Binomial Smoothing for Inventory and Information Control in Supply Chains

2026-06-08

AI Summary

This study addresses the challenge in decentralized supply chains where upstream firms, unable to directly observe market demand, must infer it from downstream orders, forcing retailers into a trade-off between inventory costs and demand predictability. The authors propose a binomial smoothing replenishment policy that allocates unit demand across a finite time window according to binomial distribution weights, achieving coordinated optimization between delayed response and information transmission. Distinct from prior approaches that focus solely on variance reduction, this strategy explicitly targets the unpredictable component of orders. Under weakly stationary Gaussian demand, the policy admits an analytical formulation and is proven to minimize upstream forecasting error while preserving invertibility for a fixed smoothing window. Compared to existing methods, it significantly reduces manufacturer forecast error at equivalent smoothing levels and achieves a constant-factor approximation to the optimal solution, thereby enhancing overall supply chain performance.

Abstract

In many decentralized supply chains, upstream firms do not observe market demand directly and instead infer downstream conditions from the order stream. A retailer's replenishment policy therefore plays a dual role: it governs inventory replenishment and shapes the information available for upstream forecasting. This creates a fundamental trade-off. Smoother orders improve upstream predictability, but delaying the response to demand can increase downstream inventory costs. We study how a retailer should optimally smooth demand in a two-tier supply chain with one retailer and one manufacturer when the manufacturer forecasts future orders from the retailer's order history. We propose Binomial Smoothing, a class of replenishment policies that implements delayed demand response by spreading each unit of demand over a finite horizon using binomial weights. The class is interpretable, easy to calibrate, and analytically tractable. Under weakly stationary Gaussian demand satisfying mild regularity conditions, we show that, for any fixed smoothing horizon, the Binomial policy minimizes the manufacturer's forecast error among all policies with the same degree of smoothing. It remains invertible, so the manufacturer can recover demand history from observed orders. More generally, Binomial Smoothing achieves a constant-factor approximation guarantee relative to an optimal policy. Our results yield a broader insight: replenishment policies should be designed not merely to reduce order variance, as in the traditional bullwhip measure, but to reduce the unpredictable component of orders. Carefully designed smoothing can improve supply-chain performance and partially substitute for information sharing, providing a concrete mechanism for coordination without collaboration.

Problem

• supply chain coordination
• demand smoothing
• order forecasting
• information asymmetry
• inventory control

Innovation

• Binomial Smoothing
• Demand Forecasting
• Supply Chain Coordination
• Order Smoothing
• Bullwhip Effect