Procurement strategies with unreliable suppliers under correlated random yields

Abstract

Problem definition: This paper studies the sourcing of a monopoly firm that procures from multiple unreliable suppliers to meet its deterministic/price-dependent demand. The suppliers’ production processes are unreliable and are modeled by correlated proportional random yields. Academic/practical relevance: As a proactive risk-mitigation tool, supply diversification has been widely studied in the literature, with the primary focus on independent supply risks. However, supply risks in practice may be correlated in nature for various reasons. By accounting for yield correlation among suppliers’ production processes, our work aims to help firms better manage their supply base and fully exploit the benefit of risk pooling through diversification. Methodology: Stochastic optimization serves as our main tool for analysis. Results: We formulate the firm’s problem in a general n-supplier setting and prove its structural properties. For a two-supplier case, we fully characterize the firm’s optimal sourcing decision and provide a unified measurement to quantify how yield correlation and characteristics jointly affect the supply base selection. Specifically, we show that when the two suppliers are highly positively correlated the firm may sole-source from the supplier with higher effective procurement cost (the procurement cost per expected delivered unit) and also higher reliability. In addition, as the production yields become more positively correlated, supply diversification becomes less likely, and the firm’s profit decreases. Moreover, assuming multivariate normally distributed yields, we generalize those results and relevant insights to the multiplesupplier case. We uncover the critical role played by yield correlation and illustrate the insufficiency of using effective procurement cost alone to qualify a supplier. Finally, we incorporate demand uncertainty to confirm the robustness of our findings. Managerial implications: Our results urge caution in selecting the optimal supply base when the yield risks are correlated. Particularly, yield correlation, effective procurement costs, and supplier reliability should be jointly taken into account; otherwise, ignoring any one of these factors may lead to suboptimal outcomes.