| Course | MT381 Construction Planning and Scheduling |
|---|---|
| Unit | Unit 5 |
| Paper type | Critical path calculation |
| Length | About 1,180 words, 7 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | BS in Business Administration |
| Updated | October 2026 |
Free sample paper for MT381 Unit 5
Day 202 and the Chain Behind It: An MT381 Unit 5 Critical Path Calculation for a Medical Office Building
[Student Name]
Purdue University Global
MT381: Construction Planning and Scheduling
Unit 5 Critical Path Calculation
[Instructor Name]
[Date]
The network and its results are composite; dates were computed with the stated script, and the sources cited are real.
Method
Dates come from arithmetic in a fixed order, the procedure Kelley and Walker (1959) set out when they introduced the critical path method. The forward pass computes each activity's early start and early finish from its predecessors' dates, its relationship types and lags. The backward pass begins at working day 202, the early finish, and computes late starts and late finishes. Total float is late finish minus early finish. Free float is the time an activity can slip before it delays the earliest date of any successor. A Python script carries out both passes for all 64 activities, and its listing is appended so the dates can be reproduced. The summary table gives each activity's duration, calendar, early and late dates, total float and free float.
The Two Calendars
Seventeen exterior activities run on the weather calendar from Unit 3, which removes 28 anticipated lost days, and everything else runs on the standard calendar. Thirty working days of steel erection therefore span 35 standard working days, from May 10 to June 29, because five anticipated lost days fall inside. The table prints both counts so the difference is not mistaken for a typing error.
Six Activities Worked by Hand
Steel erection starts on day 51, May 10, five standard days after the foundation walls and piers finish and the day after steel delivery, and it finishes on day 85, June 29.
Metal deck may begin ten days after erection begins and must end at least three days after erection ends. Taken alone, the first condition would allow the deck to start on day 61. But the finish tie requires the deck to finish no earlier than day 88, three days after erection, and seventeen exterior working days back from day 88 puts its start at day 70, June 7. The finish tie, not the start tie, controls.
Level 2 concrete on deck follows the deck start by eight days, start-to-start, so it starts on day 78, June 17, and four exterior working days later, with one lost day inside, finishes on day 82.
Exterior framing follows the pour, finish-to-start, starting on day 83 and finishing on day 103, July 26.
Framing and the air barrier are linked at both ends, five days apart at the start and three at the finish. The start tie would allow day 88, but the finish tie requires a finish no earlier than day 106, which puts the start at day 93, July 12.
Curtain wall follows the air barrier, finish-to-start, from day 107, July 30, to day 133, September 7. Dry-in follows.
Twice in six activities, the finish tie, not the start tie, decided when work could begin.
The Critical Path
The critical path, drawn in bold on the logic diagram, runs through twenty activities and three milestones: steel shop drawings, steel submittal review, steel fabrication and delivery, steel erection, metal deck, level 2 concrete, exterior framing, air barrier, curtain wall, dry-in, level 1 drywall hang, level 1 tape and finish, level 1 paint, ceilings and trim-out on levels 1, 2 and 3, test and balance, final inspections, punch list and substantial completion on day 202, December 15, 2027. The contract completion date is December 27, day 209, so the early finish carries seven working days of project float, which the backward pass does not consume because it starts from the early finish.
Near-Critical Activities
Everything within ten days of the critical path is listed so the team watches it. The foundation sequence, from mobilization through foundation walls, carries one to three days. Level 2 drywall through paint carries two days, and level 3 carries four. The switchgear chain, from submittal through permanent power, carries five days, which makes permanent power the chain likeliest to take over the path if the manufacturer's date slips.
Total Float Beside Free Float
Brick veneer carries 48 days of total float and zero free float, because paving follows it directly and shares the same margin. Reporting free float next to total float stops a subcontractor from reading the chain's margin as its own: if the mason takes all 48 days, the paving contractor has none left. Electrical rough-in on levels 2 and 3 shows the same pattern, with 29 and 31 days of total float and none free. De La Garza et al. (1991) argued that float is a shared resource with value to every party, which is why the table shows who would be spending it.
Three Findings About Critical Activities
Not every critical activity behaves the same way. The metal deck is reverse critical: the path enters at its finish, through the finish-to-finish tie from steel, and leaves from its start, through the start-to-start tie to the pour. Shortening the deck by a day pushes its start, and the pour, a day later and delays completion by a day, the opposite of what intuition suggests. The air barrier is neutral: the path enters and leaves at its finish, so changing its duration moves only its start and leaves completion unchanged. Level 1 drywall hang is critical only at its start: it can run two days longer before its finish affects tape and finish. Mubarak (2015) notes that such behavior is easy to miss in networks with start-to-start and finish-to-finish ties, and a manager who tells the deck crew to hurry could, in theory, make the schedule worse.
How the Procurement Chains Sit
The steel procurement chain is the head of the critical path: fifteen days of shop drawings, ten days of review and twenty-five days of fabrication and delivery bring steel to the site on day 50, and erection begins the next workable day. Any day lost in the architect's review moves every later critical date by a day. Curtain wall procurement, by contrast, delivers on day 85 with 21 days of total float before installation needs it, and the elevators deliver with 58 days to spare. Switchgear is the exception among the non-critical chains: its 140 days of fabrication and delivery finish on October 21, only five days before the latest date that would still let permanent power, test and balance and the final inspections happen in time.
A Check on the Script
The hand-worked activities were compared with the script's output line by line, and all twelve dates matched. A second check confirmed that every critical activity has zero total float and that the critical chain is continuous from notice to proceed to substantial completion, with no gap where a non-critical activity interrupts it.
Limits
The calculation assumes the durations and logic hold as planned and that the anticipated weather days fall as averaged. Resource limits are not yet applied, and Unit 7 tests whether the electricians the early dates require are available.
References
De La Garza, J. M., Vorster, M. C., & Parvin, C. M. (1991). Total float traded as commodity. Journal of Construction Engineering and Management, 117(4), 716-727. https://doi.org/10.1061/(ASCE)0733-9364(1991)117:4(716)
Kelley, J. E., & Walker, M. R. (1959). Critical-path planning and scheduling. Papers Presented at the Eastern Joint IRE-AIEE-ACM Computer Conference, 160-173. https://doi.org/10.1145/1460299.1460318
Mubarak, S. (2015). Construction project scheduling and control (3rd ed.). Wiley.
Reading the MT 381 Unit 5 instructions
Unit 5 asks students to calculate early and late dates, total float and free float for their network and to identify the critical path. Many sections expect a hand calculation for part of the network alongside software or script output for the rest, so the grader can see the method. Instructors want relationship types and lags applied correctly in both passes. Calendars must be handled consistently, with any difference between working and calendar days explained. The critical path should be shown on the diagram, and near-critical activities listed. Float should be interpreted, especially the difference between total and free float. Unusual behavior in networks with start-to-start and finish-to-finish ties is worth noting.
How the MT 381 Unit 5 example is put together
The method section sets out the order of the arithmetic and the two calendars. Six activities are then worked by hand with day numbers and dates, showing where finish ties controlled, under a highlighted line making that point. The critical path is named activity by activity, and the seven days before the contract date are explained. Near-critical chains are listed with their float. A section pairs total and free float, using brick and paving and the rough-in chains, with De La Garza and colleagues on shared float. Three findings follow on reverse-critical, neutral and start-critical behavior. Procurement chains are placed, the hand results are checked against the script, and limits close the paper.
MT381 Unit 5 rubric: what earns full points
Critical path papers are mostly marked on computational accuracy, correct treatment of relationship types and calendars, clear identification of the critical and near-critical paths, and interpretation of float. A hand calculation that matches the script shows the student understands what the software does. Rubrics reward correctly applied finish-to-finish and start-to-start ties in both passes. Reporting free float beside total float shows awareness of who shares margin. Identifying reverse-critical or start-critical behavior demonstrates depth. Explaining what the seven spare working days before December 27 mean shows judgment. Results should be traceable from the hand chain to the full table, and sources such as Kelley and Walker appear in APA 7. A paper that explains one surprising result well usually outscores one that lists every float value without comment.
MT381 Unit 5 help: mistakes that cost points
Students often run the software and report its critical path without showing they understand how any date was produced. Others apply a start-to-start lag in the forward pass and forget the finish-to-finish tie on the same pair, which produces dates the logic forbids. Calendar differences are frequently unexplained, so a thirty-day activity spanning thirty-five days looks like an error. Total float is reported as if each activity owned it. Few papers notice that a critical activity can behave unexpectedly. Before submitting, pick one critical activity with two kinds of ties and ask what would happen to completion if it took one day less. If the answer surprises you, explain it.
Get an MT381 Unit 5 example written to your instructions
Paste the Unit 4 network, or the activity list with durations and ties your Unit 5 prompt supplies, plus the rubric and any rule about software. Expect a free first calculation in 24-48h: both passes shown, lags handled correctly in each direction, total and free float listed, and the critical path traced activity by activity. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
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MT381 Unit 5 questions, answered
How do lags change the backward pass?
Each tie type works in reverse. A finish-to-start lag comes off the successor's late start to give the predecessor's late finish; a start-to-start lag comes off the successor's late start to cap the predecessor's late start; a finish-to-finish lag runs late finish to late finish. Mixing these up is the commonest calculation error on lagged networks.
What separates total float from free float?
Total float is how far an activity can slip without moving the project finish. Free float is how far it can slip without delaying any successor's early start. An activity can hold plenty of total float and no free float, meaning its margin is shared with what follows, as brick veneer's is with paving in the sample.
What does reverse critical mean?
In precedence networks with start-to-start and finish-to-finish ties, the critical path can enter an activity at its finish and leave at its start. Lengthening that activity then moves the finish earlier in the calculation. It is a known quirk of lagged logic, not a real opportunity, and it generally signals that the activity should be split.
Where can I find a free MT381 Unit 5 sample paper?
The complete MT381 Unit 5 critical path calculation is on this page, with a hand-worked chain and float for a medical office building.
Why is the metal deck called reverse critical in the MT381 Unit 5 sample?
The path enters the deck at its finish and leaves from its start, so shortening the deck moves its start and the next pour later and delays completion.