The named rotations, generated rather than described

The Pitman schedule is a 2-3-2 rotation over fourteen days: two on, two off, three on, two off, two on, three off. Four teams work 12-hour shifts, each averaging 42 hours a week.

Two of the four teams cover days and two cover nights, and the two on each are exact complements of one another: when A is on, B is off, which is what makes the coverage close with no gaps and no overlaps. Seven working days in every fourteen.

The reason people choose it is the weekend. Every team gets a complete Saturday and Sunday off every second week, permanently, without asking and without it being anyone's turn. And a fixed, predictable full weekend every fortnight is worth more to most people than the same number of scattered days off. The longest run is three consecutive twelves, which is the mildest of the three patterns here. The catch is that on the fixed variant the night teams are on nights indefinitely, which concentrates a real health cost onto four people rather than spreading it across sixteen. Rotate the day and night halves each cycle and you have spread it; you have also taken away the predictability that was the reason for choosing Pitman. That is a genuine trade and it belongs to your unit, not to us.

The DuPont schedule is a four-team, 28-day rotation of 12-hour shifts: four nights, three off, three days, one off, three nights, three off, four days, then seven consecutive days off.

Fourteen working days in twenty-eight, so the same 42 hours a week as everything else here, arranged into a much sharper shape. The four teams run the identical cycle offset by seven, fourteen and twenty-one days, which is the trick that makes the coverage close.

The seven consecutive days off at the end of every cycle is the entire reason anyone picks it. It is long enough to genuinely go somewhere, and no quantity of scattered rest days ever adds up to that; a week is a different kind of thing from seven days. The price is paid in the same cycle: four consecutive nights, and then a three-day turnaround from nights onto days, which is the part that is hard on a body and gets harder the older the body is. It is the most demanding pattern here, and it is the one most worth asking your night staff about rather than deciding for them.

The Southern Swing is a four-team, 28-day rotation of 8-hour shifts: seven days, two off, seven swings, two off, seven nights, three off, with each team rotating forward through all three shifts.

It is the answer for places that have decided against twelve-hour shifts, and it reaches the same 42-hour average through three eight-hour shifts a day instead of two twelves. Twenty-one shifts in twenty-eight days. The teams are offset by seven days, so on any given day one team is on days, one on swings, one on nights, and one is off.

It rotates forward, through days, then swings, then nights, which is the direction that costs a body least, because a circadian rhythm delays more easily than it advances. And it shares the nights: everybody does seven of them a cycle rather than four people doing all of them forever. The cost is the mirror of Pitman's: instead of asking four people to adjust once, it asks every person on the unit to keep re-adjusting, every cycle, indefinitely.

Pitman if predictable weekends matter most, DuPont if a real week off matters most, Southern Swing if you are not running twelve-hour shifts. And none of them if you have not asked the people who will work it.

The honest answer is that the arithmetic does not decide this. All three cover the unit, all three land on 42 hours a week, and all three are in use in real hospitals right now. So the choice is entirely about which cost your team would rather carry, and that is a question about them rather than about the pattern. What the arithmetic can do is stop you believing you have found a pattern with no cost, because there is not one: 168 hours a week of coverage divided by four teams is 42, and every arrangement of it is a rearrangement of the same load.

The one thing worth saying flatly: a rotation imposed without asking will be worked resentfully and will not survive its first bad month. Generate two or three of these, put them in front of the people who will actually live in them, and let the objections tell you which cost is the one your unit is not willing to pay.