Adaptive Inventory Policies with Regret Minimization in Lost Sales and Uncertain Supply Settings

Abstract

Managing inventory in environments with uncertain demand and stochastic supply is a critical and challenging task, especially when unmet demand results in lost sales. Traditional inventory optimization methods often assume known probability distributions, limiting their effectiveness in dynamic and data-scarce settings. This paper proposes a regret-minimizing framework for inventory control that benchmarks policies against the best fixed decision in hindsight, rather than minimizing expected costs. The approach is inherently adaptive, leveraging observed data to make robust decisions in real-time, without full knowledge of demand or supply distributions. We analyze structural properties of regret-optimal policies and demonstrate their effectiveness through theoretical insights and practical scenarios, including applications in humanitarian logistics and e-commerce. By integrating online learning with inventory management, this work advances a more resilient and data-driven approach to operating under uncertainty.