QSO 520 Module 8 Homework Complete Solution

Question: #8458

Homework Questions

A plant engineering group needs to set up an assembly line to produce a new product. The following table describes the relationships between the activities that need to be completed for this product to be manufactured:

Activity   Days   Immediate
Predecessors
   a   m   b
A   3   6   8
B   5   8   10   A
C   5   6   8   A
D   1   2   4   B, C
E   7   11   17   D
F   7   9   12   D
G   6   8   9   D
H   3   4   7   F, G
I   3   5   7   E, F, H

If using Crystal Ball, assume that the duration of each activity follows a BetaPert distribution, with the three time estimates shown for that activity. Otherwise, assume that each activity time is normally distributed with expected time and standard deviation computed as shown in equations 7-6 and 7-8, respectively, found below. Round off all activity times to two decimal places.

(a) Use simulation to determine the probability that the project will finish in 37 days or less.

(b) Use simulation to determine the probability that the project will take more than 32 days.

Useful information:
This week we will be looking at using simulations to provide guidance for decision analysis problems. Simulations, especially Monte Carlo simulations, are used widely in various fields.
Some tips for the homework:
1. In the HW problem, we are concerned with timing of a process, and the probabilities that the overall process time falls within a specified range.
2. Each of the activities in the process have a 3-point estimate associated with them which suggests a PERT distribution.
3. Use PERT analysis principals to calculate an expected value and standard deviation for use in the normal distribution random function in Excel. The equations for this equations 7-6 and 7-8, shown below. Equation 7-6 is the beta three-point estimate formula and 7-8 is the standard deviation calculation for a three point estimate distribution.
4. You will need to set up calculation of the overall process time by calculating times for each of the activities using random functions in Excel operating on the expected value and standard deviation.
5. Then you will need to 'roll up' the individual activity times into an overall process time, taking into account the dependencies of the individual activities (sketching a network diagram may be helpful here).
6. The final time calculation for the overall process can then be duplicated in a data table like the one used in the Judith's Limousine Example in the text (see below). As in the text example, 200 simulation runs is also a good number to take for this problem, as well. This data table can be used to calculate the probabilities asked for in the problem statement using the COUNTIF function in Excel.

Figure 7.6 Complete AON Network for General Foundry

One rule that we especially recommend is to place the nodes in such a fashion that all arrows point in the same direction. To achieve this, we suggest that you first draw a rough draft version of the network to make sure all the relationships are shown. Then you can redraw the network to make appropriate changes in the location of the nodes. As with the unique starting node, it is convenient to have the project network finish with a unique ending node.
Figure 7.8 Earliest Start Times and Earliest Finish Times for General Foundry

Judith’s Limousine Example:

Solution: #8468

QSO 520 Module 8 Homework Complete Solution

PATHS A-B-D-E-1 A-B-D-F-I A-B-D-G...