Stochastic Inventory Theory

Inventory theory deals with the management of stock levels of goods, with the intent of effectively meeting demands for those goods. We say the demands for goods are made by buyers and are met by sellers, regardless of whether monetary exchange is involved. Inventory of a good that is physically available is on hand stock. Demands for a quantity of a good are considered to be met when that quantity is physically transferred, out of the units on hand to the buyer. Shortages are demands that are not met immediately. Shortages are backorders if the buyers are willing to wait, and lost sales if not. Backorders are also called backlogged demand and backlogs. From time to time, the inventory manager may choose to place an order for additional quantities of the good to replenish the stock on hand. An order, for the order quantity, may be placed on an outside supplier or on an internal production facility, in which case the order quantity is a run, batch, and/or lot of the product. The order lead time is the elapsed time from the moment an order is placed until the moment the quantity ordered is received (added to the stock on hand). That definition is purposefully vague, because of the possibility that portions of an order may be delivered at different points in time. Quantities of the good that have been ordered (by the inventory manager) but not yet received are on order. System stock, also called inventory position, is the sum of stock on hand plus on order minus backorders. It represents the amount that is available to meet future demands without placing further orders.