DEVELOPMENT AND OPTIMIZATION OF A MATHEMATICAL INVENTORY MANAGEMENT MODEL UNDER DEMAND UNCERTAINTY

Abstract

Inventory management under uncertain demand requires decisions that balance ordering and holding costs against shortage risk and customer-service requirements. This article develops a mathematical framework for selecting an order quantity and reorder point when demand varies over time and replenishment lead time may expose the system to stockouts. The proposed framework combines a baseline economic order quantity relationship with a reorder-point policy, safety-stock logic, expected shortage or service-level measures, and scenario-based sensitivity analysis. The model is designed to be adaptable to empirical demand records, while clearly distinguishing analytical results from illustrative calculations. A reproducible workflow is provided for parameter estimation, optimization, and validation. Since no organization-specific demand, cost, or lead-time dataset was supplied, the numerical example and figure are explicitly illustrative and are not presented as empirical findings. The contribution is a transparent modelling structure that can be calibrated and tested for a specific inventory system before operational adoption.