PROJECT MANAGEMENT: scope/time

WBS — PMBOK Definition

"A deliverable-oriented hierarchical decomposition of the work to be executed by the project team to accomplish the project objectives and create the required deliverables. It organizes and defines the total scope of the project. Each descending level represents an increasingly detailed definition of the project work." The three parts map to: decomposition of the WORK (how), to accomplish OBJECTIVES (why), and create DELIVERABLES (what).

Deliverable vs Objective

Deliverable = the tangible output/product produced — the WHAT; relates to the work, defines scope, and should be Estimable, Parallelisable, Purchasable. Objective = the target/benefit the project aims to achieve — the WHY; relates to purpose, typically written in SMART form. A project can produce every deliverable and still fail its objectives if the deliverable doesn't create the intended benefit. (Note: some lecture slides present this comparison with the column headers swapped — check content against this definition, not just the label.)

Work Package

The smallest unit of the WBS. A set of related tasks and deliverables with: clearly defined interactions with other work packages; clear identification of inputs, outputs and internal activities; and clear estimation of cost, duration and resources.

Work Package Quality Criteria

A well-defined work package should be: Unambiguous, Understandable, Estimable, Parallelisable, and Purchasable.

Milestone

A point of control that separates work packages — used to check progress and approve moving on to the next stage of work.

Work Package Size — Small vs Large

Small WP — Pros: parallelism, estimable, easier to control the team. Cons: more WP-to-WP interactions, harder to define, duplication of work between WPs. Large WP — Pros: efficient use of the team, easier to manage the team, team knows the work best. Cons: risk of overrun, problems detected late, PM has less control.

WBS Orientation — Deliverable vs Objective vs Process

"WBS should be deliverable-oriented (what), not objective-oriented (why) or process-oriented (how)." Pros of deliverable-orientation: deliverables are easier to estimate than objectives; focuses the team on essentials; once scope is defined the "what" is fixed while "how" stays flexible; helps manage scope. Cons: can lose sight of the underlying objectives; restricts further scope changes/creativity; may overlook costly processes consuming time/resources; doesn't come naturally to most teams.

How does a WBS connect to EVA?

A work package is typically assigned a % of total project work and a matching share of the budget (e.g. "Recruit Team: Work 30%, Budget £3,000,000"). This decomposition is exactly what feeds BAC, PV and EV — completing a work package's defined % of work is literally how "% complete" is measured in EV = BAC × actual % complete.

Analogous Estimation

Estimating cost or duration based on a similar past project, adjusted for this one. Fast for early estimates, but inaccurate if the projects differ significantly.

Parametric Estimation

Estimating using a rate or statistical model (e.g. £ per feature, hours per unit) built from data across many past instances, rather than a single comparison project. Useful for repeated, measurable work; depends on the quality of the underlying model/data.

Team-Based Estimation

Estimating by asking the people who will actually do the work. Uses practical, first-hand knowledge, but can be biased or overly optimistic.

Three-Point Estimation

Estimating using three values — optimistic (a), most likely (m), pessimistic (b) — instead of a single guess, to explicitly capture uncertainty. Useful when activity duration/cost is uncertain; formulae are PROVIDED in the exam.

Gantt Chart

A chart showing project activities plotted against time, including durations, start/finish dates, overlaps and milestones. Easy to read and good for communicating a schedule, but does not automatically show the critical path, and dependencies are harder to see than in a network diagram.

PND — Project Network Diagram

A graphical way to view a project's tasks, dependencies, and the critical path. Drawn as either Activity-on-Node, or Event-on-Node/Activity-on-Arrow.

Critical Path

A sequence of activities starting from the first activity of the project and ending with the last, whose activities cannot be delayed without extending the project duration — it is the LONGEST path through the network.

Forward Pass

The calculation pass (left to right through the network) used to find the EARLIEST possible start and finish time for each activity, given its dependencies. Formula: Earliest Finish = Earliest Start + Duration.

Backward Pass

The calculation pass (right to left through the network) used to find the LATEST allowable start and finish time for each activity, without delaying the overall project. Formula: Latest Start = Latest Finish − Duration.

Total Float (TF) / Slack Time

The total amount of time an activity may be delayed from its early start date without delaying the project finish date. Formula: TF = LF − EF = LS − ES. Critical tasks have a Total Float of 0.

Free Float (FF)

The amount of time an activity can be delayed without delaying the early start date of any subsequent activity. Formula: FF = ES(next activity) − EF.

Why is FF ≤ TF?

Free Float only checks the impact on the very next activity's start; Total Float checks the impact on the whole project's finish. A delay can use up all of an activity's Total Float without making the project late, but that same delay may already push back the immediately following activity's start — so FF can never exceed TF.

Why does float exist at all?

Because parallel paths through the network are rarely the same length — a non-critical path finishes sooner than the critical path, so activities on it have spare time before they would start delaying the project.

Critical Task

An activity that cannot be delayed without delaying the whole project — i.e. it has zero float (slack).

Drag Time

The amount of time a critical activity adds to the project duration — how much it would need to be shortened by before it stops being critical. Formula: Drag = the MINIMUM of (the activity's own Duration, D) or (the minimum Total Float, TF, among the relevant parallel activities).

Why is drag capped by the parallel path's float?

Because shortening a critical activity only helps up to the point where a parallel (currently non-critical) path becomes the new bottleneck — beyond that point, further crashing gives no additional benefit to the overall project duration.

Crashing

"A schedule compression technique in which costs and schedule trade-offs are analysed to determine how to obtain the greatest amount of compression for the least incremental cost." Used to shorten the project by adding resources/cost to critical activities.

Crash Duration

Formula: Crash Duration = D − Drag. The shortest an activity can be scheduled for while still speeding up the whole project — crashing beyond this point stops helping because a parallel path becomes the new bottleneck.

Crashing Cost Curve — what it shows

As duration is compressed, cost rises non-linearly. The "trade-off zone" is where crashing meaningfully reduces duration for reasonable added cost; beyond the "limit of analysis" you enter the "fixed cost zone," where duration can't be compressed further no matter how much extra is spent — a PM should stop crashing once further cost buys no further time.

CPM — Summary

CPM finds the critical path from a PND: the Forward Pass propagates durations subject to dependencies (earliest times); the Backward Pass calculates the float/slack in the schedule (latest times). Critical activities — those with zero float — drag the project, and are the target of crashing.

PERT — Program Evaluation and Review Technique

Takes a sceptical view of single time estimates. A variation on CPM using Three-Point Estimation for each activity: shortest possible time (a), most likely time (m), and longest time if the activity overruns (b).

Triangular Distribution — Mean & Variance

Mean: t = (a + b + m) ÷ 3. Variance: σ² = (a² + b² + m² − ab − am − bm) ÷ 18. Formulae are PROVIDED in the exam.

Beta (PERT) Distribution — Mean & Variance

Mean: t = (a + 4m + b) ÷ 6. Variance: σ² = ((b − a) ÷ 6)². Weights the most-likely estimate 4× more heavily than the extremes. Formulae are PROVIDED in the exam.

PERT — Probability Calculation (z-score)

Formula: z = (deadline − expected project duration) ÷ project standard deviation. The resulting z-value is used with a standard Normal distribution lookup table to estimate the probability of finishing by that deadline. Positive z = probability above 50%; negative z = probability below 50%.

Why use PERT instead of a single fixed duration estimate?

A single estimate implies false certainty. PERT explicitly models the range of possible outcomes and lets you calculate a probability of hitting a specific deadline, rather than treating one guess as fact.