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Review problem 1 QP dolls, Inc., has developed a new doll it

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Review problem 1 QP dolls, Inc., has developed a new doll it feels could turn into a collector s item through proper advertisement. The PERT/ CPM network ... – PowerPoint PPT presentation

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Title: Review problem 1 QP dolls, Inc., has developed a new doll it


1
Review problem 1
  • QP dolls, Inc., has developed a new doll it feels
    could turn into a collectors item through
    proper advertisement. The PERT/ CPM network
    shown models the activities (or work packages) of
    the project.

H
I
B
A
D
F
C
G
E
2
  • Distribution of the total budgeted cost of
    5,280,000 and expected completion times (in
    weeks) for each of the work packages are
    summarized in the following table

3
  • a. Determine an earliest and latest schedule for
    each work package. Go to file ch7-16.cpm

4
Review problem 1 - Continued
  • Consider the situation faced by QP Dolls, Inc. in
    problem 16. Management is giving some thought to
    putting extra resources into the project so that
    it can be completed within one-half year (26
    weeks). Accordingly, each work package has been
    studied, and a set of crash times in weeks and
    costs has been developed

5
Compare
6
  • a. Determine a schedule for the work packages
    which minimizes the total cost of completing the
    project within 26 weeks. What is the minimum
    total cost? Go to file ch7-18a.cpm

7
  • b. Suppose QP will incur administrative and
    operational costs totaling 24,000 per week
    during this project. Modify your model to take
    into account these costs and solve for the
    optimal scheduling of the work packages. Did it
    change from the solution in part (a)? Go to file
    ch7-18b

Let us first understand how to model the crash
Problem using linear programming. Look at the
following small example.
8
Normal Crash Activity
Cost Time Cost Time A 1000 10 5000
8 B 2000 12 4500 8
C 1200 7 2200 6 D
1800 8 3000 5 E
500 8 1000 7
8
12
D
B
10
Finish
Due date 20
A
  • Define X as the start time of an activity.
  • Define Y as the amount of time an activity
  • is crashed.

C
E
7
8
Notice that an activity cannot start before all
its immediate predecessors are completed. This
observation leads to the following relationship
between activity A and B (for example) XB gt XA
time to complete activity A, or XB gt XA (10
YA)
Start time of B
Start time of A
Actual time to complete A after it was crashed.
This is how you build all the network constraints
one constraint for each arc, covering all the
arcs. Also, note that X(FIN) gt XD(8-YD) and
X(FIN) gt XE(8-YE).
9
In addition to these constraints, there are
constraints on the time each activity can be
crashed. For example, activity C can be crashed
by 1 at most, but activity D can be crashed by 3
at most.
Therefore we have to add the following set of
constraints YA lt 2 (10-8) YB lt 4
(12-8) .
The objective function is determined by the case
we solve Case 1 To minimize crash costs
formulate the objective function as
follows Minimize2000YA 625YB500YE and add
the due date constraint to the model, such as
X(FIN) 20. Otherwise, the optimal solution
will be not to crash and incur zero crash
costs. Case 2 To minimize the time to complete
the project change the objective to Minimize
X(FIN) dont forget that X(FIN) is the duration
of the project. You need to eliminate the
constraint X(FIN) 20 since you try to minimize
X(FIN), and instead limit the amount of funds
used to a given budget by adding the constraint
2000YA625YB500YEltTotal budget available
Total normal costs. Case 3 To minimize the total
crash costs operating costs we assume the
operating costs are proportional to the time it
takes to complete the project. Suppose the
operating costs are 100 per one time unit (a
week for example). Then we add 100X(FIN) to the
objective function formulated in case 1 and
eliminate the constraint X(FIN) 20.
10
  • b. Suppose QP will incur administrative and
    operational costs totaling 24,000 per week
    during this project. Modify your model to take
    into account these costs and solve for the
    optimal scheduling of the work packages. Did it
    change from the solution in part (a)? Go to file
    ch7-18b

11
Note that the objective function consists of
crashing costs operational costs.
X(FIN) gt XI8-YI or -XIX(FIN)YIgt8
12
The solution did not change
13
  • c. Suppose QP only budgeted 6 million for this
    project. What is the minimum time to complete
    this project if the weekly fixed costs are
    included in the model.Go to file ch7-18c2

6,000,000-5,280,000720,000
This objective function minimizes the completion
time of the project for a given budget.
14
Minimum time 30 weeks with a crash budget of
720,000
15
Review problem 2Text problem 21
  • Golden West Homes is developing a new modular
    home model. The following table outlines the
    activities of the project. Times are expressed
    in days

16
Finding critical path
  • a. Determine the expected completion time and
    the critical path for this project. Go to file ch
    7-21c for a solution without a consultant

Expected completion time 117 days. Critical
path A B C D E J L N R
17
Calculating probabilities - using WINQSB
  • b. Because of production considerations, Golden
    West will lose 10,000 if this project is not
    completed within 114 days. What is the
    probability that the project will be completed
    within 114 days?Perform probability analysis
    with WINQSB (in Results menu) P(Completion in
    114 days) .2957

18
Applying the Expected value criterion
  • c. Suppose Golden West were to hire a meeting
    planning consultant to hold the dealer meetings
    (activity N). This would cost Golden West an
    additional 1000, but the activity is guaranteed
    to take exactly three days. Considering the
    10,000 loss if the project is not completed in
    114 days, should Golden West hire the consultant?
    Go to file ch 7-21cc (with consultant).Because
    there is no variance, all the time estimates of
    activity N are the same.

19
With activity N expected to be completed in 3
days, the project is expected to be completed in
115 days. The probability to complete in 114 days
is .4284.
Expected cost (No consultant) .2957(0)(1-.2957)(
10000)7043 Expected cost (w/consultant).4284(0)
(1-.4284)10000)10006716
Hire the consultant
20
  • d. What is the most Golden West should be willing
    to pay for a meeting planning consultant who
    could hold dealer meetings in exactly three
    days?

7043 - 5716 1327
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