Chance Constraints and Value At Risk
Learning: How to consider uncertainty when developing optimization models. In particular, with the notion of chance constraints and value at risk.
Example: A maintenance facility manager wanting to determine the number of employees to schedule in order to meet the expected staff requirements.
Example: A maintenance facility manager wanting to determine the number of employees to schedule in order to meet the expected staff requirements.
Consider the requirement of 30 employees for the period between 4 PM and 8 PM. Supposed that after some data analysis, it is determined that there are ten possible requirement scenarios.
The average requirement is 30, but there is some variability. Due to this variability, there is a 50% chance that the requirement constraint for the period between 4 and 8 PM is satisfied. To increase the chance of satisfying the constraint, we can increase the number of employees available in that period. For instance, if the number of employees that start at 4:00 is changed from 13 to 15, then the chance that the constraint is satisfied increases to 70%.
Chance constraint: A type of constraint that is satisfied only in a fraction of the possible scenarios. This allows us to find solutions that are more robust than those found with expected values but that they are not trying to cover all possible scenarios. Solutions that cover all possible scenarios tend to be very expensive because they require a lot of resources.
Value at Risk (VaR): The fraction of the times a constraint is not satisfied.
Conditional Value at Risk: To account for the magnitude of violation
Simulation is the most common mechanism for developing a model with VaR constraints.
Chance constraint: A type of constraint that is satisfied only in a fraction of the possible scenarios. This allows us to find solutions that are more robust than those found with expected values but that they are not trying to cover all possible scenarios. Solutions that cover all possible scenarios tend to be very expensive because they require a lot of resources.
Value at Risk (VaR): The fraction of the times a constraint is not satisfied.
Conditional Value at Risk: To account for the magnitude of violation
Simulation is the most common mechanism for developing a model with VaR constraints.