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# A Simple Inventory Control Model

Suppose that a business knows what the annual sales of an item will be and that it seeks to arrange a delivery schedule with its supplier in such a way that an equal number of items will be delivered at regular intervals throughout the year. Associated with each delivery there is a delivery cost, which is assumed to be independent of the size of the delivery—think of it as an administrative or fixed shipping cost associated with the act of making a delivery. There is also a cost to maintain inventory, which is determined by the unit carrying cost—the cost of keeping one item in inventory for one year.
Smaller, more frequent deliveries will drive up delivery costs but keep inventory levels low, while larger, less frequent deliveries will keep delivery costs low but push inventory levels up, driving up carrying costs. The optimum delivery schedule is the one that minimizes total inventory costs: delivery costs plus carrying costs.
On the upper plot, carrying cost (blue), delivery cost (purple), and total inventory cost (gold) are plotted against the number of annual deliveries, with the optimum schedule marked with a vertical red segment if "show minimum" is checked. The vertical black segment is controlled by the "annual deliveries" slider. The lower plot shows the size of inventory over time based on the schedule determined by the "annual deliveries" slider. In this simple model, each delivery causes a spike in inventory, which declines gradually (the model assumes a constant sales rate) to zero, at which point the next delivery arrives.

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