Operations Research
Project 1
AmeriBank Case
Fahad Alhaqbani and Blake Fulbright
10/23/2013
Executive Report
Case Summary)
The president of AmeriBank is Rob Richman. He is not happy about the situation of his
bank because the competition of non-banks and foreign banks are taking his customers. There
are a good number of branches for Ameribank in the United States. Rob’s solution to his
decreasing customer base is to implement web banking which would allow his customers to
bank from home and make transactions from their personal computers. Rob’s realized that he
needs to survey people in different regions to obtain knowledge of how well Web banking will
work in each region. He outsources the surveying project to a few different companies to see
which company is willing to offer the cheapest bid. Rob has also sent out a list of requirements
that each company needs to meet in order for him to accept the bid.
Part A)
After receiving the information from Rob Richman, the president of AmeriBank, we
came to an understanding on what he wants Sophisticated Surveys to do. We took the
information we acquired from the list and implemented it into the OPL software. We input our
twelve variables into the software; these variables represented the number of people from
each area and their different ages. Initially we had nine constraints as well, three of which were
constraints on the amount of people surveyed in each area. Four more were created to
constrain the amount of people surveyed in each age group. Another was input to limit the
total number of people surveyed overall. And finally we know that we can’t survey less than
zero people from each age group and region so we made non-negativity constraints as well.
Once all of our constraints were input into the code and it was running without any bugs we
obtained the solution to how many people we should survey from each age group and area.
Part B)
We then used the solution that the OPL program gave us and multiplied it by $1.15
because as a company that is trying to make a profit we need to up charge our customer
(AmeriBank). The solution the OPL program output was $11,200 for the cost of the surveying
project. But once we took into account our profit margin it became $12,880.
1
Part C)
After reviewing our first bid he then indicated that he wanted at least fifty people from
each age group and area to be surveyed. So we added more constraints to fit the needs of
AmeriBank. After inputting the constraints and running the code we obtained our new bid
amount which we, again, multiplied by our $1.15 to account for our profit margin. The new bid
that was obtained was $13,095.625.
Part D)
Once AmeriBank reviewed our second bid they realized they wanted to limit the amount
of 18-25 year-olds surveyed to 600. And also to limit the number of people surveyed from
Silicon Valley to 650 people. After taking this into consideration and then manipulating our
constraints to fit the needs of Ameribank we obtained a new bid (including our profit margin) of
$13.311.25.
Part E)
Sophisticated Surveys made an assumption that reaching people in the younger age
group would be cheaper but they learned that this wasn’t true. The new costs for the 18-25
year-old age groups for the Silicon Valley, Big cities, and Small towns are $6.50, $6.75, and
$7.00 respectively. Once our code was changed to account for the incorrect assumption we ran
our code to find the new bid cost. The new bid cost with the profit margin included was
$13,828.75.
Part F)
Finally, Rob wanted to insure the sampling of people surveyed was done to his exact
wants so he imposed an exact percentage of people surveyed in each age group and also for
each region. These requests were then taken into consideration via the OPL program and once
the code was changed correctly the program was ran to obtain the new bid cost. The new bid
cost including the profit margin was $14,346.25.
2
Technical Report
Part A)
We took the information we acquired from the list and implemented it into the OPL software.
We used variables to be represented the number of people from each area and their different
ages. We obtained the solution to how many people we should survey from each age group and
area. Refer to text below for exact variable representation, the objective function and they
initial constraints. Refer to figure A in the appendix for the OPL code.
Variables
P1 is the number of people in the age group of 18-25 in Silicon Valley.
P2 is the number of people in the age group of 26-40 in Silicon Valley.
P3 is the number of people in the age group of 41-50 in Silicon Valley.
P4 is the number of people in the age group of 51 and up in Silicon Valley.
P5 is the number of people in the age group of 18-25 in big-cities.
P6 is the number of people in the age group of 26-40 in big-cities.
P7 is the number of people in the age group of 41-50 in big-cities.
P8 is the number of people in the age group of 51 and up in big-cities.
P9 is the number of people in the age group of 18-25 in small towns.
P10 is the number of people in the age group of 26-40 in small towns.
P11 is the number of people in the age group of 41-50 in small towns.
P12 is the number of people in the age group of 51 and up in small towns.
Age groups
Region
Silicon Valley
Big cities
Small towns
18-25
$4.75
$5.25
$6.50
25-40
$6.50
$5.75
$7.50
3
41-50
$6.50
$6.25
$7.50
51+
$5.00
$6.25
$7.25
Objective Function
Minimize:
Z=4.75*P1 + 6.50*P2 + 6.50*P3 + 5*P4 + 5.25*P5 + 5.75*P6 + 6.25*P7 + 6.25*P8 + 6.50*P9 + 7.50*P10 +
7.50*P11 + 7.25*P12
Constraints
1)
2)
3)
4)
5)
6)
7)
8)
9)
P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8 + P9 + P10 + P11 + P12 = 2000
P1`+ P2 + P3 + P4 >= 300
P5 + P6 + P7 + P8 >= 700
P9 + P10 + P11 + P12 >= 400
P1 + P5 + P9 >=400
P2 + P6 + P10 >= 550
P3 + P7 + P11 >= 300
P4 + P8 + P12 >= 300
P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12 >=0
Part B)
Sophisticated survey’s does not work for free so they want to ensure they receive a profit. They add a
15% profit margin to the original cost to ensure they make a profit. Once the bid created by the OPL
program is attained you then multiply by 1.15 which is 15% to find out the final bid cost with the
profit margin incorporated for Ameribank. Refer to the equation below for profit margin
calculation.
(4.75*600 + 6.5*0 + 6.5*0 + 5*300 + 5.25*0 + 5.75*550 + 6.25*150 + 6.25*0 + 6.50*250 + 7.50*0 +
7.50*150 + 7.25*0)*$1.15
($11200)*1.15 = $12880
4
Part C)
The first bid we proposed wasn’t good enough for Rob so he imposed a requirement that at least fifty
people from each age group and region would get surveyed. To see how we accounted for this
requirement refer to figure C in the appendix. Below is text explaining the constraints and what the new
bid price will be after adding those constraints.
Additional constraints:
p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12 >=50
Solution with objective = 11,387.5
The new bid is ($11,387.5)*1.15 = $13095.625
Part D)
The new constraints are that no more than 600 people can be surveyed from the 18-25 year-old
age group and no more than 650 can be surveyed from the Silicon Valley population. Once we
implement these constraints into our OPL code and run the program it will give us our new bid cost prior
to factoring in the profit margin. Below is text that gives the new constraints and bid price. Refer to
figure D in the appendix for the new code created for the constraints.
P1 + P5 + P9 <=600, P1 + P2 + P3 + P4 <= 650
Solution with objective value = 11,575
The new bid is ($11,575)*1.15 = $13,311.25
Part E)
Sophisticate Surveys didn’t realize the actual cost of surveying the younger age group was
higher than initially assumed. Below is a table indicating the new cost for people of 18-25 years
old in all regions. Refer to figure E in the appendix for the new code with these new costs
incorporated (look at objective function).
Solution with objective = $12,025
($12,025)*1.15 = $13,828.75
Region Survey Cost Per Person
Silicon Valley
$6.50
Big cities
$6.75
Small towns
$7.00
5
Part F)
Rob then imposes more requirements of the surveying companies. He fixes the percentage of
people surveyed for each age group and the amount of people surveyed in each region. Below
are tables indicating the new percentages for each age group and region. Refer the figure F in
the appendix for the new code in OPL.
Population Percentage of People Surveyed
18-25
26-40
41-50
51+
25%
35%
20%
20%
Population Percentage of People Surveyed
Silicon Valley
20%
Big cities
Small towns
50%
30%
Solution with objective = $12,475
($12,475)* 1.15 = $14,346.25
Recommendations)
Our recommendations for Ameribank would depend on what Ameribank finds most important
about the surveying project. If they are worried about cost then I would recommend choosing
the first bid introduced because it has the lowest cost although it doesn’t survey all the age
groups from each region. If they want to make sure at least some people from each region and
age group get surveyed then I would recommend the second bid introduced even though it is a
higher cost. So it depends on whether Ameribank believes the higher cost of surveying is worth
the benefit of surveying a broader amount of people.
6
APPENDIX
Figure A
7
Figure C
8
Figure D)
9
Figure E)
10
Figure F)
11