Note that this assignment is a problem set. It is graded only on a reasonable effort to answer each question. Grading does not reflect whether the answer is correct. A solution set will be put on Canvas after the due date of the assignment, so that you can check the correctness of your work, because the grade will only reflect effort.
CPM
You have decided to take up music video making in your spare time and are about to shoot a scene. The tasks involved, along with task times and precedence requirements, are given below.
TASK DESCRIPTION IMMEDIATE TASK TIME
PREDECESSORS (in hours)
A Set up and decorate the set _ 4 B Check the script _ 3
C Apply makeup __ 2
D Fix the stage lighting A 2
E Put on costumes C 3
F Dress rehearsal A, B, E 3
G Check audio/video equipment D 2
H Shoot the scene F, G 2
- Draw the network diagram for this project. How long will it take to complete the project?
- If tasks B and C are delayed by one hour each, how is the project completion time affected?
- Ignore the changes in Question 2. If tasks C and E are delayed by one hour each, how is the project completion time affected?
- Ignore the changes in Question 2 &3. You have been given some money that you may use to speed up any one task in the project. Explain how you would select a task to speed up.
- Ignore the changes in Question 2 – 4. You notice in fact that task A can be split into two tasks, “set up the stage” (task A1) and “decorate the stage” (task A2), each of which takes 2 hours. Also, the crew can fix the stage lighting (task D) while the stage is being decorated. However, the stage must be set up before it is decorated, and before the stage lighting is fixed. Draw a revised network for the project, and identify the critical path.
- What does this tell you about the effect of aggregation of tasks on managing a project? More specifically, what are the tradeoffs involved in splitting a task?
PERT
Marianna D’Andrea at The Enterprise Dynamics Simulation Institute, a computer-simulation consulting firm, has acquired a new client whose project is rather complicated. Furthermore the client is quite concerned about how soon the flight simulator can be delivered as the client has a hard deadline in 14 weeks when they must decide which components of their new software system (if any) to outsource.
Marianna works with a team of associates. Marianna herself interviews the client and deploys the flight simulator. Katerina builds the model while Marianna gathers data. Taddeo develops the graphical user interface for the model. Guido calibrates and tests the model.
The appropriate activities, along with their duration information in weeks, are shown below.
Activity Description Prede-cessors Expected Duration 2
S Interview Client – 2 0
A Build Model S 4.667 1.778
B Gather Data S 5.333 1
C Develop GUI S 3 0.111
D Calibrate A,B 2.5 0.694
E Test D 2.5 0.694
F Deploy Flight Simulator C,E 3 0.444
BUDGET
Assume that each person-week of time spent on Marianna’s project costs $5000. (For example, if Katerina spends 4 weeks on “build model,” then the project will incur a cost of 1 person * 4 weeks * $5000/ (person*week) = $20,000.)
- What is the expected cost of the project and its standard deviation?
- What is the P10, P50, and P90 for the projected cost? Use the PERT methodology to find these costs.
SCHEDULE
- Calculate the expected project completion time and its standard deviation. Identify the critical path. Remember to use mean activity durations, not modes, when determining the critical path.
- A new employee, Penelope, might replace Katerina. The P5, Most Likely, and P95 for her to build the model are 2, 5, and 12 weeks. What would the expected duration and std. deviation be for the “build model” activity now that Penelope has taken over? Calculate using the “modern” 3-point rules: mean = 0.63m + 0.185(a+b) and std. dev. = (b-a)/3.25.
- Assume Penelope does not replace Katerina. But Marianna is verrry nervous anyway. She wants to know when you can guarantee that the project will be complete with 95.0% certainty. (Hint: Compare the 95th percentiles of the critical path and the next longest path.).
- Consider the scenario in which Marianna is pulled off the current project immediately after interviewing the client (activity S) leaving Katerina to complete Marianna’s remaining activities as well as her own. In this case, when can Katerina guarantee that the project will be done with 95 percent certainty?
PREPARATION FOR KRISTEN’S COOKIES
- Fill in the table below: An “operation” is a step in the cookie making process, such as spooning the dough into the baking pan. Depending on the number of operations, you may need to add more rows. (Hint: In the case, you can assume when it says “you” do something, that this is Kristen. For non-people resources, you need only consider the oven and mixer for this assignment. Don’t worry about bowls, trays, etc. )
Operation How much time does
the operation take? Who and/or what performs
the operation?
