Interactive example
Six sessions.
A real assignment problem.
In this fictional example, a tutoring provider needs qualified instructors at two centers this afternoon.
Change who is available, how many seats are needed or how much you can spend. See the resulting schedule and what prevents any gaps from being filled.
Try the scheduling toolChange the afternoon.
One afternoon across two centers
Every requested seat has a place.
Same inputs.
Same operating limits.
Modeled costs, not achieved savings.
14:00–15:00
8 / 8 seats 1 room
8 / 8 seats 1 room
15:00–16:00
8 / 8 seats 1 room
8 / 8 seats 1 room
16:00–17:00
8 / 8 seats 1 room
8 / 8 seats 1 room
Math and science describe required qualifications. One instructor per group of up to eight learners. No instructor changes center during the afternoon.
What makes this plan work
All 48 requested seats fit the hard operating constraints. The objective selects the lowest cost among plans with this coverage; it does not optimize fairness or teaching quality.
What changed from the baseline?
The baseline fills the published session order, North then Riverside, choosing the cheapest eligible instructor without lookahead. The exact search compares complete alternatives using the same inputs and constraints. Neither approach is a claim about your existing process.
- North 16:00–17:00: I-02 → I-03.
- Riverside 15:00–16:00: I-05 → I-02.
- Riverside 16:00–17:00: I-05 → I-02.
In the default scenario, assigning I-03 at North preserves I-02 for two science sessions at Riverside. Both plans cover 48 seats; modeled cost changes from $330 to $322. The controls recompute the comparison above.
Inspect every assignment as a table
| Session | Subject | Instructor | Seats | Cost |
|---|---|---|---|---|
| North14:00–15:00 | Math | I-01 | 8 / 8 | $48 |
| North15:00–16:00 | Math | I-01 | 8 / 8 | $48 |
| North16:00–17:00 | Science | I-03 | 8 / 8 | $68 |
| Riverside14:00–15:00 | Math | I-04 | 8 / 8 | $54 |
| Riverside15:00–16:00 | Science | I-02 | 8 / 8 | $52 |
| Riverside16:00–17:00 | Science | I-02 | 8 / 8 | $52 |
| Session | Subject | Instructor | Seats | Cost |
|---|---|---|---|---|
| North14:00–15:00 | Math | I-01 | 8 / 8 | $48 |
| North15:00–16:00 | Math | I-01 | 8 / 8 | $48 |
| North16:00–17:00 | Science | I-02 | 8 / 8 | $52 |
| Riverside14:00–15:00 | Math | I-04 | 8 / 8 | $54 |
| Riverside15:00–16:00 | Science | I-05 | 8 / 8 | $64 |
| Riverside16:00–17:00 | Science | I-05 | 8 / 8 | $64 |
Inputs, hard constraints and decision rule
All records are synthetic. The planning period is 14:00–17:00 in three one-hour slots. North has two rooms per slot; Riverside has one. Each instructor can cover one qualified group per slot, at one center for the afternoon. A group holds up to eight requested learners; instructor cost is charged per assigned hour.
Objective: cover the most requested seats within budget, then minimize instructor cost. Ties use instructor IDs in the published session/group order. If “Require every requested seat” is checked, partial coverage is diagnostic only and cannot be accepted as a valid plan. No fairness weight or monetary shortfall penalty is invented.
Equal group capacity, fixed costs and no inter-center travel are assumptions. Attendance, teaching quality, breaks beyond this short period, labor rules and individual learning needs are not modeled. A real schedule needs rules agreed with the team using it.
| ID | Qualification | Centers | Available starts | USD |
|---|---|---|---|---|
| I-01 | Math | North | 14:00, 15:00, 16:00 | $48 |
| I-02 | Science | North, Riverside | 14:00, 15:00, 16:00 | $52 |
| I-03 | Math, Science | North, Riverside | 14:00, 15:00, 16:00 | $68 |
| I-04 | Math | North, Riverside | 14:00, 15:00 | $54 |
| I-05 | Science | Riverside | 15:00, 16:00 | $64 |
Sample instructions
A plan, plus a way
to run it again.
A tool needs clear instructions too. This sample shows what your team would check before using a plan and when to run it again.
- The decision
- Assign qualified instructors to this afternoon’s requested sessions within a $340 budget.
- Current result
- Valid under the selected coverage policy: 48 of 48 seats, $322. Baseline: 48 seats, $330.
- Operating instructions
- Confirm availability and room access, then update demand and budget. Review any gaps and compare the plans. Get approval from the person responsible before using the schedule.
- Checks and backup plan
- Check qualifications, double bookings, rooms and cost independently. Staff should try the tool themselves before relying on it. If a check fails, use the agreed manual backup and investigate.
- When to run it again
- Run it again when availability, rooms, demand or budget changes. Agree and test any new rules before adding them or extending the tool to more centers.
Illustrative afternoon decision summary
Budget $340; North 14:00 demand 8; absence none; full coverage required: no. Valid under selected policy.
| Session | Subject | Instructor | Seats | Cost |
|---|---|---|---|---|
| North14:00–15:00 | Math | I-01 | 8 / 8 | $48 |
| North15:00–16:00 | Math | I-01 | 8 / 8 | $48 |
| North16:00–17:00 | Science | I-03 | 8 / 8 | $68 |
| Riverside14:00–15:00 | Math | I-04 | 8 / 8 | $54 |
| Riverside15:00–16:00 | Science | I-02 | 8 / 8 | $52 |
| Riverside16:00–17:00 | Science | I-02 | 8 / 8 | $52 |
| Session | Subject | Instructor | Seats | Cost |
|---|---|---|---|---|
| North14:00–15:00 | Math | I-01 | 8 / 8 | $48 |
| North15:00–16:00 | Math | I-01 | 8 / 8 | $48 |
| North16:00–17:00 | Science | I-02 | 8 / 8 | $52 |
| Riverside14:00–15:00 | Math | I-04 | 8 / 8 | $54 |
| Riverside15:00–16:00 | Science | I-05 | 8 / 8 | $64 |
| Riverside16:00–17:00 | Science | I-05 | 8 / 8 | $64 |
What makes your schedule difficult?
Tell us who you need to schedule, which rules matter and how your team handles changes.