A MATHEMATICAL OPTIMIZATION FRAMEWORK FOR MINIMIZING INVENTORY COSTS AND IMPROVING CUSTOMER SERVICE LEVELS
Keywords:
Inventory Optimization, Customer Service Level, Fill Rate, Reorder Point, Order Quantity, Stochastic Demand, Shortage Cost, Mathematical Modelling, Robust OptimizationAbstract
Inventory decisions involve a fundamental trade-off between the cost of carrying stock and the cost of failing to satisfy customer demand. This study develops a mathematical optimization framework that jointly considers replenishment quantity, reorder point, inventory holding cost, ordering cost, shortage cost, and customer-service requirements. Unlike a cost-only formulation, the proposed framework treats service performance as an explicit decision constraint and evaluates alternative policies using both economic and operational indicators. A two-variable optimization model is formulated for order quantity and reorder point, with a service-level constraint based on stockout avoidance and a complementary fill-rate measure. A finite-horizon numerical experiment is used to demonstrate the solution procedure and the cost–service trade-off. The illustrative experiment uses a 12-period demand series and does not represent organizational field data. The proposed policy is selected by enumerating feasible order-quantity and reorder-point combinations and retaining policies that satisfy the prescribed service target. Sensitivity analysis further shows how the cost of service assurance changes as the required service level is increased. The framework provides a transparent basis for inventory policy design and can be extended to stochastic, robust, multi-item, multi-echelon, and distribution-free settings.
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