Mathematical models

Use mathematical techniques to link decision variables, uncontrollable variables, parameters, and result variables together:

• Decision Variables have values that describe choices.

• Uncontrollable Variables have values that are outside the decision-maker’s control.

• Parameters are fixed factors (constants).

• Intermediate Result Variables are intermediate outcomes.

• Result Variables are outcomes dependent on chosen decision variables, uncontrollable variables, parameters and intermediate results.

Quantitative models

• Quantitative relationships.
• Variables involved in the model have numerical values.
• Outcomes are numerical.

“if the sales this year are $400,000 and they increase by 10% next year, the sales will be $440,000”

Nonquantitative models (qualitative models)

• Qualitative relationships.
• Variables involved in the model have qualitative values that are represented within the model by numerical values.
• Outcomes are qualitative / numerical.

“indicate your happiness with our product on a scale of 1 (very unhappy) to 5 (very happy). …”

Results (outcomes) = f(decision variables, uncontrollable variables, parameters, intermediate results)

Types of Models

Physical models

• Physical (touchable) representations.
• A smaller or larger physical copy of an object.

Abstract models

• Generalisations of reality that remove specific details in favour of general information which is relevant for the purpose.

Object models

• Represent, describe and simplify the appearance, structure, organisation and functioning of things (objects).

Process models

• Represent, describe and simplify the dynamic nature of processes.

Descriptive Models

• Describe the reality as it is or as it is believed to be.
• E.g. mathematical models (see below).
• Useful for satisficing.

Mathematical Models

• Describe reality using mathematical language and techniques, often variables and systems of equations that relate outputs to inputs.

Simulations

• Computerised models of dynamic processes.