CHAPTER 11
Aggregation of Variables

Much of the value of a model comes from distinguishing the important factors in a system and setting them apart from the unimportant. Part of this highlighting of the essence of a system is accomplished by combining similar factors into a single aggregate. Aggregation is desirable and essential and yet a hazard. Permissibility of aggregation is determined largely by examining the decision-making policies of the separate factors that might be aggregated. Items controlled by sufficiently similar policies that depend on sufficiently equivalent information sources may be combined into a single channel. Allowable aggregation, as with other aspects of a model, depends on the purpose of the model.

IT is obvious that a model of a company or of an economy cannot possibly represent every individual decision and transaction taking place in the system. In fact, we should not want to do so, any more than we should want equations that account for each molecule of water in calculating pressures and flows in a water supply system. If individual actions are properly grouped according to similarity of circumstances, the average behavior can be more accurately described than we could hope to do for any individual incident.

How this grouping or "aggregating," is done is of the greatest importance. If there is insufficient aggregation, the model will be cluttered by unnecessary and confusing detail. If aggregation is too sweeping or accomplished by combining the wrong things, we shall lose elements of dynamic behavior that we wish to observe. Some general guides may help determine the basis for aggregation.


11.1 Using Individual Events to Formulate Aggregate Flow

Even though we speak of aggregating large groups of individual physical items and decisions, the aggregate flows must still traverse the same channels followed by individual items. As an analogy, if we were developing a model of a city water works, we should include individual reservoirs, pumping stations, major distribution lines, and groups of water consumers segregated by type and by geographical location. We should make no effort to identify a particular drop of water, but we should devise a diagram that would represent the circumstances encountered by an individual drop as it passes from wells to reservoir and through piping and pumps until it is used.

Likewise we must formulate our industrial system model by examining particular individual decisions and the sequences in their execution.

A flow diagram is first developed to represent the sequence of individual actions. For example, we might trace the path of an order, its formation, its clerical delays, its transmittal, its waiting in a backlog of unfilled orders, the shipment of goods in response to the order, and the transportation of the goods. Each item in the flow encounters these same circumstances. The channel is easiest to find and to visualize

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