Download Instructions on the Write-Up

COLUMBIA
BUSINESS
SCHOOL
B6015: Decision Models
Spring 2008
Optimization Homework 2
This assignment is to be done in groups. In your write-up, answer all the questions and
provide a thorough description of your models. Each question must be answered in words and
also must include a printout of the spreadsheet (as described below).
Instructions on the Write-Up
Try to limit your write-up to one page of text with support exhibits attached. The exhibits
should include, for each problem, a printout of your optimized spreadsheet (on one page if
possible). Please follow the style of the sample below: all important formulas are described,
constraints are included graphically as “<=” and all important parts of the spreadsheet are
labeled. Of course, the labeling can be handwritten. Another option is to use the comments
feature in Excel.
 To write a comment: either right-click on a cell (and choose “Insert Comment”) or from the
menu choose “Insert|Comment”.
 To get the comments to print: go to File|Page Setup and then pick the Sheet tab and pick
“Comments: as displayed on sheet.” Click OK or Print.
 To get the file to print with row and column headings: go to File|Page Setup and pick the
Sheet tab and check off “row and column headings.” Click OK or Print.
A
B
1 BLAND.XLS
2
3 Product:
4 Barrels to Produce:
5 Profit per Barrel:
6
7
8
9 Ingredients:
10 Corn (lbs)
11 Hops (ozs)
12 Malt (lbs)
13
14
15
C
D
E
Bland Brewery Production Problem
Ale
12
$13
Beer
28
$23
F
Total
Profit:
$800
Product Ingredient Requirements
Total
Ale
Beer
Usage
5
15
480
4
4
160
35
20
980
=SUMPRODUCT($C$4:$D$4,C11:D11)
<=
<=
<=
G
H
I
Decision Variables
C4:D4
Objective Function
=SUMPRODUCT(C4:D4,C5:D5)
Quantity
Available:
480
160
1190
Problem 1: CitiSavings and BankZero Merger (60 points)
CitiSavings (see Problem 2 in Optimization Homework 1) intends to merge with BankZero,
which has its own set of processing centers for credit card bills. BankZero’s processing
centers are in Toledo, OH and Atlanta, GA. The processing capabilities of the full set of
processing centers are as follows:
Los Angeles
Chicago
New York
Toledo
Atlanta
60,000
105,000
100,000
135,000
155,000
Daily processing
capacity
By region, the daily number of bills to be processed for the two companies’ combined
customer bases, and the transit times are as follows:
Bills to be
processed
Los
Angeles
Chicago
New York
Toledo
Atlanta
West
100,000
2
6
8
6
8
Midwest
150,000
6
2
5
2
5
East
100,000
8
5
2
5
5
South
100,000
8
5
5
5
2
CitiSavings recognizes that the combined operations would have significant excess capacity
and contemplates saving money by closing some of the processing centers. CitiSavings
estimates that the cost of closing down a facility is negligibly small, while the daily fixed
costs of operating the five facilities are as follows:
Fixed daily
operating cost
Los Angeles
Chicago
New York
Toledo
Atlanta
$12,000
$21,000
$20,000
$40,000
$30,000
CitiSavings would like to minimize the sum of the operating costs of the facilities, plus the
float.
a) (30 points) Formulate and solve this decision model. According to your analysis, which
facilities should be closed down?
b) (30 points) CitiSavings’ management would like to consider the expansion of the capacity
at the Los Angeles processing center as another option within an overall consolidation plan.
That is, in addition to either closing the center or leaving it at the current capacity, they want
to consider adding the option of expanding LA’s capacity by 15,000 bills-per-day. The
additional cost would be $3,000 per day. Extend the formulation of your problem in a) to
B6015
Optimization Homework 2
2
include this additional option and solve the resulting model. Will this extra-capacity option
be exercised?
Problem 2: Profit Maximization at Campbell Motors (40 points)
Campbell Motors is an auto dealership that specializes in the sales of cars, station wagons and
light trucks. Due to its reputation for quality and service, Campbell has a strong position in the
regional market, but demand remains somewhat sensitive to price. While evaluating the new
models, Campbell’s marketing consultant has come up with the following monthly demand
curves in which price are expressed in thousands of dollars:
Car Demand = 600 – 25 x (Car Price)
Truck Demand = 500 – 18 x (Truck Price)
Wagon Demand = 400 – 11 x (Wagon Price)
For example, if the car’s price is set at $20,000, the monthly demand for cars will be 600 – 25 x
20 = 100. The dealership’s unit costs are $17,000 for cars, $20,000 for trucks and $25,000 for
wagons. Each car requires one hour of prep labor, while each truck requires three hours of prep
labor, and each wagon requires two hours of prep labor. The current staff can supply 350 hours of
labor each month.
Determine prices at which Campbell Motors can maximize its monthly profit from the sales of
cars, trucks and wagons (Allow for fractional demands).
B6015
Optimization Homework 2
3