Optimization of Inventory Management in the Presence of Demand Volatility with Advanced Stochastic Models

Abstract

The volatility of demand makes it difficult for businesses to maintain a balance between ensuring products are available and the costs and operations associated with carrying inventory. Fixed safety-stock rules and traditional forecasting methods can be inadequate when demand distributions vary, lead times are variable and sales data is censored by stockouts. This paper proposes a decision framework for inventory optimization in the presence of a stochastic demand, a dynamic programming approach, a Monte Carlo simulation and distributionally robust optimization. Demand is treated as a random variable whose distribution can be different from season to season, product to product, and external condition to external condition. The replenishment quantities are determined as those that minimize the expected ordering, holding, shortage, and obsolescence costs with service and risk constraints. A conceptual methodology is outlined as well as an illustrative numerical comparison of fixed safety-stock, classical stochastic and volatility-responsive policies. The numerical example is not an actual scenario, and it represents the process of evaluation, not proving actual empirical results. The framework emphasises the importance of considering cost, service and downside risk all at once, rather than a point forecast. The paper identifies advanced stochastic models where the incorporation of reliable data and regular monitoring, transparency in decision rules and human oversight is most useful. Implementation must start with a small number of SKUs, apply back-testing and stress-testing and only roll out if there is operational advantage.