OPS.10.2:4 - Solution

Working mantra. Recover the recipient’s result and deadline; pass them to a description of the remaining operations and the events that enable each one. Carry that description into shared resource occupations and usable calendar windows. Use those conditions to choose a sequence and place operations, returning a complete feasible plan or the reason a proposed placement fails. Compare the plan with a necessary bound before claiming that earlier completion is impossible. Pass the feasible plan to a calculation of conditional start windows and delivery reserve. Use those windows to compare early work, postponement and deliberate protection. When a condition changes, retain completed facts, reopen the affected dependencies and resource competition, obtain the revised plan, and return its delivery consequences to the people choosing priorities and release.

OPS.10.2:4.1 - Recover the delivery question and remaining work

State the result that must be available, its deadline and its waiting origin. An internal completion can precede transport, approval or receiving acceptance. Include those operations when the promise needs them.

Separate hard requirements from preferences. “Meet all three dates” asks for feasibility. “Finish the last order as early as possible” minimizes the last completion. “Obtain the first result sooner” can prefer a different order. If competing recipients cannot all receive their earliest possible result, OPS.7 supplies the priority and commitment choice.

For each remaining operation, recover its readiness event, required predecessors, duration or bounded scenario, eligible resources, and whether it can be interrupted. Include setups, transfers and known return work when they consume relevant time. Retain completed operations and work already under way as facts; estimate only their remaining requirements.

Keep the finite work list at the detail the decision needs. If a task requires an operator only during loading, recover that phase without decomposing every machine movement. If an unknown duration could reverse the decision, compare supported bounds or obtain that particular input. A full event history is unnecessary when the supplied conditions already settle the schedule.

OPS.10.2:4.2 - Construct precedence, occupation and calendar conditions

A precedence relation states which event must occur before another operation may begin. For a continuous operation i of duration p_i, finish f_i equals start s_i plus p_i. A finish-to-start relation from i to j with required delay l requires s_j >= f_i + l. At a join, every required predecessor must satisfy its relation. An actual partial handover can use an earlier event, provided the downstream work can use that partial result.

Resource sharing adds a different condition. Two operations requiring the same exclusive resource cannot occupy it at the same time. Their order is a choice unless the operation already fixes it. For a pool, check how many eligible members are needed simultaneously; one free but unqualified person does not supply the required capability.

Recover each occupation separately. A machine may hold an order for three hours while its operator is needed only in the first hour. Represent the machine interval and that operator interval with their common start. Apply each resource’s capacity and calendar to its own intervals. Use half-open intervals, including the start and excluding the finish, when a resource can pass immediately to the next operation.

Distinguish three calendar conditions that require different placements:

• A continuous occupation must fit wholly inside an available window.
• Work that may pause can accumulate processing across open windows, with any restart cost included.
• A machine may continue through an operator’s absence when that phase needs no attendance.

A rule allowing an operation to start during working hours does not establish that its later occupied hours are available. Where several resources are needed together, find a window in which their required occupations are jointly possible.

Check that the precedence relations can be satisfied. A finish-to-start cycle with positive total required duration and delay is an obstruction. When the work actually revisits a station, represent the later visit as a later operation rather than requiring one operation to precede itself.

MMP.10 supplies the joint formulation. Keep the operational reason for a condition recoverable: actual precedence, chosen resource order, calendar closure, admission policy or deadline. A chosen order can be reconsidered without pretending the technological route changed.

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:

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.

OPS.10.2:4.4 - Derive time reserve and conditional criticality

First state the event against which reserve is measured. If the proposed final completion is C and its deadline is D, D-C is the plan’s final margin. A negative value shows that this plan misses the deadline; it does not by itself exclude another plan.

For a precedence network with fixed durations, continuous calendars and no binding resource contention, calculate early starts forward and latest starts backward. Start the backward pass from the selected final time T, retaining any earlier hard intermediate deadlines. For each successor, subtract the required intervening delay from that successor’s latest start. The earliest of those bounds and any deadline on the operation gives its latest finish; subtract its duration to obtain its latest start. Latest start minus early start is its total float relative to those targets. Free float is the delay that leaves the successors’ early starts unchanged, including their required intervening delays.

When only the final event governs this calculation, setting T to the earliest final completion identifies zero-float paths controlling that completion. An earlier intermediate deadline can instead give zero float to work protecting that intermediate event; identify which event the result concerns. Using a later final deadline adds delivery margin where other commitments permit it, so an operation on the longest precedence path can have positive deadline float. Several longest paths can exist. Serial operations may draw on the same margin, so their individual floats are not independent allowances to add together.

With shared resources, retain the selected allocations and orders when making the timing calculation. For whole-operation exclusive occupations, add the chosen resource-order relations to the precedence network; its timing is conditional on those orders. For partial occupations or calendars, use the corresponding phase and window constraints. A different allowed order or calendar can change the controlling sequence.

To assess a proposed postponement, hold the stated commitments fixed, delay that start, and refit the affected work. Identify the latest feasible placement or the set of feasible start windows that still meets the protected event. Calendar gaps can make intermediate start times infeasible even when a later window exists. A backward arithmetic pass that ignores those gaps supplies no usable postponement permission.

Call a sequence critical only with its plan, resource choices and target event recoverable. Test a claimed critical operation by changing its duration or availability and recalculating the consequence at that scope. An operating bottleneck concerns the mechanism limiting sustained flow under a workload; it need not be an operation controlling this finite deadline. OPS.9 supplies that diagnosis.

OPS.10.2:4.5 - Choose early work, deferred starts and protection

Compare start policies inside the feasible windows. Starting earlier can reveal problems and retain recovery time. Deferring can avoid aging, premature expenditure or work invalidated by a later input. Retain the recipient’s original waiting boundary in either comparison.

When protection is needed, name the event and disturbance to be absorbed. Choose an internal target earlier than the commitment, or reserve time before a consequential join. Determine its amount from the delay scenario, supported bound or risk model that matters to the decision. A final margin is available time; calling it a buffer adds a policy for preserving and using it.

For known deterministic conditions, the feasible schedule can be enough. To protect against a stated extra hour of review, add that hour to the appropriate operation and recompute the plan. This answers the scenario without inventing its probability. A service-probability claim needs the corresponding duration and dependence model; OPS.10.1 supplies that construction.

After inserting protection, recheck resource and calendar feasibility. Moving a feeding operation earlier can take another task’s reservation. Keeping two hours before final delivery does not make those hours usable before an earlier calendar closure. Do not allocate the same margin to several independent promises without checking their combined delay.

Return the selected target times, reserved intervals and response to reserve consumption to OPS.8 for release and protection. OPS.7 uses the delivery consequences for priorities; OPS.14 supplies financial comparison when it can change the start policy.

OPS.10.2:4.6 - Reconstruct the affected remainder after a change

At the current time, retain actual starts, completions and ongoing occupations. Replace the changed duration, readiness, access window, required operation or commitment. Do not restart completed work or shorten an uninterrupted operation merely to recover the former finish date.

Follow the changed operation through both its successors and the resources it shares. A task outside its precedence descendants can still lose a resource window. Include resulting admission changes and downstream joins; widen the affected set until its remaining boundary conditions are unchanged.

Try retaining unaffected reservations and the useful parts of the former plan. Refit the affected work under those commitments. If that restricted repair fails, identify which still-changeable reservation or resource order could matter and compare a broader rearrangement with its coordination cost. Failure while preserving the old order excludes only that restricted repair.

Recompute completion times, feasible postponement windows and protected reserve. Compare them with the same recipient events and deadlines. Return the actionable difference: a changed start or allocation, reserve consumed, an obtainable operating remedy, a commitment needing reconsideration, or an unresolved scheduling choice. Retain unaffected model and calculation results whose premises still hold.