An operations research study consists in building a model of the physical situation. An OR model is defined as an idealized (simplified) representation of a real-life system. This system may already be in existence or may still be an idea awaiting execution. In the first case, the model’s objective is to analyze the behavior of the system in order to improve its performance. In the second, the objective is to identify the “best” structure of the future system.
The complexity of a real system result from the very large number of elements (variables) controlling the behavior of the system. This, in turn, dictates a basic difficulty in recommending specific sources of action for each of these variables. Luckily, although a real situation may involve a substantial number of variables, generally a small fraction of these variables truly dominate the behavior of the system. Thus, the simplification of the real system in terms of a model concentrates primarily on identifying the dominant variables and the relationships governing them.
Suppose that the objective is to determine the level of production at the plan. Looking at the overall system, one sees that a large number of variables directly influence the level of production. Some examples of these variables follow.
1.Production department: Available machine hours, available labor hours, specific sequencing of operations on machines, in-process inventory, number of defective items produced, inspection rate.
2.Materials department: Available stock of material, rate of delivery of purchased material, storage limitations.
3.Marketing department: Sales forecast, intensity of advertising campaign, capacity of distribution facilities, effect of competitive products.
Each of the above variables affects (directly or indirectly) the level of production.
Yet it is staggering task to try to establish explicit relationships between these variables and the level of production.
The first level of abstraction calls for defining the “assume real” system in terms of its dominant variables. A little reflection shows that the system can be represented primarily by two variables:
1. One representing the rate of production of the item.
2. One representing its rate of consumption.
In determining the rate of production, variables such as available machine hours, available labor hours, sequencing, and availability of material must be considered in order to predict as realistic a production rate as possible. The consumption rate is determined in terms of the variables associates with the marketing department. In other words, the simplification from the “real” system to the “assumed real” system is effected by “lumping” several variables in the real system into a single variable in the assumed real system.
It is easier now to think in terms of the assumed real system. From the production and consumption rated, one can establish measures of the excess or shortage inventory for a given production level. A model abstracted from the assumed system may thus be constructed to balance the costs of excess and shortage inventories, respectively. Of course, this model is not the only one that can be abstracted from the assume system. For example, one may be interested in determining the production level so that the maximum excess inventory remains below a certain upper limit.