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Logic, Paths, and Schedule Optimization
Project Management · Chapter 3: Building a Comprehensive Project PlanSection 3.10 · lesson 24 of 7312 min · free with a free account
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In this lesson
How activity logic sets project duration and how to shorten it.
- Define activities and link them with finish-to-start, start-to-start, finish-to-finish, or start-to-finish relationships
- Apply leads and lags and calculate every path's length to find the critical path
- Choose the cheapest crashing steps by cost per day saved while tracking which paths are longest
- Compare crashing with fast tracking and describe what the schedule baseline holds
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Transcript
Everything said in the video, section by section (1,713 words). Read along, or search it.
Opening Question
Thirty-Six Days of Work in Twenty-One
A library is refitting its reading room. Ten activities, with durations that add up to thirty-six working days. Yet the schedule says the project takes twenty-one. And the sponsor wants it done in eighteen. Why twenty-one, not thirty-six? And what's the cheapest way to cut three days? Both answers come from the logic between activities.
Activity Definition
Verb-and-Object Activities and Milestones
Start with activities. Activity definition breaks each work package into activities: pieces of work a person or crew performs, that take time, and can be put in order. A work package called shelving supply and installation becomes three activities: order the shelving, receive the delivery, install the shelving. Each activity gets a short unique identifier, a name in verb-and-object form, a description of what's included and how completion is recognized, and a duration in working days. A bare noun like shelving could mean buying it or inspecting it. Install the shelving says what's done to what. A milestone is different: a zero-duration marker of a significant point, like reading room open to readers. No work, no duration, no resources.
Schedule Logic
Mandatory and Discretionary Links
Durations alone don't make a schedule. Run all ten activities one after another, and the project takes all thirty-six days. Start them all on the first morning, and it takes only as long as the longest one: six days. Where a real project falls between those extremes depends on which activities must wait for which. That's schedule logic, or sequencing. The logic comes from the dependency log. Mandatory links, forced by physics, contract or law, are fixed: shelving can't be installed before it's delivered. Discretionary links are the team's preferred order, like painting before fitting lights. They're the first place to look when a schedule must get shorter.
Four Relationships
Finish-to-Start Through Start-to-Finish
Each link has one of four relationship types. The first word refers to the predecessor, the second to the successor. Finish-to-start, the most common: the successor can't start until the predecessor finishes. You can't pack loaves still in the oven. Start-to-start: the successor can't start until the predecessor starts. A proofreader begins once the first pages of a program exist. Finish-to-finish: the successor can't finish until the predecessor finishes. Testing a scores page can start early, but can't end before the final scores upload. Start-to-finish: the successor can't finish until the predecessor starts. The old phone line can't stop until the new one starts. Start-to-finish is rare. It reads backward, the situations are uncommon, and a simple finish-to-start link from a milestone like new line live usually says it more clearly.
Leads and Lags
Curing Adhesive and Overlapping Electricians
Links can also carry a lag or a lead. A lag is a deliberate wait between linked activities, when nobody works on that link. At the library, flooring adhesive must cure. Flooring ends on day 10. A plain finish-to-start link would start shelving on day 11. With a two-day lag, days 11 and 12 pass, and shelving starts on day 13. Record the reason, so nobody deletes it as padding. A lead does the opposite: the successor starts before the predecessor finishes. Painting ends on day 9, so lighting would start on day 10. With a two-day lead, electricians start on day 8, overlapping the painters. A lead claims the overlap is safe; if it isn't, the result is rework. Software writes a lag as F S plus two days, and a lead as F S minus two: a negative lag. On a path, lags add days and leads subtract them.
Activity List
Ten Reading Room Activities and Links
Here's the full activity list, with every link finish-to-start. A, measure the room, two days. B, draw the layout, three, after A. C, order the shelving, two, after B. D, strip the old fittings, three, after A. E, lay the flooring, five, after D. F, paint, four, after D. G, receive the shelving delivery, six, after C. H, install the shelving, four, after both E and G, with the two-day lag from E. I, install the lighting, three, after F, with the two-day lead. And J, move in the books, four, after H and I.
Critical Path
Three Paths and the Longest One
A path is a continuous chain of linked activities, from the start to the finish. To list them all, start at A and follow every successor, branching where an activity has two. A leads to B and to D. B goes to C, G, H and J: that's path one. D goes to E, then H and J: path two. And D also goes to F, then I and J: path three. Every activity appears on at least one path. Path one: two plus three plus two plus six plus four plus four is twenty-one days. Path two: eighteen days of durations, plus the two-day lag, is twenty. Path three: sixteen, minus the two-day lead, is fourteen. The project can't finish until every path does, so the longest path sets the duration: twenty-one days, not thirty-six. That longest path is the critical path. A delay on it delays the whole project, day for day. Path two, at twenty, is near-critical: slip it more than a day, and it becomes the longest.
Quick Check
Painting Takes Seven Days
Quick check. Suppose painting, activity F, takes seven days instead of four. Nothing else changes. How long does the whole project take now? Pause, and decide. Twenty-one days. Path three was fourteen; three more days of painting make it seventeen, still shorter than path one. So the project doesn't move: the delay sits off the longest path, and path three has days to spare.
Schedule Compression
Options for Meeting an Eighteen-Day Target
Now the target. The first schedule is just arithmetic. It knows nothing of the sponsor's date. Here the target is eighteen days, three short of twenty-one. The project could question the date, cut scope through change control, accept a later finish, or optimize the schedule while holding scope fixed. Schedule compression has two standard techniques, crashing and fast tracking, and both work only on the longest path. Crashing shortens an activity by adding resources, like extra people, overtime or premium delivery, at a cost. Options are compared by cost per day saved: extra cost divided by days saved.
Crash Options
Six Steps and Diminishing Returns
Six crash steps are on offer. X1, order the shelving faster: one day off path one, for one hundred dollars. X2, the first day off the shelving delivery: one hundred fifty. X3, a second day off the delivery: two hundred fifty. Both are on path one. X4, a day off the flooring, on path two: one hundred eighty. X5, a day off installing the shelving, on paths one and two: three hundred. X6, a day off moving the books, on all three paths: three hundred sixty. The delivery steps show diminishing returns: each extra day costs more, since work can't be divided without limit, and every activity has a minimum duration.
Worked Example
Buying Three Days for Seven Hundred Thirty Dollars
Choose one step at a time, checking which paths are longest. At first: twenty-one, twenty and fourteen. Only path one matters, so buy the cheapest step on it: X1, one hundred dollars. Now paths one and two are both twenty. Cutting path one alone no longer shortens the project. A step must cut both. X5 cuts both for three hundred. X2 plus X4 would cost three hundred thirty. So buy X5: nineteen and nineteen. X5 can't be used again. X6 would cut both for three hundred sixty, but X2 plus X4 costs three hundred thirty. Buy those: eighteen and eighteen. Total: one hundred, plus three hundred, plus three hundred thirty: seven hundred thirty dollars. A check of every combination confirms nothing cheaper reaches eighteen. X3 was never bought: two hundred fifty on path one alone would leave path two untouched. In larger networks, cheapest-first isn't guaranteed to be cheapest overall.
Fast Tracking
Ordering Shelving Before the Layout Is Final
Fast tracking takes the other route. It overlaps activities planned in sequence, by turning finish-to-start into start-to-start, or adding a lead. No new resources. Here, order the shelving one day before the layout drawing is final: a one-day lead from B to C. Path one drops from twenty-one to twenty, at no extra spending. But path two is still twenty, so the project gains only one day. The price is rework: if the final layout changes the number of shelving units, the order must change. The saving is certain; the cost arrives only if the guess is wrong. Fast tracking applies mainly to discretionary logic. Mandatory logic can't be overlapped without breaking its reason.
Quick Check
Cheapest Route to Nineteen Days
Quick check. Suppose the sponsor would accept nineteen days instead of eighteen. Using the crash options, what's the cheapest total cost? Two hundred fifty, four hundred, or four hundred thirty dollars? Pause, and decide. Four hundred. X1 brings path one to twenty for one hundred. Then both paths are twenty, and X5 cuts both for three hundred. Two hundred fifty, X1 plus X2, shortens only path one, so the project stays at twenty. Four hundred thirty, X1 plus X2 plus X4, works but costs more.
Comparison
Known Money Versus Possible Rework
Compare the two. Crashing changes the resources on an activity. Its cost is direct, known in advance, and rises per day as the limit nears. Fast tracking changes the logic between activities. Its up-front cost is little or nothing, but the cost of rework is uncertain. Crashing risks cost overruns and coordinating added people. Fast tracking risks rework and errors from acting on incomplete information. One trades money for time at a known price; the other trades a chance of rework, at an unknown one. Which is more tolerable depends on the budget, how well the overlapped work is understood, and how costly a late surprise would be.
Schedule Baseline
The Approved Version Progress Is Measured Against
When logic, durations and any compression are settled, the schedule becomes the schedule baseline: the approved version that progress is measured against. It holds the activity list, every relationship with its leads and lags, the calculated dates of activities and milestones, the assumptions behind them, and the schedule contingency. It records which activities were crashed or overlapped. The sponsor usually approves it, accepting the dates, and the costs and risks of compression behind them. After approval it changes only through change control. And it stays separate from the current schedule, the working copy of actual dates and forecasts.
Key Takeaways
Relationships, Paths, and Compression
To recap. Name activities with verbs, and link them with finish-to-start, start-to-start, finish-to-finish or start-to-finish. Add lags for real waits and leads for safe overlaps: lags add to a path, leads subtract. The longest path sets the duration. Watch the near-critical ones. Compress only the longest path: crashing costs known money, fast tracking risks rework.
About Project Management at UPI Study
Project Management (Business 230) is a self-paced online course of 73 video lessons in 12 chapters, from starting and defining a project to planning, budgets, scheduling tools, proposals, contracts, execution, monitoring, closure, teams and certification. It carries a NCCRS credit recommendation for 3 semester credits.
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About Logic, Paths, and Schedule Optimization
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