Managing supply risk: Robust procurement strategy for capacity improvement

We consider a buyer's procurement strategy from a supplier with random capacity. The supplier can exert an unobservable effort to improve its capacity. The buyer is ambiguous about the parameters of the supplier's capacity distribution. We introduce an ellipsoidal uncertainty set to represent the uncertain parameters and analyze how the buyer determines the optimal order quantity and the wholesale price. Using the worst-case criterion, we completely characterize the structure of the optimal robust procurement strategy. We show that the optimal robust wholesale price becomes larger as the degree of parameter uncertainty increases; and the buyer's worst-case expected profit is decreasing in the degree of parameter uncertainty. We then establish an upper bound for the impact that parameter uncertainty may have on the buyer's profitability. This upper bound can serve as a measure for the buyer to evaluate the benefit of reducing parameter uncertainty. Finally, we extend the results by considering general L^p -normuncertainty sets, general capacity distributions, and random demand. Our findings provide managerial guidelines on the design of the robust procurement strategy in practice.