Monte Carlo Simulations and Linear Optimization Review

These flashcards cover key concepts and definitions related to Monte Carlo simulations, sensitivity reports, linear optimization, and decision-making processes in business contexts.

What does the Monte Carlo simulation help summarize?

The range of possible outcomes and associated probabilities through key metrics, often called summary variable values.

What are summary variable values?

Metrics that encapsulate the financial performance and variability of a project or investment, aiding in decision-making.

What are decision variables in Monte Carlo simulations?

Inputs or parameters of a model that remain constant throughout multiple trials.

What are uncertain variables?

Variables randomly sampled from probability distributions that change across trials in a simulation.

What do output variables represent?

Outcomes that we want to understand or predict, recalculated after each simulation trial.

What is an example of a summary variable?

Net present value, return on investment, or cash flow.

How does a high standard deviation affect ROI predictions?

Indicates increased risk despite a potential for a positive ROI if the mean is also high.

How is expected value calculated?

As a weighted average of possible outcomes.

What is loss risk?

The percentage of trials that result in losses.

What is the upside prospect at 10%?

The amount that will be made more than or equal to in 10% of the trials.

What does the sensitivity report help assess?

How changes in coefficients or constraints could affect optimal decisions and the objective value.

What is the significance of binding constraints?

They occur when slack/surplus is zero, meaning the final value equals the constraint's right-hand side.

What does shadow price indicate?

The change in the optimal objective function value per unit increase in the right-hand side of a constraint.

What defines a non-binding constraint?

A constraint with non-zero slack or surplus, meaning the solution isn't constrained by it.

What is a binary variable?

A decision variable that can take only two values, typically 0 or 1.

What is the objective of linear optimization in project selection?

To maximize net return from selected projects while adhering to budget constraints.

What happens if the total allowed coefficients for changes exceed 100%?

The optimal solution will no longer be valid.

What is the first part of formulating a linear optimization model?

Identifying decision variables associated with project selections.

What input is needed to state constraints in a linear optimization model?

Specifications on production amounts and available resources for selected projects.

What characterizes a mutually exclusive constraint?

If one project is selected, another cannot be selected.

How is opportunity cost related to the shadow price?

Opportunity cost can be interpreted as the influence of shadow price on the profit due to constraints.

What indicates that a project must be selected in a project outcome?

A co-requisite constraint, indicating that certain projects must be mutually inclusive.

What is the purpose of linear optimization in a fixed cost problem?

To minimize overall costs while meeting demand requirements.

How is a feasible region represented in a graph?

By shading areas where all constraints are satisfied.

What do unit profits indicate in relation to decision variables?

They impact the profitability of a project, assessed during sensitivity analysis.

What is the 100% rule in sensitivity analysis?

It states that the sum of the proposed changes must not exceed 100% of allowable changes for the optimal solution to remain valid.