SIMULATION

INTRODUCTION

Simulation is a technique that:

• models all possible cases of entering possible variables (singles or combinations) to a specific process or a specific formula in a simulation model.
• runs this model. These run variables are:

- random variables (if the variables domain is big or unlimited).

- all variables (if the variables domain is limited and small).

• depicts the running result in a cumulation graph.

Simulation model is also known as prediction model or forecasting model.

Simulation can be used to tackle problems in many fields such as finance, engineering, supply chain and science.

Examples of forecasted outcomes are:

• net risk impact on a project from applying all possible combinations of risks.
• total project cost from applying all possible costs for every single activity considering (in every run) different sets of assumptions and constraints.
• total project duration from applying all possible durations for every single activity considering (in every run) different sets of relationships, assumptions and constraints.

Seeing all possible outcomes from these examples eases identifying the best or optimum option.

MONTE CARLO SIMULATION

The most common and most applied simulation technique is Monte Carlo simulation (also known as “Multiple Probability Simulation”).

Typically, the simulation is performed by running a simulation model that:

• developed for this simulation.
• includes number of variables and all their possible combinations.

A computer software is used to run the simulation model which may be several thousands runs.

Monte Carlo simulations calculates only the entered data.

This requires ensuring that the entered data is:

• correct data.
• all required data.

Example: To perform a quantitative risk analysis using Monte Carlo simulation, build in a model all possible combinations of:

• individual project risks (event risks).
• sources of uncertainty (non-event variability/ambiguity risks).

Run the model to evaluate the corresponding potential impact of each combination on achieving project objectives.

Illustrate the potential impact of each combination by (and/or):

• histogram
• "S-curve" of a cumulative probability distribution

To develop simulation models for Monte Carlo analysis use:

• for cost risk model, the project cost estimates.
• for schedule risk model, the schedule network diagram and duration estimates.
• for an integrated quantitative cost-schedule risk model, both.

Example for Monte Carlo simulation:

For a project of planned cost “1000000$”, a simulation model is developed including all possible:

• individual project risks (event risks).
• sources of uncertainty (non-event variability/ambiguity risks).

The model is run for 2000 times for the cost probability in a Monte Carlo application.

It gave the following results:

• Value (M$) 0.8 0.9 1.0 1.1 1.2 1.3
• Iterations or appearance number (times) 100 300 400 550 400 250 = 2000
• Cumulative Iterations (times) (for S-curve) 100 400 800 1350 1750 2000
• Probability (%) (= Cum iterations / 2000) 5% 20% 40% 68% 88% 100%

As each input in a Monte Carlo simulation have multiple possible values (due to variability, ambiguity or potential individual risk), they are randomly chosen for each run during the simulation.

Outputs represent the range of possible outcomes for the project (e.g., project end date, project cost at completion).

Typical outputs can be illustrated by:

• a histogram:

- which presents the simulation results on the X axis Vs the number of iterations on the Y axis.

- In the above example, it is Values ($) on the X axis Vs Iterations (times) on the Y axis.

- The most likely outcome (expected value) is the outcome of the highest iterations.

• an S-curve (cumulative probability distribution):

- which presents the simulation results on the X axis Vs the probability of achieving (the simulation result or less) on the Y axis.

- In the above example, it is Values ($) on the X axis Vs Cumulative Probability (%) on the Y axis.

- The most likely outcome (expected value) is the outcome of the steepest inclination on the curve.

Monte Carlo simulation enable to conduct criticality analysis to determine:

• which elements (individual risk or uncertainty source) in the risk simulation model have the greatest effect on the project items.
• which project items (e.g. activities, costs, resources) have highest expected effect.
• for a quantitative schedule risk analysis, the criticality index for each risk simulation model element which is the frequency of element appears on the critical path to the total runs number in %age.

Criticality analysis allows to focus risk response planning on:

• most effecting elements.
• most potentially effected items.

However, the results from a Monte Carlo simulation are predictions not guaranteed future results.