Construction Scheduling, Critical Path, Readiness, and Earned Value Exercises

These exercises treat construction scheduling as an engineering release problem. The aim is not to make a programme look complete, but to decide whether the work package, constraints, inspections, weather buffer, productivity evidence and earned-value status support the next field action.

Assume simplified screening calculations unless an exercise states otherwise. Real construction control should also follow the contract programme, drawing revision control, temporary-works procedure, inspection and test plan, safety plan, permit conditions, environmental constraints and change-control process.

Release Evidence Notes

Construction schedule evidence must be tied to a named work package, drawing revision, workface, responsible crew, access condition, inspection hold point and acceptance criterion. A critical path or earned-value index that is not connected to field readiness can create a false release signal.

Good evidence separates logic from capacity. CPM, float, PPC and earned-value screens should be reconciled with workface access, permits, material availability, inspection resources, crew availability, weather risk, rework, temporary-works release and documented recovery actions.

Engineering Boundary Notes

These exercises are screening tools. They do not replace contractual delay analysis, full resource-loaded scheduling, 4D construction simulation, method-statement review, temporary-works design, safety risk assessment or site-specific production control. When a schedule result conflicts with field evidence, the field constraint controls the release decision.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Work readiness	1, 6, 16	Constraint removal, package readiness and look-ahead release	Decide whether a work package may enter the weekly plan.
Network logic	2, 3, 4, 13, 15	CPM, total float, free float, inspection delay and crashing	Decide whether resequencing or acceleration is required.
Performance control	5, 8, 9, 10, 11, 12, 14	PPC, CPI, SPI, recovery rate, crew loading and productivity	Decide whether production evidence supports the forecast.
Release governance	7, 17, 18	Weather buffer, commissioning readiness and final schedule gate	Decide whether schedule release is justified.

Exercise 1: Work-Package Readiness Index

A foundation work package has 14 required readiness items. Eleven are complete. Two missing items are hard gates, and one is a soft coordination item. The release rule requires all hard gates complete and at least 85\% total readiness. Decide status.

Solution

Readiness percentage is:

The percentage is below the threshold:

Also, two hard gates are missing. Therefore the work package is not releasable.

Engineering Comment

The hard-gate failure is enough to block release even before the percentage check. A readiness index should never average away missing permits, drawings, inspections or temporary-works approval.

Plausibility Check

Three missing items out of fourteen is more than ten percent missing, so a value below 85\% is expected.

Exercise 2: Critical Path for a Small Civil Sequence

A civil sequence has activities:

Activity	Duration	Predecessor
A mobilize	2\ \text{d}	none
B excavate	4\ \text{d}	A
C utilities locate	3\ \text{d}	A
D formwork	3\ \text{d}	B, C
E pour concrete	1\ \text{d}	D

Find project duration.

Solution

The controlling merge into D is the later of B and C.

A finishes at:

B finishes at:

C finishes at:

D starts at day 6 and finishes at:

E finishes at:

Engineering Comment

The excavation branch controls the merge. If utility locating slips by one day, it still may not delay the pour, but excavation delay directly affects the path.

Plausibility Check

The longest chain is A-B-D-E: 2+4+3+1=10 days.

Exercise 3: Total Float for a Noncritical Activity

In the previous sequence, utility locating C finishes on day 5, while D cannot start until excavation B finishes on day 6. Find total float for C.

Solution

Total float at the merge is:

Since D can start on day 6:

Engineering Comment

The one-day float is small. The planner should not consume it casually if utility conflicts could trigger redesign or permit review.

Plausibility Check

C is one day shorter than the controlling excavation branch, so one day of float is logical.

Exercise 4: Free Float Before an Inspection Hold Point

An inspection can occur no earlier than day 12. The preceding task finishes on day 10, and no successor can start until inspection is complete. Find free float before the hold point.

Solution

The task can slip until the inspection earliest start:

Engineering Comment

This float exists only if the inspection appointment is fixed and the inspector remains available. If the appointment is lost, the float calculation changes.

Plausibility Check

There are two calendar days between finish and inspection, so the result is direct.

Exercise 5: Percent Plan Complete

A weekly plan includes 32 committed tasks. Twenty-six were completed as promised. Compute PPC and decide whether it passes a 80\% weekly reliability threshold.

Solution

Because:

the weekly plan passes.

Engineering Comment

PPC passes narrowly. The missed tasks should still be coded by cause, because repeated permit or material misses indicate a planning-system failure.

Plausibility Check

Twenty-six of thirty-two is slightly above four-fifths, so a result just over 80\% is plausible.

Exercise 6: Constraint-Removal Gate

A look-ahead package has 9 constraints. Seven are removed. The remaining two are material certification and access permit. The release rule requires all safety, permit and quality constraints closed. Decide status.

Solution

Numerical closure is:

However, one remaining constraint is a permit and one is quality documentation. Since both are required categories, release is blocked.

Engineering Comment

Constraint logs are not simple progress counters. A single open permit can stop field release even when most checklist items are complete.

Plausibility Check

With two open items the percentage is below 80\%, and the category rule also fails.

Exercise 7: Weather-Buffer Allowance

A two-week earthworks window has 10 planned workdays. Historical data suggest 0.18 weather-loss days per workday. The plan includes a 2 day buffer. Check expected buffer margin.

Solution

Expected weather loss is:

Buffer margin is:

Engineering Comment

The expected-value buffer passes only weakly. If the activity is critical or weather losses are clustered, a probabilistic or contingency review is needed.

Plausibility Check

An 18\% loss rate over ten days gives just under two lost days.

Exercise 8: Earned Value Forecast

A package has planned value PV=240000, earned value EV=210000 and actual cost AC=260000. Compute CPI, SPI and cost variance.

Solution

Cost variance is:

Engineering Comment

The package is both over cost and behind planned progress. The release decision should verify field quantities, not only reported percent complete.

Plausibility Check

Earned value is less than both planned and actual cost, so both indices should be below one.

Exercise 9: Recovery Production Rate

A crew has 420\ \text{m} of duct bank remaining. Baseline production is 35\ \text{m/d}. The recovery plan must finish in 10 days. Find required daily rate and increase over baseline.

Solution

Required rate:

Increase:

Percentage increase:

Engineering Comment

A 20\% production increase may be possible, but only if workface access, inspections, materials and crew density support it.

Plausibility Check

Finishing in ten days means about forty meters per day, slightly above the baseline rate.

Exercise 10: Milestone Confidence from Guarded Finish

A milestone must finish by day 60. Current forecast finish is day 56, but the planner requires a 5 day guard for uncertain inspections. Decide status.

Solution

Guarded finish is:

Because:

the milestone fails the guarded release screen.

Engineering Comment

The unguarded forecast appears to pass, but the inspection uncertainty consumes the apparent margin.

Plausibility Check

There are only four days of raw float and the guard requires five.

Exercise 11: Crew-Hour Loading

A work package needs 640 labor hours over 8 days. One crew provides 8 workers for 8 hours per day. Determine whether one crew is enough.

Solution

Crew capacity is:

Shortfall:

Engineering Comment

One crew is not enough unless the plan adds overtime, a second crew, resequencing or productivity improvement.

Plausibility Check

The crew provides 64 hours per day for eight days, which is clearly below 640 hours.

Exercise 12: Productivity from Installed Quantity

A crew installed 180\ \text{m}^2 of formwork in 45 crew-hours. Baseline productivity is 3.5\ \text{m}^2/\text{h}. Check performance.

Solution

Actual productivity:

Improvement over baseline:

Engineering Comment

The crew is outperforming baseline. Before using the rate for forecasting, confirm that the measured area, crew composition and workface difficulty are comparable.

Plausibility Check

Four square meters per hour is slightly above 3.5, so a mid-teen percentage improvement is reasonable.

Exercise 13: Inspection Delay Float Consumption

An activity has 3 days total float. A required inspection is delayed by 2.5 days. Compute remaining float.

Solution

Engineering Comment

The task remains noncritical, but only barely. Any additional defect correction or inspector delay will put it on the critical path.

Plausibility Check

The delay consumes most of the original three-day float.

Exercise 14: Cost and Schedule Variance

A structural package has EV=480000, PV=500000 and AC=455000. Compute schedule variance and cost variance.

Solution

Schedule variance:

Cost variance:

Engineering Comment

The package is behind planned progress but under cost for the earned work. The recovery plan should focus on sequence and constraints, not only cost.

Plausibility Check

EV below PV gives negative schedule variance; EV above AC gives positive cost variance.

Exercise 15: Schedule Compression Cost Decision

Crashing an activity saves 3 days and costs 18000. The project delay cost is estimated at 9000 per day. Check whether crashing is economically justified.

Solution

Delay cost avoided:

Net benefit:

Engineering Comment

The crash option is economically justified by this screen, but only if the activity is on the critical path and the added resources are constructible.

Plausibility Check

Saving three days at 9000 per day is worth more than the 18000 crash cost.

Exercise 16: Look-Ahead Release Count

A six-week look-ahead has 24 planned packages. The release rule requires at least 18 constraint-free packages. Current count is 16. How many additional packages must be cleared?

Solution

Engineering Comment

Only two more packages are needed numerically, but they must be the right packages for the sequence. Clearing low-priority work does not protect the critical path.

Plausibility Check

The current count is close to the threshold, so the shortfall is small.

Exercise 17: Commissioning Readiness Date

Commissioning needs electrical completion, controls checkout and water test. Forecast finish days are 42, 45 and 43. Commissioning may start only after all are complete plus a 2 day documentation guard. Find earliest start.

Solution

The controlling prerequisite is:

Add guard:

Engineering Comment

The controls checkout controls commissioning readiness. The guard protects against missing test records or incomplete signoff.

Plausibility Check

The start must follow the latest prerequisite, then move two days later.

Exercise 18: Construction Schedule Release Gate

A schedule release requires CPM logic checked, all hard constraints closed, weather buffer positive and CPI/SPI above 0.90. Results are: logic checked, one hard constraint open, weather buffer 0.4 days, CPI 0.95, SPI 0.88. Decide status.

Solution

The release rule is all-of. Two conditions fail:

and:

Therefore release is blocked.

Engineering Comment

The cost index and weather buffer cannot compensate for an open hard constraint and weak schedule performance.

Plausibility Check

An all-of gate fails when any required condition fails; here two conditions fail.

Common Release Mistakes

• Treating CPM dates as credible when permits, inspections, drawings or materials are not ready.
• Averaging hard-gate constraints into a readiness percentage.
• Reporting PPC without coding reasons for missed commitments.
• Using earned value without physically verified quantities.
• Crashing noncritical work and expecting the project finish to improve.
• Consuming weather or inspection float without a recovery trigger.

Validation Package Checklist

• Work-package readiness record with hard gates, soft constraints and owner.
• CPM logic review with current drawing and method-statement assumptions.
• Float report tied to inspection, permit and workface constraints.
• PPC and missed-commitment cause coding from weekly planning.
• Weather buffer, productivity and crew-hour evidence for the relevant location.
• Earned-value quantities tied to inspected, accepted field progress.
• Recovery actions, guard bands and release authority documented.