9.2 Sports Scheduling: An Introduction to Integer Optimization

9.2 Sports Scheduling: An Introduction to Integer Optimization

Quick Question

For each of the decisions below, indicate if the decision variables would be binary, integer, or neither.

  1. We have 20 students, and we want to assign them to one of two groups.

 Binary  check
 Integer  close
 Neither  close
Check Show Solution

Explanation The first and third decisions require binary decision variables, since they are both assignment problems. In the first case, we'll have a binary decision variable for each student (20 decision variables). In the third case, we'll have a binary decision variable for each person (15 decision variables). The second decision requires integer decision variables, since the owner needs to decide how many of each item to send to each store (15 decision variables). Since fractional items would not make sense, the decisions are integer. The fourth decision does not need binary nor integer decision variables, because the amount in grams can be fractional.

  1. The owner of 5 clothing stores needs to decide how many shirts, pants, and hats to send to each store, given historical sales data.

 Binary  close
 Integer  check
 Neither  close
Check Show Solution

Explanation The first and third decisions require binary decision variables, since they are both assignment problems. In the first case, we'll have a binary decision variable for each student (20 decision variables). In the third case, we'll have a binary decision variable for each person (15 decision variables). The second decision requires integer decision variables, since the owner needs to decide how many of each item to send to each store (15 decision variables). Since fractional items would not make sense, the decisions are integer. The fourth decision does not need binary nor integer decision variables, because the amount in grams can be fractional.

  1. After try-outs, the coach of a basketball team needs to decide which people should make the team (15 people tried out).

 Binary  check
 Integer  close
 Neither  close
Check Show Solution

Explanation The first and third decisions require binary decision variables, since they are both assignment problems. In the first case, we'll have a binary decision variable for each student (20 decision variables). In the third case, we'll have a binary decision variable for each person (15 decision variables). The second decision requires integer decision variables, since the owner needs to decide how many of each item to send to each store (15 decision variables). Since fractional items would not make sense, the decisions are integer. The fourth decision does not need binary nor integer decision variables, because the amount in grams can be fractional.

  1. A fertilizer company is trying to decide how much (in grams) of three different compounds to add to each bag of fertilizer.

 Binary  close
 Integer  close
 Neither  check
Check Show Solution

Explanation The first and third decisions require binary decision variables, since they are both assignment problems. In the first case, we'll have a binary decision variable for each student (20 decision variables). In the third case, we'll have a binary decision variable for each person (15 decision variables). The second decision requires integer decision variables, since the owner needs to decide how many of each item to send to each store (15 decision variables). Since fractional items would not make sense, the decisions are integer. The fourth decision does not need binary nor integer decision variables, because the amount in grams can be fractional.

Note that you will need to answer all of the questions above before checking your answers.

Course Info

Learning Resource Types

theaters Lecture Videos
notes Lecture Notes
assignment_turned_in Problem Sets with Solutions