"Two fundamental questions that must be answered in controlling the inventory of any physical good are when to replenish the inventory and how much to order for replenishment. In this book we shall attempt to show how these questions can be answered under a variety of circumstances. Essentially every decision which is made in controlling inventoried in any organization, regardless of how complicated the inventory supply system may be, is in one way or another associated with the questions of when to order and how much to order. There are certain types of inventory problems, such as those concerned with the storage of water within dams, in which one has no control over the replenishment industry. (In other words, the ressuply of the inventory of water within the dam depends on the rainfall, and the organization operating the dam has no control over this.) We shall not consider this type of problem here. The only problems with which we shall concern ourselves are those in which the organization controlling the inventory has some freedom in determining when, and in what quantity, the inventory should be replaced. On other hand, we shall assume that, in general, the inventory system has no control over the demands which occur for the item, or items, which it stocks. Again, this is just the opposite of what one encounters in dealing with inventory problems such as storage of water within dams, since the efflux of water through the dam is completely within the control of the organization operating the dam. In short, we are going to consider the type of inventory problem encountered in business, industry, and the military.
We shall concentrate on showing how mathematical analysis can be used to help develop operating rules for controlling inventory systems. When mathematics is applied to the solution of inventory problems, it is necessary to describe mathematically the system to be studied. Such a description is often referred to as a mathematical model. The procedure is to construct a mathematical model of the system of interest and then to study the properties of the model. Because it is never possible to represent the real world with complete accuracy, certain approximations and simplifications must be made when constructing a mathematical model. There are many reasons on this. One is that it is essentially impossible to find out what the real world is like. Another is that a very accurate model the real world can become impossibly difficult to work with mathematically. A final reason is that accurate models often cannot be justified on economic grounds. Simple approximate ones will yield results which are good enough so that the additional improvement obtained from a better model is not sufficient to justify its additional cost."
- —Thomson McLintock Whitin and George F. Hadley, Analysis Of Inventory Systems, 1963