Find the critical path in an RFP response

Finish boundary

Name the event the network is supposed to finish

A completed draft, an approved offer and a recorded submission are different events. Define the terminal milestone precisely enough that a person outside the writing team can inspect its evidence. If the analysis stops at release-ready files, call it the path to release readiness and retain the separate delivery plan. If it claims to cover submission, include the required preparation, authorized sending and confirmation steps. A final manuscript alone cannot prove that whole path.

Keep three times visible: the calculated forecast, the internal target and the buyer’s controlling deadline. Preserve the official source, lot, response stage and time-zone basis of the last one. Derive the internal target from the remaining delivery operations and the reserve the authorized team has chosen. Do not move the buyer deadline to make the model fit, or quietly turn an internal target into a buyer requirement.

Public Services and Procurement Canada’s preparation reference tells suppliers to inspect pre-closing deliverables, closing time and the stated submission method. Its scope is Canadian federal opportunities. Here it supports a specific intake check: include the applicable delivery events before declaring the network complete. It does not set a universal upload allowance or validate another buyer’s procedure.

Fix a status instant for the calculation. Completed work needs an observed completion record and the correct version; unfinished work needs a remaining duration. A review completed on yesterday’s price file may be reopened by a changed price. Preserve the earlier review as history, but do not use it as a completed predecessor for the revised offer unless its authority confirms that it still applies.

Network evidence

Make every link explain why a successor must wait

Use the controlled work packages as the scope inventory, then express their executable activities and handoffs. A package may contain evidence retrieval, validation and answer drafting, each with a different owner or release condition. A shared evidence activity appears once, with links to all of its consumers. An overall summary row is not another activity to add to the detailed durations.

For each link, state the actual dependency: which accepted input releases which next operation. A technical decision may feed both the service answer and the cost calculation. The commercial review may wait for the cost result but not for the company profile. Departmental order is not sufficient reason to serialize independent work. Conversely, two tasks drawn side by side are not independent if they consume the same unresolved decision.

Separate active work from elapsed waiting. If the evidence custodian needs an hour after a confirmed two-day queue, preserve both elements and their basis. If the date is merely requested, mark it unconfirmed. An unknown external response time is not zero. You can calculate an explicitly conditional scenario, but cannot promote it to an evidenced forecast because the software requires a number.

The simple calculation below uses finish-to-start links with no lag and one shared working calendar. For overlapping work, describe the accepted intermediate output that permits the overlap. Use a separate intermediate milestone where practical. A negative lag that means “start before the evidence is ready” hides an assumption about rework and permission. Unroll bounded review-and-correction rounds rather than leaving a logical cycle that cannot be calculated.

GAO’s Schedule Assessment Guide distinguishes finish-driving sequences from paths marked critical by float, especially when constraints or multiple calendars intervene. It also warns that missing logic invalidates the result. The bid application is to inspect the causal chain behind the displayed colour, using the guide as scheduling guidance rather than as a tender compliance standard.

Worked network

Calculate both branches before deciding where to intervene

Fictional Brackenmere Service Systems has eight remaining activities for one bid. All prerequisites outside the table are assumed complete and accepted at time 0. Time is measured at working-day boundaries on one agreed calendar: a two-day activity starting at 3 finishes at 5. There are no holidays, resource conflicts, additional waiting periods or overlaps in this teaching model. Durations are scenario assumptions, not benchmarks for real bids.

The evidence branch is A, four days to obtain the specified authorized evidence; B, one day to validate it; and C, two days to complete the technical answer. The commercial branch is D, three days for a defined partner input, followed by E, two days for its cost check. F reconciles both accepted branches in one day. G takes one day to produce the approved release-ready package. H takes two working days for the separately authorized delivery and confirmation process. Its completion condition is the procedure-specific submission record, assumed achievable within that duration for this example.

Forward calculation takes the latest predecessor finish at each merge. A, B and C reach time 7; D and E reach time 5. F therefore starts at max(7, 5) = 7. G finishes at 9 and H at 11. The eight durations add to 16 working days of activity duration, but they do not form one sequence. Nor are those 16 days necessarily person-days: an external wait can occupy schedule time without equivalent labour.

For the table’s backward pass, fix the end at the unconstrained earliest finish of 11, not at the buyer deadline. Subtract each duration from its latest finish, and set a predecessor’s latest finish to the earliest latest start among its successors. The evidence branch has zero total float against that endpoint. D and E each show two days, shared along their branch. Delaying D by two days leaves E no remaining branch allowance. The two cells do not provide four days.

Timing allowance

A zero-float path can still finish before the deadline

Assume Brackenmere’s controlling buyer deadline is time 12 and the internal release-ready target is time 10. The two-day H activity is already in the network. Forecast release readiness at 9 is one day ahead of the internal target; forecast confirmed submission at 11 is one day ahead of the buyer deadline. Those are two views of the same one-day end allowance, not two independent reserves. The two-day delivery activity is planned work and waiting, not unused float.

A second backward pass anchored to required finish 12 would move the latest times one day later in this simple model. That gives the driving chain one day of deadline-relative allowance and the other branch three. It does not change the earliest finish of 11 or remove the evidence branch as its driver. Label which endpoint produced each float value; mixing the table’s unconstrained values with the deadline-relative values creates an apparently contradictory report.

Free float asks a different question: how much can this activity slip without moving its immediate successor’s earliest start? D has zero free float because E starts at 3 as soon as D finishes. E has two because F cannot start until C finishes at 7. D can use shared total float only by moving E. That matters when E’s reviewer has a booked slot: the logical allowance may not be available in the resource calendar.

Use latest safe dates as conditional limits, not invitations to wait. Record the endpoint, calendar, duration basis and required residual reserve behind each date. If an external input is due at its mathematical limit and its owner has not confirmed delivery, the plan is exposed even while the arithmetic balances. Negative deadline margin reports a recovery requirement; a date constraint cannot perform the missing work.

Feasibility

Check whether the calculated starts can occur

The Brackenmere table deliberately assumes resource independence. In a live bid, match each scheduled interval to the person’s confirmed allocation and the decision authority required. Two reviews of two days each cannot overlap merely because they belong to different work packages. If the same qualified reviewer must perform both, test an authorized sequence or a qualified substitute and recalculate the downstream finish.

NASA’s Schedule Management Handbook, revision 2 effective 15 March 2024, addresses resource loading and the need to review the consequences of leveling. It also calls for current remaining durations and a common status date. These are NASA scheduling practices; their use here is to expose an unsupported reviewer overlap and prevent stale progress from controlling the forecast.

A committee slot has an input cutoff as well as a meeting time. Missing the cutoff by fifteen minutes can move a decision to the next session even when its active review takes only an hour. Model the admissible slot, preparation requirement and possible outcome. A reserved meeting proves availability, not approval. An adverse or deferred decision needs its own remaining-work scenario and may block release entirely.

Calendar exchange needs equal care. RFC 5545 distinguishes floating local times from UTC and local times tied to a time zone. A floating appointment can refer to different instants for different recipients. Preserve a fixed event’s time-zone meaning when exporting the plan. The calendar format does not determine the buyer’s deadline or grant access to an approval session.

Intervention test

Measure the gain at the finish, not just at the task

In a scenario copy, reduce A from four to two days while preserving its evidence and acceptance conditions. The technical branch now finishes at 5, exactly when the commercial branch finishes. F, G and H add four days, so submission moves from 11 to 9. Both branches now drive the finish. Reducing A again to one day produces no further gain: the commercial branch still arrives at 5. The first intervention saves two days at the finish; the second saves only local task time.

Conversely, reducing D from three days to one in the original plan leaves submission at 11. The evidence branch still reaches the merge at 7. If D instead stretches to six days, its branch reaches 8, the full finish becomes 12, and the one-day deadline margin disappears. At seven days for D, the finish becomes 13, one day beyond the assumed deadline. These comparisons change only D or A as stated; they do not assume an unmentioned faster review.

Before presenting a saving as available, explain how the change can occur. Earlier access to already validated evidence may shorten A; extra writers may not. Parallel review may shorten a queue only if the reviewers hold the required authority and receive usable inputs. Removing a mandatory check is a different, potentially impermissible scope change, not a scheduling improvement. Include added cost, rework exposure and displaced commitments for the actual decision maker.

Test plausible delays on near-driving branches as well as gains on the current driver. Keep correlated assumptions together: if one missing service decision affects both the technical answer and the cost check, do not model its effects as unrelated favourable events. A deterministic network and a few scenarios do not establish a probability of on-time delivery. Use a justified risk model and competent review before attaching a confidence percentage.

Agent handoff

Return the network, its limits and the next authorized decision

An agent’s useful output includes the input snapshot, activity and edge tables, calendar references, duration evidence, completed-work records, resource assumptions, calculation method and selected finish. For each activity, preserve early and late times, the endpoint used for float, controlling predecessor, source quality and unresolved conditions. Include the current driving chains and any tested branch that can take over. Retain a readable explanation beside the machine-readable fields.

Report one of: forecast supported under stated assumptions, conditional on named inputs, infeasible against the stated deadline, network invalid, or authority missing for the proposed intervention. Multiple blockers can coexist. A network with a cycle is not merely late; it needs repair. A network with an unknown mandatory external event has no supported whole-bid finish, even if the internal portion is fully calculated.

W3C PROV-DM provides separate concepts for plans, activities and revised entities. They support keeping a schedule version distinct from execution evidence and linking a revised forecast to its predecessor. The model does not prove that a scheduled review happened. That distinction matters when an automated report consumes a plan as if it were a completion log.

Within granted access, an agent may inspect supplied schedules, check links, calculate timing, compare scenarios and draft an internal recommendation. It must not book people, contact a buyer or partner, obtain private evidence, change live commitments, spend money, waive checks, approve an offer or submit it without separate authority. A proposed earlier date is not a message the agent is entitled to send on someone else’s behalf.

After each material status change, preserve the old forecast, update remaining durations from current evidence and recalculate affected successors and resource conflicts. Name the changed driver and the resulting decision deadline. If the schedule is infeasible, route the record to the existing recovery or pursuit authority. The completed work product is an inspectable scheduling decision, with its open conditions intact.