Companies that manufacture products or sell goods and services maintain inventory to meet the varying demands of the end customer and to provide buffer stock at each stage as a product moves from raw material to final product. The items in inventory may cost under a dollar each or be a luxury car worth $50,000 or more. The item can be as small as a computer chip or as large as an airplane. The article in stock might be an engine or a bottle of wine with a shelf life measured in years or a bunch of grapes or donated blood that loses value in a matter of days or weeks. In every case one core decision is how many items of a specific type (e.g., blood type, car model, or bottle of wine) should be kept in inventory.
One of the earliest applications of mathematical models for business decision making was published by F.W. Harris in 1913 and addressed the question, "How much to order?" The problem assumed a constant demand. The main costs were for placing orders and for capital tied up in inventory. More frequent orders of smaller size reduced inventory costs but increased ordering costs. Less frequent orders of larger size had the reverse effect. This problem was modeled as a single variable equation whose minimum point could be found by differentiation and setting the derivative equal to zero. The solution to this problem was named the Economic Order Quantity or EOQ for short.
If the demand for the product is uncertain, there is an added challenge. If inventory is kept too low, it is possible that when a customer places a request there will be nothing in stock to sell. This unmet demand may represent a lost opportunity, or it may be possible to back order the item by incurring some added transportation expense. If the product is perishable or seasonal, then there is the problem that excess inventory may need to be thrown away or sold at a loss.
The automotive industry offers a classic example of capital tied up in inventory. At any one time there are more than 2.5 million finished vehicles at various locations around the US starting with the assembly plants, in transit, and finally ending up at new car dealerships. The total retail value exceeds $50 billion. This inventory was created to provide customers a variety of choices to pick from and to smooth out the monthly production plan in the face of seasonal demand. When demand slackens, automotive companies offer thousands of dollars of discounts per vehicle in order sell off excess inventory.
Probabilistic Inventory - Perishables
This module explores the decision, how many hot dogs to purchase for sale at each high school basketball game in the presence of uncertain demand. It is representative of a broad class of probabilistic inventory problems in which the item that is produced or bought loses value over time. In this instance, the object is assumed to lose all of its value when the game is over. The term perishable inventory applies to a wide range of products: food, blood in a blood bank, seasonal clothing, newspapers and magazines. In each case, a decision has to be made as to how much to produce or buy. This class of problems was originally labeled the "Newsboy Problem". A daily newspaper is an extreme example of a perishable commodity, as it loses almost all of its information value the next day, when a new edition hits the streets.
The seats on an airplane or rooms in a hotel present a different spin on the same core problem. The number of seats and rooms can be viewed as inventory that is subject to random demand and is used up each day. Any seat not sold on a given flight or room not rented on a given night is inventory that was wasted. In this context, the inventory available is essentially constant each day and the challenge facing management is to develop a pricing strategy that maximizes the total revenue generated by increasing demand. The complex strategies airlines use to price tickets were first initiated by American Airlines and are broadly labeled "yield management." Delta Airlines also implemented a yield management system that was credited with generating $300 million more revenue per year. It is a concept that is also being adopted hotel chains such as Marriott Hotels with an estimated impact of $100 million additional revenue per year. Hertz developed and launched its yield management system to handle its car rental business in 55 cities in 1991.The broadcast industry faces an analogous situation with regard to selling their inventory of advertising slots. They have to determine how much to sell at a lower price to the "upfront market" and how much to reserve for sale later at a higher price to the "scatter market." The application of yield management systems has gained added impetus with the growth of the Internet that has enabled decision makers to offer last minute deals to a wide audience .
Information and Process Management
Operations researchers have developed an extensive array of mathematical models to optimize inventory decisions under a wide variety of conditions and mathematical assumptions. However, at least as important, if not more important, to holding down inventory costs is the effective use of information systems to track and forecast demand for a specific product type, at a precise location, and for a particular season of the year. This must then be coupled with efficient management of the supply chain to provide the product when and where it is needed. Wal-Mart has grown to be the largest company in the world, with over $220 Billion in sales in 2001, by setting the standard for effectively tracking its inventory and managing the relationship with its supplier base. In the world of manufacturing, Dell Computers has been the pioneer with its build-to-order system. This has enabled it to keep inventory costs low and avoid the problem of having to dispose of obsolete components and systems, a problem that plagues the dynamic computer industry.