OPS.10.2:4.3 - Place the work and distinguish the resulting conclusions
For a small case, start with operations whose required predecessors have been placed. Choose an eligible operation, find its earliest jointly available placement after readiness, reserve the required intervals, and continue. Several reservations may be made within one long machine operation when its attendance phases allow other work.
At a resource conflict, compare the competing orders. A near deadline or a long downstream continuation can guide the first attempt; neither is a universal priority theorem. Preserve alternatives when that first attempt fails or gives an inadequate result. Inserting work into a gap, leaving a resource temporarily idle, or changing an uncommitted order can permit a schedule that a simple dispatch rule misses.
Once the relevant orders are fixed, calculate the earliest times consistent with them. With continuous availability and finish-to-start relations, each start is the maximum of its readiness and predecessor finishes plus their required intervening delays. Chosen resource-order relations also contribute predecessors. For partial attendance, connect the occupied phases, not the finish of an unrelated unattended phase. With calendars, move each proposed occupation to the next jointly permitted window and propagate the resulting finish.
Check the complete candidate against every required operation, precedence, occupation, calendar and completion event. A feasible assignment is a witness that the modeled work fits; the participants must still have the stated access and capability.
Use cheap necessary bounds before a larger search. A required dependency chain cannot finish faster than its ordered work permits. A resource cannot supply more mandatory occupation than its available capacity in the required window. A continuous operation cannot use several disjoint short windows as one long window. Passing these bounds does not construct a schedule.
Return the actual strength of the result:
| Obtained result | Supported conclusion |
|---|---|
| Complete feasible schedule meeting the dates | Those dates are attainable under the stated conditions. |
| Feasible completion C and lower bound L on the earliest possible completion | The optimum lies between L and C. Equality establishes an earliest completion. |
| Necessary condition incompatible with the deadline, or a complete valid search excluding every permitted schedule | The deadline is impossible within that modeled arrangement. |
| A failed priority rule, restricted sequence or interrupted search | That attempt found no satisfactory plan; other permitted schedules remain unresolved. |
CMP.4 supplies justified search when the operational choices remain numerous. CMP.5 supplies relaxations and bounds. Give the specialist the actual resource and calendar conditions and the conclusion needed; the name of a solver does not determine either.
Stop when a suitable plan or sufficient obstruction answers the decision. Further optimization is useful only when its possible improvement matters.