BANA201B_Homework_2_Group_B2
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University of California, Irvine *
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Course
149101
Subject
Industrial Engineering
Date
Apr 3, 2024
Type
Pages
7
Uploaded by SuperHumanLoris4024
BANA201B
Homework 2
Group members: Group B2
Abby Chung
Ambuj Upadhyay
Aysan Habibzadeh
Ping-Yen Chung
Siddharth Yadav
Question 1
Help Matt formulate the problem of scheduling games during the four-day period while
maximizing revenue. Explicitly write down your decision variables, the objective function,
and constraints. What kind of optimization problem have you defined?
Solution 1
To help Matt formulate the problem of scheduling NBA games over the specified four-day period
to maximize revenue, we'll define the decision variables, the objective function, and the
constraints, detailing the type of optimization problem we have defined.
Decision Variables:
Let x
ij
be a binary decision variable where:
- i represents the game (1 to 20),
- j represents the day (1 for Thursday, 2 for Friday, 3 for Saturday, 4 for Sunday),
- x
ij
if game i is scheduled on day j, and 0 otherwise.
Objective Function:
Maximize total revenue from TV commercials, which is the sum across all games and days of
the product of the game's popularity rating, the revenue multiplier for the day, and whether the
game is scheduled on that day x
ij
Where revenue
ij
is the revenue generated by scheduling game i on day j, calculated by
multiplying the game's popularity rating by the day's revenue multiplier.
Constraints:
1. Game Slot Availability:
2. Each Team Plays At Most One Game Per Day
3. At Least One High Popularity Game Per Day:
- For each day, at least one game with a popularity rating of 1.25 or higher must be scheduled.
4. Los Angeles Teams Constraint:
- Ensure the Lakers and Clippers do not host on the same day.
5. Super Bowl Sunday Constraint:
- No game with a popularity rating above 1.4 is scheduled on Sunday.
6. Knicks and Jazz Back-to-Back Games Constraint:
- Ensure these teams play on Thursday and Friday, with no games on Saturday and Sunday.
Type of Optimization Problem:
This is a
Mixed Integer Linear Programming (MILP)
problem. It's linear because the objective
function and all constraints are linear with respect to the decision variables. It's mixed-integer
because the decision variables are binary (either 0 or 1).
This formulation captures the essence of the scheduling challenge, balancing the need to
maximize revenue against the operational and managerial constraints imposed by the NBA
schedule.
Question 2
Solve this problem using Python/Pyomo and Gurobi.
a. Write code to represent the model in Python/Pyomo and solve it with Gurobi. With your
report, include a pdf generated by printing the Jupyter Notebook to pdf after running all
parts of the notebook (so the pdf includes both your code and the output from the code,
as described in the “Homework Formatting Instructions” document).
Solution 2.a
Jupyter notebook attached(BANA201B_Group_B2_Question_2.ipynb)
PDF of the Jupyter notebook attached(BANA201B_Group_B2_Question_2.pdf)
b. Which games are assigned to each of the 4 days? What is the maximum revenue?
Solution 2.b
Day
Match
1
2, 4, 5, 8, 14
2
1, 9, 11, 18, 19, 20
3
3, 6, 7, 15, 16, 17
4
10, 12, 13
The match 1 should be scheduled on day 2
The match 2 should be scheduled on day 1
The match 3 should be scheduled on day 3
The match 4 should be scheduled on day 1
The match 5 should be scheduled on day 1
The match 6 should be scheduled on day 3
The match 7 should be scheduled on day 3
The match 8 should be scheduled on day 1
The match 9 should be scheduled on day 2
The match 10 should be scheduled on day 4
The match 11 should be scheduled on day 2
The match 12 should be scheduled on day 4
The match 13 should be scheduled on day 4
The match 14 should be scheduled on day 1
The match 15 should be scheduled on day 3
The match 16 should be scheduled on day 3
The match 17 should be scheduled on day 3
The match 18 should be scheduled on day 2
The match 19 should be scheduled on day 2
The match 20 should be scheduled on day 2
Maximum Revenue = $31.95 million
Question 3
Matt is notified by the NBA commissioner about a new restriction on the number of back-
to-back games (i.e., a team plays games on two consecutive days, e.g., Thursday and
Friday). According to this new restriction and in order to have equity in the number of
back-to-back games among all the teams throughout the season, Matt cannot assign
back- to-back games for the following two teams during the four-day time period:
Phoenix Suns and Los Angeles Lakers. Explain in detail how the current formulation
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