Business Analytics AG3

Submission Instruction:

 Individual or Group Submission (groups of 2-4),

 Only one word document (.doc or .docx) by one student from each group,

 Pay attention to the due date and try to make timely submissions (penalty for late submissions),

 Put a table in the first page and include names, student IDs, and a group photo for verification.

 The solution will be briefly discussed in class (in the first session after the due date).

Chapter 11: Linear Optimization Models

CSUSM Power Generation supplies electrical power to residential customers in 9 different cities throughout

the U.S. Its main power generation plants are located in La Belle, Dayton, and San Antonio. The following

table shows the major residential markets for CSUSM Power Generation, the annual demand in each market

(in Megawatts or MWs), and the cost to supply electricity to each market from each power generation plant

(prices are in $/MW).

Distribution Costs

La Belle Dayton San Antonio Demand Requested

(MWs)

Seattle $370.54 $639.38 $125.50 734.47

Portland $391.88 $771.88 $110.52 883.58

San Francisco $178.13 $275.00 $356.26 2450.10

Boise $391.88 $412.50 $237.50 499.75

Reno $237.50 $570.00 $427.50 895.36

Bozeman $457.19 $495.16 $255.94 609.02

Laramie $346.13 $453.89 $391.88 975.17

Park City $356.25 $346.25 $511.72 644.00

a. Assuming there are no restrictions on the amount of power that can be supplied by any of the

power plants, what is the optimal solution to this problem? What is the total annual power

distribution cost for this solution? [In addition to optimal solution, provide the mathematical

formulation and Excel Model.]

b. In reality, however, there are some restrictions on the supply as follows.

 Each power plant has a maximum capacity of 3,800 MWs of power to be supplied,

 The company requires that the supply for the power plant in San Antonio to be at least

20% of the total supply by CSUSM power plants,

Given these realistic constraints, what is the optimal solution? What is the annual increase in

power distribution cost that results from adding these constraints to the original formulation?

c. In part b, if the power demand for Boise increases by 200 MWs, how much the optimal total

cost will increase? Assuming that the total demand requested by cities can increase, which

city’s extra demand will be more costly to be satisfied? Use shadow prices from sensitivity

report to answer this question.

d. Please search for alternative solutions by creating a scenario that forces zero values in the

optimal solution to take positive numbers without increasing the total cost. Provide your

formulation or spreadsheet model.

Chapter 12: Integer Linear Optimization Models

CSUSM Investment Company has collected a total of $3,000,000 from students, staff, and faculty to

invest in 10 mutual fund alternatives with the following diversification and operational restrictions:

 No more than %20 of the total amount should be invested in any one fund.

 No investment lower than $80,000 should be made (i.e., if a fund is chosen for investment, then at

least $80,000 should be invested in it).

 At least one fund should be chosen from each fund type.

 No more than two from Growth & Income funds.

 Investment in fund 5 is conditional on investing in fund 10 (you can invest in fund 5 only if fund

10 is chosen for investment).

 The total amount invested in pure bond funds must be at least 50% of the amount invested in

Growth funds.

Using the following expected returns, formulate and solve a model that will determine the investment

strategy that will maximize expected annual return. What assumptions have you made in your model?

How often would you expect to run your model?

Fund Fund Type Expected Return (%)

1 Growth 5.42

2 Growth 6.65

3 Growth 6.82

4 Growth & Income 7.10

5 Growth & Income 7.84

6 Growth & Income 7.23

7 Stock & Bond 6.35

8 Stock & Bond 6.95

9 Bond 5.2

10 Bond 5.4