3.2 Project Planning & Control: Scope and WBS, Gantt Charts, Critical Chain (CCPM), Risk & Earned Value

3.2 Project Planning & Control

Schedule math is only part of project management. The NCEES specification also lists scope, cost, risk analysis, Gantt charts, and CCPM. Industrial engineers manage plant expansions, equipment installations, ERP rollouts, and improvement programs, and all of them are judged on scope, time, and cost.

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1. Scope and the Work Breakdown Structure (WBS)

The scope statement defines deliverables, acceptance criteria, exclusions, assumptions, and constraints. The work breakdown structure decomposes that scope into deliverables and then into work packages small enough to estimate, schedule, and assign.

• The 100% rule: the WBS includes all of the work in the scope, and only that work. Each level must add up exactly to its parent.
• Work package size: a common rule of thumb is between 8 and 80 hours of effort, or no longer than one reporting period.
• Scope creep is uncontrolled growth in scope. Prevent it with a baseline and a change control process: a change request is evaluated for its effect on cost, schedule, and risk and is approved or rejected, often by a change control board.

The triple constraint links scope, time, and cost. Changing one changes at least one of the others or the quality of the result.

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2. Gantt Charts and Resource Leveling

A Gantt chart (named for Henry Gantt) draws each activity as a horizontal bar on a calendar, often with precedence arrows, milestones, and a progress line. It is easy to read for status reporting, but on its own it hides float and dependencies, which is why it is usually built from a CPM network. Using the project from the previous section (weeks):

Activity      Wk: 0   2   4   6   8   10  12  14
A Design          ████████                          (critical)
B Order robot     ████████████░░                    (1 wk float)
C Fixtures                ████████████░░░░          (2 wk float)
D Floor prep              ██████                    (critical)
E Install                       ██████████          (critical)
F Test                                    ████      (critical)
░ = total float

Resource leveling shifts activities within their float so that resource use (crews, cranes, budget) does not exceed limits or swing sharply. Leveling that needs more than the available float lengthens the project. Resource conflicts can also make the "critical path" a resource chain rather than a pure precedence chain, which is the starting point for CCPM.

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3. Critical Chain Project Management (CCPM)

Eliyahu Goldratt's Critical Chain (1997) applies the Theory of Constraints to projects. It argues that individual estimates hide large safety margins that are then wasted, because people start late (student syndrome), work expands to fill the time (Parkinson's law), and early finishes are not passed on.

CCPM practice:

1. Aggressive estimates: schedule each task at roughly a 50% confidence duration, often about half of the padded estimate.
2. Critical chain: the longest chain of dependent tasks considering both precedence and resource conflicts.
3. Project buffer: pool the removed safety into one buffer at the end of the critical chain.
4. Feeding buffers: place buffers where non-critical chains feed the critical chain, so their delays do not reach it.
5. Resource buffers: alert critical-chain resources before they are needed.
6. Buffer management: track buffer consumed against chain completed (a "fever chart"). Green means no action, yellow means plan recovery, and red means act.

Buffer sizing example. A critical chain has four tasks with padded estimates of 10, 8, 12, and 6 days (36 days total). Aggressive estimates of half each total 18 days, so the safety removed is 5, 4, 6, and 3 days.

• Cut-and-paste method: buffer = 50% of the chain = 9 days, so the plan is 18 + 9 = 27 days.
• Root-square-error method: buffer = $\sqrt{5^2 + 4^2 + 6^2 + 3^2} = \sqrt{86} = 9.3$ days. Pooling works because tasks rarely all overrun at once.

Either way, the promised date is well under the 36 days obtained by adding padded estimates.

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4. Project Risk Analysis

Risk management cycle: identify risks, assess probability and impact, plan responses, and monitor.

A probability-impact matrix scores each risk (for example 1 to 5 on each scale) to rank them. For quantitative analysis, compute each risk's expected monetary value (EMV):

$EMV = P(\text{event}) \times \text{Impact}$

Example:

• Late robot delivery: 20% chance, $50,000 impact, EMV = $10,000.
• Floor rework: 10% chance, $80,000 impact, EMV = $8,000.
• An energy rebate (an opportunity): 30% chance of saving $20,000, EMV = −$6,000.

The net expected cost is $12,000, a reasonable starting contingency reserve. Decision trees and Monte Carlo schedule simulation extend the same idea.

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5. Cost Control with Earned Value Management (EVM)

EVM combines scope, schedule, and cost into three measures, all in dollars:

• PV (planned value): budgeted cost of work scheduled to date.
• EV (earned value): budgeted cost of work actually performed (percent complete × BAC).
• AC (actual cost): what that work actually cost.
• BAC (budget at completion): the total budget.

Worked example. A $200,000, 10-week automation project is reviewed at week 5. PV = $100,000, the work is 45% complete so EV = $90,000, and AC = $110,000.

• $CV = 90{,}000 - 110{,}000 = -\text{\textdollar}20{,}000$ (over budget)
• $SV = 90{,}000 - 100{,}000 = -\text{\textdollar}10{,}000$ (behind schedule)
• $CPI = 90{,}000 / 110{,}000 = 0.818$ and $SPI = 0.90$
• $EAC = 200{,}000 / 0.818 = \text{\textdollar}244{,}444$, so $VAC = -\text{\textdollar}44{,}444$ and $ETC = \text{\textdollar}134{,}444$
• $TCPI = (200{,}000 - 90{,}000)/(200{,}000 - 110{,}000) = 1.22$

Finishing on budget would require 22% better cost efficiency than planned for the rest of the project, while the team is currently 18% worse. That is unrealistic, so management should rebaseline the budget or reduce scope through change control.