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How is optimization used in inventory control?

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optimization problem — optimization Constraint set bounded by the five lines x₁ = 0, x₂ = 0, x₁ = 8, x₂ = 5, and x₁ + x₂ = 10. These enclose an infinite number of points that represent feasible solutions.

In the context of operations research, optimization is used in inventory control to balance the conflicting costs associated with holding stock.1

Inventory management involves determining optimal purchase or production lot sizes and reorder points to minimize the total cost of a system. This process requires balancing two opposing sets of costs:1
* Costs that increase with inventory size: These include capital investment, storage, insurance, taxes, depreciation, deterioration, and obsolescence.1
* Costs that decrease with inventory size: These include shortage costs (lost sales), setup or preparation costs, and unit purchase or production costs (which may decrease due to quantity discounts or the efficiency of long production runs).1

Mathematical models for single items are typically solved using calculus. For more complex scenarios—such as when order quantities for multiple items are interdependent due to limited storage or production time—the problem becomes more difficult and may require breaking it into smaller, interacting components or using simulation to test decision rules.1