Chapter 14 — Exercises

Work these with a pencil, a table, and no scheduling software. The point is not to be fast; it is to know what the software should have told you. Selected answers are in Appendix J; additional worked networks are in Appendix B.

Difficulty legend: ⭐ basic · ⭐⭐ applied · ⭐⭐⭐ advanced judgment · ⭐⭐⭐⭐ extension / research

Convention reminder: all networks in these exercises use the elapsed-time convention from §14.6.1 — ES = 0 for the first activity, EF = ES + Duration. Durations are work days (WD) unless stated otherwise.

Part A — Conceptual Understanding ⭐

A1. In one sentence each, name the four jobs a schedule does (§14.1), and identify which one most baseline schedules are actually built for.

A2. State the forward-pass rule and the backward-pass rule in your own words. Explain why one takes a maximum and the other takes a minimum, in terms of what is physically happening on the job.

A3. Define total float, free float, interfering float, and independent float. For each, state in one sentence what it protects.

A4. An activity has total float of 9 days and free float of 0. What does that combination tell you about the activity's position in the network, and who bears the cost if the activity uses all nine days?

A5. Distinguish hard logic, soft logic, and resource logic. Give one construction example of each that is not from this chapter.

A6. Why is a start-to-finish (SF) relationship almost always a modeling error on a building project?

A7. Explain, in terms of the backward pass, why an activity with no successor gets an enormous total float. Why is that dangerous rather than merely inaccurate?

A8. What is negative float, and what is the difference between negative float against a contract date and negative float against an owner's operational date?

A9. Name the five rules of good activity definition from §14.3.2, then explain why the duration cap exists. What disease does a 60-day activity produce in your monthly updates?

A10. Why does a cash-flow curve take an S shape? Why does the money peak before the craft headcount does?

A11. What is the difference between a baseline schedule being accepted and being approved, and why does the distinction matter to the contractor eighteen months later?

A12. Give two reasons a project might legitimately have more than one critical path, and state what that condition does to the cost of buying a single day back.

Part B — Applied Analysis ⭐⭐

B1. A superintendent tells you: "Steel is the critical path. It's always the critical path." Write the three-sentence reply you would give a first-year field engineer who repeats that to you, and describe the one thing you would ask the scheduler to show you.

B2. A subcontractor's schedule for its scope contains 62 relationships, of which 41 are start-to-start or finish-to-finish with lags between 3 and 22 days. What do you suspect, and what two questions do you ask?

B3. You inherit a schedule with 14 constrained activities out of 340, including a Mandatory Finish on the "Building Dried-In" milestone. Explain precisely what that mandatory constraint does to the network's ability to compute a critical path, and describe what you would see in the monthly update that would fool you.

B4. Your interior partitions duration is computed as 18,600 LF ÷ (310 LF/day × 3 crews) = 20 work days. List five things that must be true for that 20 days to be achievable, and identify which of the five you would put in writing during buyout.

B5. An owner's representative asks you to absorb an 11-day scope addition "in the float." Write the five questions from the §14.6 decision framework you would answer before responding, and state what information you would put in the meeting minutes regardless of the outcome.

B6. Kestrel's baseline for Northgate contained two work days of project float against a 565-day contract. Argue both sides: (a) why this is normal and defensible, and (b) why it should have prompted a conversation with Meridian before the baseline was submitted.

B7. Your schedule shows the money peaking in month 10 and the craft workforce peaking in month 14. A colleague says one of the two curves must be wrong. Explain why both can be right and what staffing mistake you would make if you believed your colleague.

B8. Compare a line-of-balance schedule and a CPM network for: (i) Harbor Ridge's 34-lot subdivision, (ii) the Cottonwood Creek bridge, and (iii) the Northgate interiors. For each, say which you would use as the primary tool and why.

B9. Kestrel's house rule is that any path with total float of 10 work days or fewer is managed as critical. Propose the threshold you would use on (a) a 92-day production house, (b) a 425-day community center, and (c) a 565-day hospital. Justify each number in terms of how fast a path can lose float on that kind of job — not as a percentage of the contract time.

Part C — Calculations and Deliverables ⭐⭐–⭐⭐⭐

C1 — Willow Street substructure and steel network ⭐⭐

Here is a seven-activity fragnet for the Willow Street Community Center substructure and structure.

(a) Run the forward pass. State the project duration. (b) Run the backward pass. (c) Compute total float and free float for every activity. (d) Identify the critical path. What is surprising about it? (e) You can expedite the steel package (D) for $1,900 per day saved. How many days of expediting actually shorten the project? At what point does it stop helping, and why?

C2 — Durations from quantities ⭐⭐

Compute the duration in work days for each activity below using duration = quantity ÷ (production rate × number of crews), then state one assumption you are making that, if wrong, would change your answer.

C3 — Calendar and money ⭐⭐

Willow Street's contract time is 425 calendar days. Assume 121 weekend days in the span, 9 observed weekday holidays, and a 14-day weather allowance for exterior work. Willow Street's general conditions budget is $680,000 and liquidated damages are $1,200 per calendar day.

(a) How many work days do you actually have? (b) What is the daily general-conditions burn rate, in dollars per calendar day? (c) What is the total daily exposure to slipping substantial completion? (d) Your network computes a 268-work-day longest path. How many work days of project float do you have, and what is that float worth in dollars if you had to buy it back? (e) A subcontractor asks for a 9-work-day extension on a critical activity, offering a $14,000 credit in exchange. Take it or refuse it? Show the arithmetic.

C4 — Auditing a schedule for phantom float ⭐⭐⭐

A subcontractor's 210-activity schedule reports 26 work days of total float on its driving path. Your audit finds:

1. A Finish On constraint on the schedule's completion milestone, set 15 work days later than the date in the subcontract.
2. Seven activities with no successor, of which three are genuine predecessor work. Tying them in properly extends the driving path by 5 work days.
3. One FS−8 negative lag between "hang drywall" and "tape and finish," which when modeled correctly as a start-to-start relationship with a realistic offset extends the path by 4 work days.
4. Durations sampled at roughly 12 percent longer than the subcontractor's own manpower commitments support.

(a) What is the corrected total float? (b) Which of the four findings does not change the CPM arithmetic, and why does it still matter? (c) Write the three-sentence email you send to the subcontractor's project manager.

C5 — Perturbing the Northgate fragnet ⭐⭐⭐

Return to the ten-activity Northgate network in §14.6.2 (base duration 103 WD, critical path A–B–E–G–H–I–J). A differing site condition adds 6 work days to activity E (spread footings), taking it from 18 to 24 work days.

(a) Re-run the forward pass and give the new project duration. (b) Re-run the backward pass. (c) Give the new total float for every activity. (d) Does the critical path move? What happens to the float on the steel procurement chain, and why is that worse news than it sounds?

C6 — Cost-load a schedule and draw the S-curve ⭐⭐⭐

Willow Street's $6,800,000 contract sum is distributed across six summary activities. Assume each activity's value spreads evenly across the months it spans, and that a month is one billing period.

(a) Build a table of monthly billing and cumulative billing for months 1 through 14. (b) Plot the cumulative percentage. Does it produce an S? Where is it steepest, and why? (c) Willow Street holds 5 percent retention throughout. In which month does cumulative billing first exceed 50 percent, and what is the cumulative retention held at that point? (d) Your actual billings through month 7 are 12 percent below your curve. Name three different explanations and say what evidence would distinguish among them.

C7 — Build the network from a narrative ⭐⭐⭐

A subcontractor gives you this description of its scope on a two-story building: "We'll get our overhead ductwork in on both floors, then our piping, then we'll do the in-wall work. Once the walls are closed we come back for grilles, diffusers, and thermostats, and then we start up and balance. We've got one sheet-metal crew and one pipe crew."

(a) Convert the narrative into an activity list with a responsible party, an area, and a duration basis for each activity. Assume six weeks of overhead work per floor if resources allow. (b) Draw the network. Mark every relationship as hard, soft, or resource logic. (c) Identify the one sentence in the narrative that creates a resource constraint, and show how it changes the duration.

C8 — Line of balance at Harbor Ridge ⭐⭐⭐

Colton Reyes is building out the 34-lot Harbor Ridge subdivision for Tessa Bright Homes. His framing crew completes one house every 4.5 work days, and his drywall crew completes one house every 4.0 work days. Drywall starts lot 1 on work day 12; framing completes lot 1 on work day 4.5. Both crews move through the lots in numerical order, and drywall on any lot obviously cannot start until framing on that lot is finished.

Let framing complete lot n on day 4.5n, and let drywall start lot n on day 12 + 4.0(n − 1).

(a) At which lot does the drywall crew catch the framing crew — that is, at which lot would drywall be scheduled to start before framing has finished? (b) Draw the two production lines on a chart of lot number (vertical) against work day (horizontal). What does the crossing point look like, and why is this picture more useful to Colton than a 1,394-activity CPM network? (c) You have three ways to fix it: slow the drywall crew to match framing, speed the framing crew to match drywall, or increase the head start before drywall begins. Compute the head start required to avoid any collision through all 34 lots, and say which of the three fixes you would actually choose on a production homebuilding operation and why.

Part D — Judgment and Ethics ⭐⭐⭐

D1. Your project executive asks you to add 12 percent to every duration in the baseline "so we have some room." Write your response. If you refuse, propose the alternative and explain how you would make the contingency visible and manageable instead.

D2. Two months into a job, the owner issues a change. Your scheduler points out that if you resequence two soft-logic relationships in this month's update, the changed work will fall on the critical path and the delay becomes compensable. Nothing you would be writing is false. Explain precisely what is wrong with doing it, and what the likely consequence is if you are found out in a claim three years later.

D3. A subcontractor submits a schedule showing completion three weeks ahead of its subcontract date. Do you accept it? Write the two sentences you would add to your acceptance letter.

D4. Your contract's schedule specification says all float is owned by the owner. Your baseline contains 22 days of float on the enclosure path. What do you do differently during the job because of that clause — in your reporting, your notices, and your buyout — and what would you have negotiated before signing if you could go back?

D5. The acceleration on Northgate cost $168,000 and recovered 17 days, and it also produced trade stacking, a rework event, and a spike in near-misses in weeks 34–36. Write the paragraph you would add to an acceleration proposal that discloses the non-monetary cost honestly. Then argue the other side: what is the risk of putting that paragraph in a document the owner will read?

Part M — Mixed and Interleaved Practice ⭐⭐–⭐⭐⭐

M1. (with Chapter 12 and Chapter 13) Take one line from your Willow Street detailed estimate — pick a self-perform item with a quantity and a crew. Produce both a duration and a labor cost from the same production rate, showing every step. Then change the production rate by 20 percent and show what happens to both numbers. Write one sentence explaining why an estimator and a scheduler who disagree about a production rate are having the same argument twice.

M2. (with Chapter 6) Choose the five activities in your Willow Street schedule with the greatest schedule risk. For each, get three-point durations (optimistic, most likely, pessimistic), compute the expected duration and the approximate standard deviation, and compare the expected duration to what you put in the schedule. Then add the five to your Chapter 6 risk register with a response and an owner.

M3. (with Chapter 10) Build the room-level interior sequence for one Willow Street multipurpose room: overhead rough-in by trade, inspection, close walls, ceiling grid, finishes. Now do it for six rooms with one crew per trade, and show where the crews collide. Which relationships in your answer are hard, and which are resource logic?

M4. (with Chapter 13) Using your Willow Street general conditions estimate, compute the daily burn rate. Then take three activities from your schedule with different amounts of float and compute what each one's float is worth in dollars. Rank them. Does the ranking match your intuition about which activities matter most?

M5. (with Chapter 27, looking forward) Take the next six weeks of your Willow Street CPM and produce a look-ahead. For every activity in it, list the constraints that must be removed before the work is genuinely ready. How many of those constraints are visible anywhere in the CPM?

M6. (with Chapter 29, looking forward) Take your Willow Street baseline and simulate month six: mark three activities complete, two in progress, and one not started that should have been. Recalculate by hand. What is your new forecast completion date, and what would you write in the narrative that accompanies the update?

M7. (with Chapter 15, looking forward) You have a schedule that computes 11 work days longer than the contract time allows. Write the half-page you would put in front of a bid/no-bid meeting: what the overrun is, what it would cost to compress it, what the residual risk is, and whether you would recommend bidding the job. State explicitly what you would need to believe for the answer to be yes.

Part E — Research and Extension ⭐⭐⭐⭐

E1. Find a real, publicly posted construction bid package from a public agency in your region — most state DOTs, school districts, and municipal purchasing portals publish them. Locate the Division 01 schedule specification. Summarize, in one page: the required software and format, the baseline submission deadline, the maximum activity duration, whether cost or resource loading is required, what the specification says (or does not say) about float ownership, the update frequency, and what the specification requires if the schedule shows a completion date other than the contract date. Compare it to what this chapter recommends and note where they differ.

E2. Identify a contracting agency that requires a formal schedule assessment, and obtain the current assessment criteria directly from the agency's own published guidance rather than a secondary source. Compare the checks to the thirty-minute review in §14.8. Which of the agency's checks are structural, and which require human judgment? Write a short note on why the numeric thresholds you find may differ from numbers quoted elsewhere.

E3. Interview a working scheduler or project controls manager for twenty minutes. Ask: (1) what percentage of the schedules they receive from subcontractors are CPM networks versus bar charts; (2) the most common defect they find; (3) the last time the critical path on one of their jobs moved, and what moved it; and (4) how they handle float ownership when the contract is silent. Write up the answers and compare them to this chapter. Where the practitioner disagrees with the book, say who you think is right and why.