Descriptive vs. prescriptive models

A quantitative model can be

• Descriptive, if its purpose is to shed some light on the relationships between two (or more) variables of interest (e.g., do sales depend significantly on advertisement expenditure?) or to predict system performance as a function of some design variable (e.g., the average waiting time in the queue, as a function of the number of tellers in a bank).
• Prescriptive, when the aim is (more ambitiously) to find a solution, subject to economical or technological constraints, so that costs are minimized or profits are maximized (see, e.g., the optimal mix problem).

Typical examples of descriptive models that we cover in the book are

• Simulation models for performance evaluation (Section 9.7)
• Linear regression models.
• Time series models for forecasting.

All of these models are used to generate information that helps in coming up with a decision, but they are not aimed at generating the decision directly. Examples of prescriptive models whose output is the decision itself are

• The economic order quantity model (Section 2.1)
• Linear programming models (Chapter 12)

It should be clear that prescriptive models are more ambitious and, in principle, they could even be used to automate the decision process. This applies to strictly technical problems, especially when the time to make a decision is quite limited. In most business settings, however, prescriptive models should be regarded as decision supports, and we must be aware of their limitations:

• The output is affected by data uncertainty (which is not only of a statistical nature; demand is uncertain because we cannot forecast the future exactly, whereas some cost are hard to quantify–how much is the inventory holding cost for an item?). Sensitivity analysis should be an integral part of a quantitative analysis.
• Some tradeoffs between conflicting objectives are difficult to assess quantitatively, possibly requiring the interaction between multiple stakeholders.
• More often than not, we have to approximate parts of a problem to make it tractable, and expert judgment is needed to evaluate the impact on these simplifications on the viability of the model and of the solution that we obtain from solving it. This process is called model validation.

Because of these limitations, it is sometimes argued that quantitative analysis should be confined to academia, and that common sense and a lot of practical experience are what is really needed. It is certainly true that human knowledge is an extremely valuable asset; what is not true is that it is incompatible with quantitative analysis. Furthermore, there is another more and more important factor: time. The rate of change in business conditions is faster and faster. For instance, when you change a product line, you have to redesign the whole supply chain to support its production. There is simply no time to do that manually, and some automatic support is needed. Intuition and experience are essential, but they are not enough.