Linear Programming Scenario: You need to schedule fraternity members to ‘person’ a tailgate reception from 9am until 3pm. Please use the Solver function in Excel.
Based on your insight into attendance and past tailgates, you have determined the minimum number of people you need to properly provide service to the alumni – in 40 minute ‘time slices’. It’s okay to have more during a time period – we just cannot have less.
Starting at 9am-940 – need at least 3 people.
940-1020 – need at least 4 people
1020-1100 – need at least 8 people
1100-1140 – need at least 7 people
1140-1220 – need at least 6 people
1220-1300 – need at least 5 people
1300-1340 – need at least 7 people
1340-1420 – need at least 2 people
1420 -1500 – need at least 2 people
Scheduling shifts: You wish to determine an ‘aggregate’ schedule – for fraternity members to work 2 hour shifts – meaning 3 consecutive ‘time slices’.
This aggregate schedule tells us “How many people work each shift?”.
1. How many 2 hour shifts are possible in this scenario? No funny partial things.
2. For simplicity sake, let’s limit the number of shifts to five: Starting at 9, 1020, 11, 1220 and 1. What’s the minimum number of total fraternity members needed to at least meet the minimum service requirements?
3. There are multiple solutions to Question 2. Fraternity members have indicated that it sucks that they have to work on game day – so they have associated a ‘dislike’ measure with the five shifts: 9 (8), 1020 (6), 11 (3), 1220 (4), 1 (7). Find the best way to at least meet the minimum service requirements my minimizing the total dislike measure (Think of it as a cost).