Which class should go to the hired hall?
Five classes, five room-slots, and one of them costs money by the head. The class you send to the hired hall is the smallest one, not the biggest, and that is worth $141 a day.
School Starter Optimization free
After you install, this is the model to open.
Fit the Timetable Without a Clash
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
The answer
- Cheapest clash-free day
- $224.60 against $366.20 for the obvious arrangement
- The move
- Data Skills 19 students to the hired hall, not the 78
- Hall bill
- $100.60 $55 hire plus $2.40 a head for 19
- Saved
- $141.60 a day, from one assignment
Five classes and exactly five places to put them: two slots in the lecture theatre, two in the seminar room, and one in a hall you have to hire, which is only free at 09:00. Two rules make this a timetable rather than a list. The seats-short line stops a 78-student class going into a 36-seat room. The two same-lecturer lines are the clash rule: one lecturer teaches both Intro Stats and Data Skills, so those two cannot land in the same slot.
The hired hall is the only place where cost varies, at $55 plus $2.40 a head, and that is where the whole decision lives. The sheet opens on the arrangement that feels obvious, which is that the room shortage is caused by the big class, so the big class goes outside: Intro Stats and its 78 students to the hall for $242.20, everything else indoors, $366.20 for the day.
Click Run and the optimizer returns $224.60, which is $141.60 less, by sending Data Skills and its 19 students to the hall for $100.60 and putting Intro Stats in the lecture theatre at 11:00. When a hired venue charges by the head, the class you push out should be the smallest one that still fits, and the instinct to move the biggest problem is exactly backwards.
Notice the clash rule quietly doing its job as well: Data Skills is in the hall at 09:00, so Intro Stats has to take the 11:00 theatre slot rather than the 09:00 one. Two things worth trying. Raise the hall's fixed fee from $55 to $400 and rerun: the answer does not move at all, because five classes into five places means somebody is in the hall whatever you do, and a fee you cannot avoid never changes a decision.
Only the per-head part does. Then put Data Skills at 46 students instead of 19. Now three classes are too big for a seminar room and you own only two rooms that fit them, so the hall stops being a choice and becomes a capacity release valve: the optimizer sends Research Methods out at $160.60 for a total of $284.60, because it is the smallest class that no longer fits indoors.
What the model does not know is that a 78-person class in a community hall is a worse class, or that students have to walk between rooms. Replace the class names and sizes, put your own recharges in the room-cost line, and add one more same-lecturer line for every lecturer who teaches two of the classes.
The model
It arrives on a tab called Template: Fitting the Timetable, carrying these columns:
- Students (count)
- Hired hall 09:00 (1=yes)
- Placed (count, should be 1)
with the model computed beside the data:
| Same lecturer at 09:00 (Intro Stats and Data Skills) | 1 |
| Same lecturer at 11:00 (Intro Stats and Data Skills) | 1 |
| Total room cost for the day ($) | 366.2 |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
Next question
- Did the workshop actually move anyone?Did the Training Change Each Person's Score?
- How many teachers will next summer actually need?How Many Students Next Term?
- Build the course yourself or license one?Is the New Course Worth Building?
- Does a small cohort need fewer replies?How Many Responses for a Course Survey?
- How often does the cohort miss its budget?What If the Cohort Does Not Fill?
- Two tasks both have slack. Can you spend it twice?When Will the Course Be Ready?
Every model like this one, and the method behind them: Optimization in Google Sheets.