Information Design and Sharing in Supply Chains

We study the interplay between inventory replenishment policies and information sharing in the context of a two-tier supply chain with a single supplier and a single retailer serving an independent and identically distributed Gaussian market demand. We investigate how the retailer’s inventory policy impacts the supply chain’s cumulative expected long-term average inventory costs C in two extreme information-sharing cases: (a) full information sharing and (b) no information sharing. To find the retailer’s inventory policy that minimizes C , we formulate an infinite-dimensional optimization problem whose decision variables are the MA( ∞ ) coefficients that characterize a stationary ordering policy. Under full information sharing, the optimization problem admits a simple solution and the optimal policy is given by an MA(1) process. On the other hand, to solve the optimization problem under no information sharing, we reformulate the optimization from its time domain formulation to an equivalent z -transform formulation in which the decision variables correspond to elements of the Hardy space H 2 . This alternative representation allows us to use a number of results from H 2 theory to compute the optimal value of C and characterize a sequence of ϵ -optimal inventory policies under some mild technical conditions. By comparing the optimal solution under full information sharing and no information sharing, we derive a number of important practical takeaways. For instance, we show that there is value in information sharing if and only if the retailer’s optimal policy under full information sharing is not invertible with respect to the sequence of demand shocks. Furthermore, we derive a fundamental mathematical identity that reveals the value of information sharing by exploiting the canonical Smirnov–Beurling inner–outer factorization of the retailer’s orders when viewed as an element of H 2 . We also show that the value of information sharing can grow unboundedly when the cumulative supply chain costs are dominated by the supplier’s inventory costs.