Designing Information Delays in Supply Chains

This paper studies how a downstream retailer in a decentralized two-tier supply chain can implicitly transmit demand information to an upstream supplier through the structure of its order stream in the absence of an explicit information-sharing mechanism. We distinguish our work from prior work by introducing the notion of information delay and by linking optimal implicit information sharing to the group delay of the retailer's ordering transfer function. We show that pure delay is strictly suboptimal, while fractional-delay mechanisms can reshape the order autocorrelation to improve supplier forecastability and reduce system-wide inventory costs. Using Hardy-space factorization, we develop a tractable family of invertible ARMA policies that approximates the theoretically optimal (but non-rational) limiting filter derived by Caldentey et al. (2025) and preserves its informational delay properties. This construction yields sharp guidance on how policy complexity, as measured by the degrees of the ARMA policies, impacts supply chain costs. We further extend the analysis to memory-constrained suppliers and characterize how the complexity of the retailer's policy should scale with the supplier's finite forecasting window, highlighting when, perhaps counterintuitively, increasing policy complexity can become counterproductive.