Inventory Theory

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1. Definition of the Inventory Theory

Inventory theory (or more formally the mathematical theory of inventory and production) is the sub-specialty within operations research that is concerned with the design of production/inventory systems to minimize costs. It studies the decisions faced by firms and the military in connection with manufacturing, warehousing, supply chains, spare part allocation and so on; it provides the mathematical foundation for logistics.

Inventories are materials stored, waiting for processing, or experiencing processing. They are ubiquitous in modern business. Observation of almost any company balance sheet reveals that a very significant part of its assets comprise inventories of raw materials, products within the production process, or finished products. Most managers don't like inventories, because they are like money placed in a drawer, assets tied up in investments that are not earning money. They also incur costs for the care of the stored material and are subject to spoilage and obsolescence. The goal of programs such as "just-in-time" manufacturing is to reduce inventory levels.

In spite of all these bad features, inventories do have positive purposes. Raw material inventories provide a stable source of the materials required for production. A large inventory requires less replenishment and may reduce ordering costs because of economies of scale. In-process inventories reduce the impacts of the variability of the production rates in a plant and protect against failures in the processes. Final goods inventories provide for better customer service. The variety and easy availability of the product is an important marketing consideration. There are other kinds of inventories, including spare parts inventories for maintenance and excess capacity built into facilities to take advantage of the economies of scale of construction.

Because of their practical and economic importance, the subject of inventory control is a major consideration in many situations. Questions must be constantly answered as to when and how much raw material should be ordered, when a production order should be released to the plant, what level of safety stock should be maintained at a retail outlet, or how in-process inventory is to be maintained in a production process. These questions are amenable to quantitative analysis through the subject of inventory theory.


2.1 Basic Terms that Describe Inventory Models
There are six components that determine profitability. These are:

1. The costs of ordering or manufacturing the product
2. Holding costs. This includes the cost of storage space, insurance, protection, taxes, etc. 3. Shortage costs. This cost includes delayed revenue, storage space, record keeping, etc. 4. Revenues. These costs may or may not be included in the model. If the loss of revenue is neglected in the model, it must be included in shortage cost when the sale is lost. 5. Salvage costs. The cost associated with selling an item at a discounted price. 6. Discount rates. This deals with the time value of money. A firm could be spending its money on other things, such as investments.

Inventory models are classified as either deterministic or stochastic. Deterministic models are models where the demand for a time period is known, whereas in stochastic models the demand is a random variable having a known probability distribution. These models can also be classified by the way the inventory is reviewed, either continuously or periodic. In a continuous model, an order is placed as soon as the stock level falls below the prescribed reorder point. In a periodic review, the inventory level is checked at discrete intervals and ordering decisions are made only at these times even if inventory dips below the reorder point between review times.

2.2 Flow, Inventory and Time
An inventory is represented in the simple diagram of Figure 1. Items flow into the system,...
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