MGT 611 - Project Analytics Question 1
A project is made of the following activities:
Duratio Predecessor(s
ES
EF
LS
LF
slac
Task
n
2
k
A
2
B
20
A
C
5
A
Ꭰ
20
C
E
17
B,C,D
F
11
D
G
2
E,F
1. Complete the table above - ES, EF, LS, LF, Slack
2. What is the critical path? What is the project duration?
3. Refer to the critical path you found in 2. Assume that every activity is normally distributed.
Each activity's mean is given in the table above. Each activity's standard deviation is 20%
of its mean (for example, the mean duration of activity A is 2 and its standard deviation is
0.4). What is the probability that the project will last more than 48 days?
Z
F(X)
Z
F(X)
Z
F(x)
-2.5
0.006
-1
0.159
0.5
0.691
-2.4
0.008
-0.9
0.184
0.6
0.726
-2.3
0.011
-0.8
0.212
0.7
0.758
-2.2
0.014
-0.7
0.242
0.8
0.788
-2.1
0.018
-0.6
0.274
0.9
0.816
-2
0.023
-0.5
0.309
1
0.841
-1.9
0.029
-0.4
0.345
1.1
0.864
-1.8
0.036
-0.3
0.382
1.2
0.885
-1.7
0.045
-0.2
0.421
1.3
0.903
-1.6
0.055
-0.1
0.46
1.4
0.919
-1.5
0.067
0
0.5
1.5
0.933
-1.4
0.081
0.1
0.54
1.6
0.945
-1.3
0.097
0.2
0.579
1.7
0.955
-1.2
0.115
0.3
0.618
1.8
0.964
-1.1
0.136
0.4
0.655
1.9
0.971 Question 2
BP has three potential sites where it can build a drilling rig. Due to its past experience, the CEO
has instructed his management team to choose no more than one site.
The costs, the revenues and the estimated outcomes for each site are given in the table below.
Probabilities for the different outcomes
Site
Costs
(in million $)
E1 (Overflowing) E2 (Wet)
Expected revenue: Expected revenue:
30$M
E3 (Dry)
Expected revenue:
5$M
$0
A
2
0
0.8
0.2
B
8
0.3
0.5
0.2
C
6
0.2
0.4
0.4
For example, it costs $8M to build a drilling rig in site B. There's a 30% chance for El with
potential revenue of $30M; 50% chance for E2 with potential revenue of $5M; and a 20% chance
for E3 with zero revenue.
1. Calculate the EMV
2. How much would the company be willing to pay for perfect information on all three sites
(together)? Note that after finding out the true nature of each site, the company can still
choose no more than one site.
3. After a close vote, the company decided not to drill in sites A and B. It was also decided
that site C would be chosen only if it were profitable to drill there. In addition, the
company's CEO determined that site C could not be overflowing (state E1). Assuming
that is true, how much would the company be willing to pay for perfect information on site
C now? Question 3
"Milky Milk" has three (3) warehouses and five (5) retail stores. The company needs to transport
its milk tanks from the warehouses to the stores. The supply in each warehouse, the demand of
each store and the transportation cost per gallon from each warehouse to each store are all given
in the table below:
Store
1
2
3
4
5
Suppl
y
$2.1
$4.1
$1.6
$2.0
$3.3
Warehouse 1
170
0
0
0
0
Warehouse 2 $0.9
$4.2 $5.5
$3.1 $3.6
150
0
0
0
0
Warehouse 3 $3.8
$5.1
$0.8
$4.0
$1.8
130
0
0
Demand
35
70
65
180
40
For example, in warehouse 2 the company has 150 gallons of milk; the demand in store 5 is for 40
gallons; the cost of transporting one (1) gallon of milk from warehouse 2 to store 5 is $3.60.
The objective is to satisfy the demand in each store while minimizing transportation costs.
You may assume that the company can transport parts of a gallon; for example, the company may
transport 3.3 gallons of milk from warehouse X to store Y.
Answer the following and also submit the Solver spreadsheet with your answers. Please indicate
the actual answers in this document.
1. What is the total cost of satisfying all the demand?
2. How much milk should be transported from each warehouse to each store to satisfy the
demand?
