Simulation models

Learning outcome statements

The learning outcome statements relevant for this section are:

1. demonstrate an understanding of the uses of simulation models, including the Monte Carlo technique
2. identify the benefits and limitations of simulation models

What are simulation models

Definitions

Simulation models

These are mathematical representations of real-world systems that allow analysts to study complex processes, evaluate different scenarios, and predict potential outcomes.

Simulation models enable businesses to analyze uncertainties and make data-driven decisions by simulating different conditions without the risk of implementing changes in the real world. Simulation models are widely used in finance, manufacturing, healthcare, and logistics.

One of the most well-known simulation techniques is the Monte Carlo method, which uses random sampling and statistical modeling to estimate probabilities of different outcomes. This technique is particularly useful for risk assessment, pricing financial derivatives, and project management, where multiple uncertain factors influence results. For example, financial analysts use Monte Carlo simulations to evaluate investment risks by modeling thousands of potential market scenarios.

A Monte Carlo simulation differs from a what-if or goal-seeking analysis: instead of testing one scenario, it draws random values from each input’s probability distribution over many iterations to build a full distribution of outcomes. The process:

1. Build a model linking the uncertain inputs to the outcome, and assign each input a probability distribution.
2. Map random-number ranges to each value in proportion to its probability (e.g., a 30% chance of demand = 100 units gets random numbers 00-29).
3. Draw random numbers, compute each trial’s outcome, and repeat for hundreds or thousands of trials.
4. Summarize the trials into a distribution, such as the expected value and the probability of a loss.

Example: Monte Carlo demand simulation

A company models demand as three outcomes: 100 units (30% probability), 150 units (50% probability), and 200 units (20% probability), mapped to random-number ranges 00-29, 30-79, and 80-99.

Answer: A random draw of 62 falls in 30-79, so that trial’s demand is 150 units. Repeating the draw thousands of times builds the full distribution of likely demand, from which management can read the expected demand and the probability of falling short of a target.

Simulation models versus sensitivity analysis

While both sensitivity analysis and simulation models explore how outcomes change under varying assumptions, their scope is different.

A simulation model, like the Monte Carlo method, is a broad tool used to replicate a real-world system by using mathematical representations and random sampling to generate a wide range of possible outcomes. Its goal is to understand how a system behaves and to predict potential results under various conditions.

Aspect	Simulation model	Sensitivity analysis
Inputs varied	Many, often with probability distributions	One or a few at a time
Output	A range of outcomes and their likelihoods	How much the result changes
Purpose	Predict overall system behavior	Identify which inputs matter most

Sensitivity analysis can be a component of a larger simulation model. For example, after running a simulation, analysts might use sensitivity analysis to determine which of the many uncertain inputs contributed most to the variation in the final results.

Benefits and limitations of simulation models

Benefits

• Handling complex systems: Simulation models can analyze complex and dynamic systems that are difficult to study using traditional analytical methods.
• Risk-free experimentation: Businesses can test various strategies and scenarios in a simulated environment before implementing them in reality, reducing risks and costly mistakes.
• Better decision-making: Simulation models provide insights into how different variables impact outcomes, allowing for better planning and resource allocation.
• Quantifying uncertainty: The Monte Carlo method and other simulation techniques help quantify the range and likelihood of outcomes, giving decision-makers a probability distribution rather than a single-point estimate.

Limitations

• High computational demand: Running simulations, especially Monte Carlo models, requires significant computing power and time, making them resource-intensive.
• Dependence on input data: The accuracy of simulations relies on high-quality data. If input assumptions are incorrect, the results may be misleading.
• Complexity in interpretation: While simulations provide detailed insights, interpreting large volumes of simulated data can be challenging and may require advanced analytical skills.
• Not always practical: In some cases, simulations may be impractical due to time constraints or data availability limitations.
• No guaranteed optimum: Simulation shows likely outcomes under the assumptions entered; it doesn’t identify the single best decision the way an optimization model (e.g., linear programming) does, and its results vary from run to run.

Despite these challenges, simulation models remain powerful tools for decision-making, enabling businesses to mitigate risks, optimize performance, and prepare for uncertain future scenarios.