Managing supply chain risks with dual sourcing: Bayesian learning of censored supply capacity

Dual sourcing is a common strategy for mitigating supply chain risks, with supply capacity uncertainty being one of the most significant risks. However, firms often have limited knowledge about uncertain supply capacity, and can only observe it when the delivered quantity is less than the ordered amount. This leads to censored supply capacity observations. To investigate how supply capacity learning affects dual-sourcing decisions, we propose a model of a firm sourcing non-storable substitute products from an expensive reliable supplier and an inexpensive unreliable supplier to meet a deterministic time-varying demand over a finite horizon. The unreliable supplier has a random capacity with an unknown parameter. The firm updates its belief about this parameter using Bayesian learning and adapts its sourcing decisions to balance the tradeoff between maximizing current profits based on its current belief (exploitation) and increasing the precision of its belief for future periods (exploration). We use Bayesian dynamic programming to determine the firm's myopic sourcing policy and partially characterize its optimal sourcing policy. We apply a state space reduction technique to Weibull distributed capacity, resulting in an inductively solvable optimization problem. The optimal sourcing policy can be obtained under a condition that ensures splitting the demand between the suppliers is optimal. For exponentially distributed capacity, the optimization problem has a recursive closed-form solution, and the optimal sourcing policy is such that the optimal order quantity from the reliable (unreliable) supplier is smaller (greater) than the myopic quantity. We complement our analytical results with numerical examples and discuss extensions to random demand and inventory carryover.