8.2. Generic problem conceptualization

Problems, as conceptualized by Ackoff, have five types of components:

1. The one(s) faced with the problem, the decision maker(s).

2. Those aspects of the problem situation the decision maker can control: the controllable variables.

3. Those aspects of the problem situation the decision maker cannot control but those which, together with the controlled variables, can affect the outcome of his choice: the uncontrolled variables.

4. Constraints imposed from within or without on the possible values of the controlled and uncontrolled variables.

5. The possible outcomes produced jointly by the decision maker’s choice and the uncontrolled variables.

The above conception of a problem can be represented by the following statement:

\[\begin{split} \text{The value of the outcome} = \text{a specified relationship betweeen} \\ \text{the controlled variables and the uncontrolled variables} \\ \end{split}\]

Or more formally:

\[ U = f(X,Y) \]

This means that the utility or value of an outcome \(U\) is a function of two types of variables: controllable \(X\) and uncontrollable variables \(Y\).

A simple example

Consider an architect working on the design of a mixed use building (office space and different types of apartments). The municipality wants to maximize the number of affordable apartments whereas the project developer wants to maximize profit. The architect can control the building’s geometry (width, length, height) and how much space to allocate to offices and different types of apartments. However, the architect cannot control height restrictions set by the municipality and investment restrictions set by the project developer and the restrictions imposed by the plot size. It is then task of the designer to find a mix of office space and apartments that has the highest utility/value/preference for both the municipality and project developer. The utility is thus a representation of both money and number of affordable apartments.