“Sorry, we’re out of that item.” How often have you heard that during shopping trips? In many of these cases, what you have encountered are stores that aren’t doing a very good job of managing their inventories (stocks of goods being held for future use or sale). They aren’t placing orders to replenish inventories soon enough to avoid shortages. These stores could benefit from the kinds of techniques of scientific inventory management that are described in this chapter.
It isn’t just retail stores that must manage inventories. In fact, inventories pervade the business world. Maintaining inventories is necessary for any company dealing with physical products, including manufacturers, wholesalers, and retailers. For example, manufacturers need inventories of the materials required to make their products. They also need inventories of the finished products awaiting shipment. Similarly, both wholesalers and retailers need to maintain inventories of goods to be available for purchase by customers.
The total value of all inventory—including finished goods, partially finished goods, and raw materials—in the United States is more than a trillion dollars. This is more than $4,000 each for every man, woman, and child in the country.
The costs associated with storing (“carrying”) inventory are also very large, perhaps a quarter of the value of the inventory. Therefore, the costs being incurred for the storage of inventory in the United States run into the hundreds of billions of dollars annually. Reducing storage costs by avoiding unnecessarily large inventories can enhance any firm’s competitiveness.
Some Japanese companies were pioneers in introducing the just-in-time inventory system—a system that emphasizes planning and scheduling so that the needed materials arrive “just-in-time” for their use. Huge savings are thereby achieved by reducing inventory levels to a bare minimum.
Many companies in other parts of the world also have been revamping the way in which they manage their inventories. The application of operations research techniques in this area (sometimes called scientific inventory management) is providing a powerful tool for gaining a competitive edge.
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How do companies use operations research to improve their inventory policy for when and how much to replenish their inventory? They use scientific inventory management comprising the following steps: 1. Formulate a mathematical model describing the behavior of the inventory system. 2. Seek an optimal inventory policy with respect to this model. 3. Use a computerized information processing system to maintain a record of the current inventory levels.
4. Using this record of current inventory levels, apply the optimal inventory policy to signal when and how much to replenish inventory. The mathematical inventory models used with this approach can be divided into two broad categories—deterministic models and stochastic models—according to the predictability of demand involved. The demand for a product in inventory is the number of units that will need to be withdrawn from inventory for some use (e.g., sales) during a specific period. If the demand in future periods can be forecast with considerable precision, it is reasonable to use an inventory policy that assumes that all forecasts will always be completely accurate. This is the case of known demand where a deterministic inventory model would be used. However, when demand cannot be predicted very well, it becomes necessary to use a stochastic inventory model where the demand in any period is a random variable rather than a known constant.
There are several basic considerations involved in determining an inventory policy that must be reflected in the mathematical inventory model. These are illustrated in the examples presented in the first section and then are described in...