Multiple Objectives
CIS 418
An Example of Multiple Objective Optimization
Removing snow in Montreal.
Goal: minimize the expense and at the same time maximize contaminant removal (salt, sand). Different removal sites have different capacities.
Simon Business School CIS-418 Ricky Roet-Green
2
*source – Ragsdale
Formulate the problem
• Objective:
– Minimize cost (assume that it costs k$ per km travelled * ft3 of snow) / Maximize the amount of contaminants removed
• Decisions:
– From each sector to which sites are we removing the contaminant snow. 5X10=50 decision variables.
• Constraints:
– Site capacity
– You cannot remove snow that does not exist
– Non-negative decision variables
Go to the excel file “Non-Linear Problem”->”Montreal Snow removal” and find the optimal solution.
Simon Business School CIS-418 Ricky Roet-Green
3
Handling conflicting objectives
•
Conflicting objectives:
– Maximum amount of contaminants that can be removed – Minimum cost
How can you use Optimization Parameter Analysis to create a plot showing minimum cost of removal for a given level of contaminants removal?
– Set the constraint R.H as a parameter.
– Run optimization report: objective as a function of the parameter
– Plot the efficient frontier by using “Chart”->”Multiple Optimizations”
•
Simon Business School CIS-418 Ricky Roet-Green
4
Selecting an operating point on the efficient frontier
• Efficient Frontier – classic definition: The efficient frontier is the set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return.
• Efficient Frontier – in our case: The set of optimal amount of contaminants removed for a defined level of cost (budget), or the set of optimal cost for a defined amount of contaminants removed.
• What point on the curve the city may want to choose to operate? Why?
Simon Business School CIS-418 Ricky Roet-Green
5