Worked example: Algorithm for a Stage Change

What this is

A completed, timed and tested algorithm for the 90-second kitchen-to-waiting-room change. The arithmetic below is correct and you can mark against it: the jobs total 116 seconds of work, four crew running in parallel finish in 55 seconds, and the worst case with the table legs is 65 seconds. Show it after pupils have attempted their own timing table.

The dependencies worked out first

The vending-machine flat stands where the kitchen table was → the table must be struck before the flat comes on.
The noticeboard hangs on the flat → the flat must be standing first.
The row of waiting-room chairs goes where the kitchen chairs were → all four kitchen chairs must be off first, which takes 16 s.
Nothing else depends on anything, so everything else can run at the same time as everything else.

Evidences criterion 1: the plan starts from dependencies, not from the order the lists happen to be printed in.

The timing table

Seconds	Crew A	Crew B	Crew C	Crew D
0–8	Table off, with B (upstage door)	Table off, with A	Kitchen chairs off, stage right	Kitchen props into the box
8–12	Table off — ends at 12	Table off — ends at 12	Kitchen chairs off	Waiting at stage left with stack 2
12–16	Flat on, with B	Flat on, with A	Kitchen chairs off — ends at 16	Waiting (door rule: A and B have it)
16–24	Flat on	Flat on	Rug off, upstage door	Chair stack 2 on
24–32	Flat on — ends at 32	Flat on — ends at 32	Chair stack 1 on	Stack 2: align 3 chairs — ends at 32
32–40	Hang the noticeboard — ends at 40	Water cooler (ends 38), then stand by	Stack 1 on to 34, then align 3 chairs	Magazines and sign — ends at 38
40–55	Final check against the setting list	Final check	Final check	Final check, wings clear, stand by

Total time: 55 seconds. Spare out of 90: 35 seconds. If the table legs have to be folded, every job on the A/B track shifts by 10 s: the flat is up at 42, the noticeboard at 50, the check runs 50–65. Worst case 65 seconds, 25 to spare.

The jobs add up to 116 seconds of work (44 s of striking, 72 s of setting). Four crew in parallel do it in 55, because the change is limited by its longest chain — table, then flat, then noticeboard — not by the total.

Evidences criterion 2: 116 seconds of work compressed into 55 by running four tracks at once, and the bottleneck chain is named rather than guessed at.

Note the deliberate idle time: D waits from 8 to 16 because the kitchen chairs are not clear yet, and because the door rule allows only A and B through until 12. Idle time that is explained is planning; idle time that is not noticed is a collision.

The algorithm, written out

CREW A and B 1 Lift the kitchen table. 2 IF the table clears the upstage doorway THEN carry it straight off (12 s) ELSE fold the legs first (+10 s), then carry it off 3 WAIT until the table is clear of the doorway. 4 Carry the vending-machine flat on from stage left and stand it on the tape mark. (20 s) 5 A: hang the noticeboard on the flat. (8 s) B: set the water cooler downstage of the flat. (6 s) CREW C 1 REPEAT FOR EACH of the 4 kitchen chairs: carry it off through the stage-right wing. (4 s each) 2 Roll the rug and carry it out of the upstage door. (8 s) 3 Carry chair stack 1 on from stage left. (10 s) 4 REPEAT FOR EACH of the 3 chairs in stack 1: line it up with its tape mark. (2 s each) CREW D 1 Clear kettle, mugs and tablecloth into the prop box. (8 s) 2 WAIT at stage left until all 4 kitchen chairs are off. 3 Carry chair stack 2 on. (10 s) 4 REPEAT FOR EACH of the 3 chairs in stack 2: line it up with its tape mark. (2 s each) 5 Set the magazines and the "Please wait to be called" sign. (6 s) ALL CREW 6 Check the stage against the setting list, clear the wings, stand by for lights up. (15 s)

Evidences criterion 3: the IF gives an instruction for both outcomes, so nobody has to improvise in a blackout. Evidences criterion 4: three REPEATs replace ten identical lines, and the chair count lives in one place if the director asks for a seventh chair.

The two control structures as a flowchart

The same two structures drawn as a flowchart. The loop arrow returning to "place the next chair" is what makes it a REPEAT rather than three copies of one instruction.

The dry run — completed by a partner

Step read out	Works?	If it breaks, what breaks
A and B: table off, 0–12	Yes	—
C: four kitchen chairs off, 0–16	Yes	Goes stage right, so the door rule is not broken
D: chair stack 2 on at 8	No	Two kitchen chairs are still in that row at 8 s. Fixed: D waits until 16.
A: noticeboard at 32	Yes	Flat is standing at 32, so the dependency holds — but only just
C: rug out of the upstage door, 16–24	Yes	Door is free from 12, and C is on their own in it

The one change I would make after the dry run: move the noticeboard from A to D. D is finished at 38 and A is the one who might be 10 seconds late if the legs have to be folded, so hanging the noticeboard off the critical chain drops the worst case from 65 s to 57 s.

Evidences criterion 5: the algorithm was genuinely broken by the test — the original plan had D setting chairs into a row that was not clear — and the fix is justified by the timings rather than by preference.

Why this response is secure

The dependencies are established before the timings, so the plan cannot ask anybody to set something into an occupied space.
The parallel tracks are real: 116 seconds of work becomes 55 seconds of blackout, and the limiting chain is identified.
Both branches of the IF have an instruction, and the cost of the slower branch is carried through the whole timetable to a worst case of 65 seconds.
The REPEATs keep one instruction for six chairs, which is why changing the chair count is a one-word edit.
The dry run found a genuine fault and the improvement is argued from the critical chain, not from tidiness.