BANA201B The National Basketball Association

BANA201B

Prof. John Turner

Homework 2

Please read “Homework Formatting Instructions”

Be sure to read the description below carefully

The National Basketball Association (NBA) is composed of 30 teams which are divided into two

conferences of three divisions with five teams each. NBA games are divided into regular season

and playoffs. The NBA regular season follows an asymmetrical round-robin tournament

(otherwise known as uneven paired competition) format where the number of games between any

two teams depends on their conference and divisional affiliations. In an NBA season each team

plays 82 games, 41 at home and 41 on the road; in total, there are 1230 games in an NBA season.

Each regular season takes approximately 180 days, spanning from mid-October to mid-April.

Games are scheduled throughout the day, every single day except the All-star game break which

is a one-week period in which 代 写BANA201B The National Basketball Association the NBA All-star game as well as other events (e.g., slam dunk

contest, three-point shooting contest, rising stars match, etc.) take place. Holidays (e.g., Christmas

and MLK day) and weekends are more popular times to watch NBA games. Multiple national and

local TV channels air the NBA games, including ESPN, TNT, ABC, and NBA-TV.

Scheduling the entire 1230-game season and assigning games to dates, arenas, and TV channels is

an extremely challenging task. Matt Winick, Senior Vice President of Scheduling and Game

Operations is the main person responsible for producing the NBA regular season schedule. Matt

has decided to break the scheduling task into two parts: i) for each four-day period, selecting a set

of games that should be played, and then ii) assigning the selected games to specific days within

this 4-day period. Matt’s wishes to produce a schedule that maximizes the revenue generated from

airing TV commercials.

In this assignment, you will help Matt produce the NBA game schedule for a four-day time period

which spans Thursday, February 4 through Sunday, February 7. The following table liststhe games

Matt has selected to be played during this time period, as well as popularity ratings for each game

on a scale of 0 to 2, with 0 being the least popular and 2 being the most popular. The popularity

rating is determined by the ranking of the host and guest teams, location, and overall popularity of

those franchises.

Matt estimates that the NBA’s revenue for each game is directly related to its popularity rating. In

general, games played on Thursday generate $1 million in revenue for each popularity point,

Friday games generate $1.5 million in revenue for each popularity point, and weekend games

generate $2 million in revenue for each popularity point. However, since Sunday, February 7th

coincides with the National Football League (NFL) Super Bowl, the games played on that Sunday

will generate only $0.5 million in revenue for each popularity point. As an example, the first game BANA201B

Prof. John Turner

(Celtics at Lakers) in the table below would generate $2M in revenue if played on Thursday, $3M

if played on Friday, $4M if played on Saturday, and $1M if played on Sunday.

Game

Abbreviation Popularity Rating

 

Matt must consider the following managerial constraints when producing the schedule:

1. Each team should play at most one game each day.
2. At least one game with a popularity rating of 1.25 or higher should be assigned to each

day.

1. Due to using the same arena (i.e., Staples Center) the two Los Angeles teams, Lakers and

Clippers, cannot host a game on the same day.

1. Because of Super Bowl, Sunday cannot have a game with popularity rating above 1.4 (it is

okay to have a game with popularity rating of exactly 1.4 on Sunday).

1. Continuing their road trip from the days prior to this 4-day block, the New York Knicks

and Utah Jazz will need to play the rest of their road games as back-to-back games on

Thursday and Friday, with no games on Saturday and Sunday to have time to get back to

their home cities for their Monday home games.

Given the above information, please answer the following questions:

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?

2. Solve this problem using Python/Pyomo and Gurobi.
3. Write code to represent the model in Python/Pyomo and solve it with Gurobi. Withyour report, include a pdf generated by printing the Jupyter Notebook to pdf afterrunning all parts of the notebook (so the pdf includes both your code and the outputfrom the code, as described in the “Homework Formatting Instructions” document).

Which games are assigned to each of the 4 days? What is the maximum revenue?

1. Matt is notified by the NBA commissioner about a new restriction on the number of backto-back games (i.e., a team plays games on two consecutive days, e.g., Thursday andFriday). According to this new restriction and in order to have equity in the number ofback-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 BANA201B

Prof. John Turnerand Los Angeles Lakers. Explain in detail how the current formulation should be modifiedto address the back-to-back games constraint. Do you expect the total revenue to be higheror lower than in your original formulation, once this constraint is added to the model?Apply these changes and re-solve the problem. How much does the total revenue change?

4. The NBA usually selects very popular games to be broadcast on national television.

Multiple TV channels including TNT, ESPN, ABC, and NBA-TV have doubleheader ortripleheader series, featuring two or three highly-rated games within the week. In particular,the TNT doubleheader series, with half-time report by NBA Hall of Famers ShaquilleO’Neal and Charles Barkley, normally hosts the most popular games. The NBA wishes to

assign two highly-popular games to a TNT doubleheader on one of the days within thefour-day block from February 4th-7th. The NBA wants to make sure that if game 1 (Celticsat Lakers) is selected, then one of the following two games, game3 (Blazers at Bucks) or

5 (Jazz at Nets), should be included in the TNT doubleheader. Modify your formulationfrom part 1 of this assignment to incorporate the doubleheader scheduling requirement.Please describe any variables and constraints that you add or modify in your formulation.You do not need to re-solve the problem.