ART OF MODELING
The illustrative models developed in Previous are true representations of real situations. This is a rare occurrence in OR, as the majority of applications usually involve (varying degrees of) approximations. Figure 1.1 depicts the levels of abstraction that characterize the development of an OR model. We abstract the assumed real world. from the real situation by concentrating on the dominant variables that control the behavior of the real system. The model expresses in an amenable manner the mathematical functions that represent the behavior of the assumed real world.
To illustrate levels of abstraction in modeling, consider the Tyko Manufacturing Company, where a variety of plastic containers are produced. When a production order is issued to the production department, necessary raw materials are acquired from the company's stocks or purchased from outside sources. Once the production batch is completed, the sales department takes charge of distributing the product to customers.
A logical question in the analysis of Tyko's situation is the determination of the size of a production batch. How can this situation be represented by a model?
Looking at the overall system, a number of variables can bear directly on the level of production, including the following (partial) list categorized by departments.
1. Production Department: Production capacity expressed in terms of available ma-chine and labor hours, in-process inventory, and quality control standards.
2. Materials Department: Available stock of raw materials, delivery schedules from outside sources, and storage limitations.
3. Sales Department: Sales forecast, capacity of distribution facilities, effectiveness of the advertising campaign, and effect of competition.
Each of these variables affects the level of production at Tyko. Trying to establish ex-plicit functional relationships between them and the level of production is a difficult task indeed.
A first level of abstraction requires defining the boundaries of the assumed real world. With some reflection, we can approximate the real system by two dominant variables:
1. Production rate.
2. Consumption rate.
Determination of the production rate involves such variables as production capacity, quality control standards, and availability of raw materials. The consumption rate is determined from the variables associated with the sales department. In essence, simplification from the real world to the assumed real world is achieved by "lumping" several real-world variables into a single assumed-real-world variable.
It is easier now to abstract a model from the assumed real world. From the production and consumption rates, measures of excess or shortage inventory can be established. The abstracted model may then be constructed to balance the conflicting costs of excess and shortage inventory-i.e., to minimize the total cost of inventory.
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