Chapter 8 b625aswc08.pptx - Chapter 8 Linear Programming...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 8 Linear Programming: Sensitivity Analysis and Interpretation of Solution 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Sensitivity Analysis Recall in the formulation of the linear programming problem that we have an objective (to min cost or max profit, for example) and we have limits or constraints on what we can do. We have decisions to make on what we can control (choosing values for the decision variables) and we have some things we have no control over (the parameters of the problem). Sensitivity analysis is essentially about understanding how the values of the decision variables change given a change in a parameter. 2
Image of page 2
Sensitivity Analysis In sensitivity analysis we compare every change to the original or base solution to a problem. For example, before I worked with a problem of a company making bowls and mugs. We found a solution. Sensitivity analysis is esentially a scenario analysis game. We can play many scenarios, but we play each 1 at a time and we also compare a scenario with the base solution. Some call this a postoptimality analysis Let’s use the problem we worked on as the basis for our work here. 3
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Here is a basic linear programming problem we developed before. We want to Maximize profit Z= 40b + 50m, but we have constraints 1b + 2m <= 40 (labor), 4b + 3m <= 120 (clay), b, m >= 0. b and m are the decision variables and represent the amount of each item the company produces. Some of the parameters are the profit contributions of each item the firm makes. In the profit function these contributions are coefficients on the decision variables (here we have values 40 and 50). 4
Image of page 4
There are also parameters in the contraints. Recall that there was only 40 hours of labor available and only 120 pounds of clay available. The parameters are called the “right-hand-side” values of the constraints. So, in sensitivity analysis we can check on the following scenarios: 1) Changing an objective function coefficient, 2) Changing a limiting value on a constraint (a “right- hand-side” value, or Remember: do 1 at a time and compare to base soultion. 5
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Both constraints m b (40, 0) (0, 20) (0, 40) (30, 0) You may recall from our previous work using the problem of bowls and mugs that the constraints look like this and the shaded area is the feasible region. The next slide shows us the corner points and the profits at each corner. (24, 8) 6
Image of page 6
Corner points Our three corner points are (30, 0), (0, 20) and (24, 8). Profit is 40b + 50m. Profit at each point (30, 0) 1200 (found by 40[30] + 50[0] = 1200 + 0) (0, 20) 1000 (24, 8) 1360. Corner (0, 0) should also be checked - profit is 0 there. 1360 is highest profit. Make 24 bowls and 8 mugs. 7
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Both constraints m b (40, 0) (0, 20) (0, 40) (30, 0) Remember profit was Z = 40b + 50m and the best point was (24, 8) with profit = 1360. So the profit line can be written 1360 = 40b + 50m or m =(1360/50) – (40/50)b. This line has m intercept (0, 1360/50) or (0, 27.2) and b intercept (1360/40, 0) or (34, 0). I put in this profit line here. This is the optimal solution.
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern