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One way of including the uncertainty in your decision process is by performing scenario analysis. This is a straightforward technique, but highly effective and easy to understand. It is a common practice in many industries when e.g. doing risk assessments or for understanding the effect of strategic change. The basic principle is that a set of scenarios is determined that represents the possible input data of a business model. The output (the solution) of the business model for each scenario is determined separately and evaluated against other solutions using a certain performance measure. This provides an insight in the consequences and required decisions to be made for each specific scenario.
If the set of scenarios is large and the requirement is to get insight in the behavior of your business, exact point solutions are no longer important and we speak of experiments and determine the average optimal solution, the 95% percentile, etc. Experiments (also referred to as the Monte Carlo method or simulation) are also useful in studying systems with a large number of coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures.
Scenario Analysis in AIMMS
AIMMS is highly suitable to run and analyze scenarios and to perform experiments. With the integrated data management facilities, AIMMS offers the ability to create various scenarios; either by reading in, calculating, or randomizing input data instances. Each scenario can initiate the model to calculate the optimal solution of your business model. On an individual scenario, sensitivity analysis (shadow pricing, at bound, MIP search tree etc.) can already give insight into the specific data changes. Efficiency is assured by the AIMMS update technology (only changes with respect to a previous scenario are computed).
Once all solutions are determined, a side-by-side view and data comparison of both the input scenarios and optimal solutions are available in the AIMMS GUI. Results can also be analyzed using the AIMMS procedural language, comparing results on an output data level. When using the Histogram functionality (especially useful when doing large experiments), additional statistical information such as average, frequency, deviation, skewness, bounds, etc. becomes available and can be used to get understanding of the model behavior.
Additional Information:
- “Case Management” & “Creating Histograms” - AIMMS User’s Guide (Chapter 17, 19.3).
- “Sensitivity Analysis” - AIMMS Optimization Modeling (Chapter 4).
- Example “Experiment” - AIMMS Installation.
- http://en.wikipedia.org/wiki/Monte_Carlo_method
Other ways of modeling uncertainty:
- Uncertainty modeling (overview)
- Scenario Analysis
- Stochastic Programming
- Robust Optimization
