1 / 23

A Case Study

A Case Study. Jake Blanchard Spring 2010. Introduction. These slides contain a description of a case study of an uncertainty analysis You should use this as a model for your final projects. The Case. We are concerned with widget production

bebe
Télécharger la présentation

A Case Study

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. A Case Study Jake Blanchard Spring 2010 Uncertainty Analysis for Engineers

  2. Introduction • These slides contain a description of a case study of an uncertainty analysis • You should use this as a model for your final projects Uncertainty Analysis for Engineers

  3. The Case • We are concerned with widget production • The question is how many widgets should we produce in order to maximize profit • Assume you are a manufacturer of widgets, which are purchased seasonally • Fixed production costs are $40,000 per year • The unit cost varies between $2,000 and $2,400 above the fixed costs, depending on the year. • Demand typically fluctuates from 30 to 50 units per year. • The off-season sales price is $500 each for the first ten units and between 0 and $500 for the remainder. • The sales price is fixed at $8,000 per unit. Uncertainty Analysis for Engineers

  4. Variables • P=profit • M=# manufactured • D=demand • S=in-season sales • UP=unit price • UC=unit cost • TO=total off-season revenue • Off=off-season price (first 10) • OffExtra=price for rest of widgets • I=inventory (M-S) • F=fixed cost • TC=total cost • R=revenue Uncertainty Analysis for Engineers

  5. Algorithm • P=R-TC • TC=F+UC*M • R=UP*S+TO • I=M-D Uncertainty Analysis for Engineers

  6. Input Distributions • To start, assume all distributions are uniform, with the limits defined on the previous slide • Also consider the case where the distributions are normal, with the same means and variances as the uniform distributions Uncertainty Analysis for Engineers

  7. Analysis • What is profit, assuming all variables are at their mean (this is first order approximation of the mean)? • What is first order estimate of variance? • What is sensitivity for all random inputs? • Plot histogram for profit. • Plot histogram for normal distributions. Uncertainty Analysis for Engineers

  8. First Order Estimate of Profit • Putting in all mean values and setting M=40 gives a profit of $192,000 • If we vary M, the first order estimate of the mean profit is Uncertainty Analysis for Engineers

  9. First Order Estimate of Variance • For M=40-, variance is estimated to be 2.1e7 $2 • For M=40+, variance is estimated to be 1.9e9 $2 Uncertainty Analysis for Engineers

  10. Sensitivity Uncertainty Analysis for Engineers

  11. Sensitivity Uncertainty Analysis for Engineers

  12. Results for M=40 • Mean Profit from MC is $170,000, compared to $190,000 first order estimate • Mean variance from MC is 6.6e8, compared to estimates of 2.1e7 below 40 and 1.9e9 above 40 Uncertainty Analysis for Engineers

  13. Profit Histograms – M=30 Uncertainty Analysis for Engineers

  14. Profit Histograms – M=40 Uncertainty Analysis for Engineers

  15. Profit Histograms – M=50 Uncertainty Analysis for Engineers

  16. Mean Profit vs. M Uncertainty Analysis for Engineers

  17. Normal Distributions • Now repeat for normal distributions Uncertainty Analysis for Engineers

  18. Results for M=40 • Mean Profit from MC is $175,000, compared to $190,000 first order estimate (Unif dist gave $170,000) • Mean variance from MC is 6.64e8, compared to estimates of 2.1e7 below 40 and 1.9e9 above 40 (Unif Dist gave 6.6e8) Uncertainty Analysis for Engineers

  19. Profit Histograms – M=30 Uncertainty Analysis for Engineers

  20. Profit Histograms – M=40 Uncertainty Analysis for Engineers

  21. Profit Histograms – M=50 Uncertainty Analysis for Engineers

  22. Mean Profit vs. M • No change in this plot Uncertainty Analysis for Engineers

  23. Decision • How many widgets should we manufacture? Uncertainty Analysis for Engineers

More Related