15.071 | Spring 2017 | Graduate

# The Analytics Edge

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

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

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

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

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.