly System Under Supply Uncertainty

We consider an assemble-to-order system where one of the components faces uncertainty in the supply process in which the actual available quantity is equal to some random fraction of the production quantity. Demand is assumed to be price-dependent. We analyze how the supply uncertainty of one component affects the product pricing and production quantities of all the components under the assembly structure. We show that it is profitable for the firm to assemble the product only if the product price exceeds a certain threshold. This price threshold increases as the unit cost of each component or the degree of variability of the supply reliability distribution increases, but it is independent of the underlying demand function and demand distribution. Also, the optimal product price decreases as supply uncertainty decreases. We further show that under deterministic demand, the components can be managed independently such that the production quantity or unit cost of the component with supply uncertainty does not affect the optimal production quantity of the other components, as long as it is profitable to assemble the product. However, when demand is stochastic, the optimal production quantity of each component depends on the supply reliability distribution as well as the unit costs of the other components. For a fixed product price, the optimal production quantities of the components are smaller when the unit product price is low, and they are higher when the unit product price is high as compared to the case with no supply uncertainty.