L4 - Sensitivity Analysis

Question 1

So what happens if we have uncertainty in our coefficients?

Answer 1

• Caused by measurement errors or incomplete information
  
  • c E [c_L,c_U]
• In the objective function –> if we saw a coefficient (x2) increase -, the line will rotate and flatten around the optimal point –>rotates too much (big change) and it will change the optimal plan
  
  • But will effect the profit function
  • If (x1 increased) –> flatter –> would have to reduce profits to still go through the optimal point
  • steeper –> would have to increase profits to still go through the optimal point
• The limit in which we can increase a coefficient before the optimal plan changes is when the isoprofit is parallel to the slope of a constraint
  
  • have infinitely as many solutions

Question 2

What is the allowable range?

Answer 2

If constraints on the objective function is c E (C_L,C_U) the allowable range is the the values the constraints can change to without the optimal point change

• Up to the point, it is parallel with a constant and have an infinite number of solutions
• Thus an allowable increase/decrease is the difference between the upper and lower bound and the current constraint value
  
  • allowable range is the difference between the allowable increase and decrease

Question 3

Important to remember when using the LinProgSensitivity program in MATLAB?

Answer 3

• Make sure the b is transposed
  
  • LinProgSensitivty (c,A,b’)

Question 4

When do we get an infinite allowable increase/decrease?

Answer 4

• When the optimal point is on the axis and we are only producing one type of good
  
  • the constraint can keep increasing but the optimal point wont change

Question 5

Why is it good that the optimal point does not change from a managerial perspective?

Answer 5

• Costs of changing production
  
  • Do you have the capacity to increase production or make a whole factory redundant because its not as optimal to produce one type of good anymore
• However, if the constraint increases/decreases more than the allowable range
  
  • increase –> Make more profit by change the optimal point as costs are too high
  • decrease –> reduce losses by changing the optimal plan

Question 6

What does the reduced cost mean in the LinProg function?

Answer 6

• If you increase production of that variable by 1 unit it will increase cost(reduce profits) by that amount