1 / 11

PROJECT PLANNING

PROJECT PLANNING. BY. MONTE CARLO SIMULATION. Part II. Prof. Dr. Ahmed Farouk Abdul Moneim. Probability Density Functions Activities Durations :. Rand. Triangular. 0 ≤ Rand ≤ 1. a. m. t. b. Rand. Truncated Normal. t. t MIN. t e. t MAX. Rand. Truncated Exponential. t.

colby-freeman
Download Presentation

PROJECT PLANNING

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. PROJECT PLANNING BY MONTE CARLO SIMULATION Part II Prof. Dr. Ahmed Farouk Abdul Moneim

  2. Probability Density Functions Activities Durations: Rand • Triangular 0 ≤ Rand ≤ 1 a m t b Rand • Truncated Normal t t MIN t e t MAX Rand • Truncated Exponential t Rand t MIN t MAX From Tables OR Excel Normal Distribution • Truncated Weibull Φ(Z) t t MIN t MAX Z Prof. Dr. Ahmed Farouk Abdul Moneim

  3. Truncated Normal Distribution GIVEN a Probability = Rand Find the corresponding value of t t-Plane Show that the following function is the right PDF T MIN t T e T MAX f (Z) Rand Z-Plane 0 Z Z MIN Z MAX Z Take the Inverse function of Φ (Φ-1 ) Prof. Dr. Ahmed Farouk Abdul Moneim

  4. Triangular Distribution Rand 1-Rand GIVEN a Probability = Rand Find the corresponding value of t Rand H h h Area of the Triangle = (b-a)*H/2 = 1 a m t b t Then Area of the Left part of the Triangle = (m-a)*H/2 = If Otherwise Prof. Dr. Ahmed Farouk Abdul Moneim

  5. f(t) • Truncated Exponential Distribution Consider the following Probability Density Function μ - T Min To show that this is a PDF, the integral over the whole Range R should equal to one Now, find an expression for the mean μ t T Max T Min t Important Notice! For TRUNCATED Exponential Distribution, The following condition SHOULD BE SATISFIED As R tends to Infinity Prof. Dr. Ahmed Farouk Abdul Moneim

  6. f(t) • Truncated Exponential Distribution Rand t T Max T Min t Prof. Dr. Ahmed Farouk Abdul Moneim

  7. f(t) • Truncated Weibull Distribution Consider the following Probability Density Function T Min t t Prof. Dr. Ahmed Farouk Abdul Moneim

  8. Truncated Weibull Distribution f(t) Rand T Min t t Prof. Dr. Ahmed Farouk Abdul Moneim

  9. ** From Tables or Excel *** **** Prof. Dr. Ahmed Farouk Abdul Moneim

  10. SUMMARY • Distribution • Simulated Time t • Truncated Normal If • Triangular Otherwise • Truncated Exponential • Truncated Weibull Prof. Dr. Ahmed Farouk Abdul Moneim

  11. Example See Excel Sheet for solution Prof. Dr. Ahmed Farouk Abdul Moneim

More Related