OPS.10.2:5 - Archetypal Grounding

OPS.10.2:5.1 - A deliverable with a join and shared deadline margin

A report needs preparation P, taking four hours, and evidence extraction E, taking two. Different people can perform them concurrently from time zero. Review V takes three hours after both finish; release R takes one hour after review. These resources are independently available, durations are known, and release completes delivery. The deadline is hour ten.

The precedence path P-V-R takes eight hours and controls earliest delivery. E has two hours of free float before its delay moves V’s early start. Starting E at hour two preserves delivery at eight and may avoid producing an input earlier than useful. Starting it at four instead gives V at 6-9 and R at 9-10, consuming all final margin.

P, V and R each have two hours of total float against ten, but they share those hours. Delaying P by two moves V to six and R to nine; another two-hour delay of V would miss the deadline.

To preserve one hour before the external deadline, use an internal delivery target of nine. The latest starts become P at one, E at three, V at five and R at eight. They jointly give one feasible deferred plan with the intended final reserve.

Return to execution of the earliest-start plan. At hour two, preparation is found to need three further hours instead of two. E is already complete. Continue P to five, then V at 5-8 and R at 8-9. The new final margin is one hour. The changed input reopens preparation and its successors; E’s completed result remains available.

OPS.10.2:5.2 - A failed short-task priority is not an impossible deadline

Two jobs are ready at zero. U needs three hours of one specialist followed by seven hours of unattended equipment work. V needs two hours of that specialist followed by one unattended hour. The equipment is different for the two jobs, all resources are continuously available, and both results are required by hour ten.

Doing the shorter specialist task first gives V at 0-2, its equipment at 2-3, U at 2-5 and its equipment at 5-12. That plan misses the deadline.

Doing U first gives specialist intervals U at 0-3 and V at 3-5. U’s equipment runs at 3-10 and V’s at 5-6. Both dates are met. U’s own required chain takes ten hours, so the plan also attains the lower bound for the last completion.

In the first plan, the chosen resource relation V-before-U makes V part of the sequence controlling the final finish. In the second plan, V can finish well before U. That criticality was a consequence of the selected order. Five hours of specialist demand alone revealed neither the successful order nor the ten-hour completion.

OPS.10.2:5.3 - Shared attendance still permits machine overlap

Five orders arrive at zero. Each needs A for two hours and then B for three, with order 1-5 on each station. Each station has one continuously available machine; there are no setups, returns or other work. B completion makes an order ready for its customer. No operation is interrupted. Admit the first two at zero and the next order immediately when a B completion frees one of the two places.

With independent station resources, earliest A intervals are 0-2, 2-4, 5-7, 8-10 and 11-13. B finishes at 5, 8, 11, 14 and 17.

Now both stations use one operator. A requires continuous attendance; B requires attendance only in its first hour and holds its machine for all three hours. The old A intervals conflict with B attendance. Recovering the phases yields this revised plan:

At hour two, start B1 before A2; then place A2 inside B1’s unattended phase. Repeating that choice keeps B working continuously. The operator’s intervals do not overlap, and no more than two orders are admitted and unfinished.

B cannot begin before hour two and must process five orders sequentially for three hours each. Every completion therefore satisfies f_Bi >= 2+3i; the plan attains all five bounds. The shared operator changes starts at A without delaying any recipient result.

Customer times average eleven hours. Internal times are 5, 8, 6, 6 and 6 hours, averaging 6.2; the remaining average 4.8 hours occurs before admission. These quantities retain their different event boundaries.

OPS.10.2:5.4 - A calendar gap makes final margin unusable for a test

A maintenance test becomes ready at hour two. It needs a rig and an engineer together for three uninterrupted hours. A separate analyst then needs one hour to issue the acceptance result and is available throughout. The rig is available from two to ten; the engineer from zero to five and from six to ten. Acceptance is due at eight.

The test fits at 2-5 and acceptance work at 5-6. The final margin is two hours, but the test cannot be postponed by one hour: 3-6 crosses the engineer’s absence. The next complete test window starts at six, giving acceptance at ten. Within the original deadline, the margin can postpone the analyst’s work, not the test.

Before execution, the engineer’s first window is shortened to end at four. Common availability before the latest possible test finish at seven is 2-4 and 6-7: three hours in total, but no continuous three-hour interval. This excludes acceptance by eight. The earliest remaining test is 6-9 followed by acceptance at 9-10.

The obstruction identifies a useful remedy to investigate: restore attendance through five or obtain another qualified continuous window ending by seven. Merely reporting three available engineer-hours, or silently allowing the test to pause, does not answer the stated operation.

These examples are constructed scheduling cases. Their conclusions follow from the stated intervals and bounds, not from measured industrial performance.