Critical path method Study Guide

📖 Core Concepts Critical Path – the longest chain of dependent activities; its length equals the shortest possible project duration. Zero Total Float – activities on the critical path cannot be delayed without pushing the whole project out. Total Float (TF) – time an activity can slip without delaying the project finish: \(\text{TF}= L{F}-E{F}\). Free Float (FF) – time an activity can slip without delaying any successor: \(\text{FF}=E{F}-E{S}^{\text{next}}\). Sub‑critical / Near‑critical Paths – parallel paths shorter than the critical path; near‑critical paths may become critical if delays occur. Critical Path Drag – the amount a critical activity adds to the project’s total duration; if no parallel work exists, drag = activity duration. Crash Duration – minimum possible duration of an activity when extra resources are added (usually at higher cost). Resource Leveling – re‑schedules to respect limited resource availability, possibly creating a new “resource‑critical” path. Resource Smoothing – shifts activities within their total float so resource limits are met without changing the project finish date. 📌 Must Remember Critical Path = longest duration path → defines project length. Zero total float ⇔ activity is critical. TF = LF – EF ; FF = EF – ES of the earliest successor. Fast‑track = add parallelism; Crashing = add resources (costly). Prioritize reducing activities with highest drag. Resource leveling can create a new, longer schedule; smoothing cannot. Small estimate changes → possible new critical path; always re‑run CPM after updates. 🔄 Key Processes Build the Project Model List all activities (WBS). Estimate durations. Define predecessor‑successor relationships. Schedule Calculation (Forward & Backward Pass) Forward Pass: compute Earliest Start (ES) & Earliest Finish (EF). Backward Pass: compute Latest Finish (LF) & Latest Start (LS) without delaying the project. Identify activities where ES = LS (or EF = LF) → critical path. Float Determination \( \text{TF}=L{F}-E{F}\) (or \(L{S}-E{S}\)). \( \text{FF}=E{F}-E{S}^{\text{next}}\). Drag & Crash Analysis Compute drag for each critical activity. Evaluate crash cost‑time trade‑off; choose activities where cost per unit time saved is lowest and drag is high. Resource Adjustment Leveling: shift activities respecting resource limits → may extend project. Smoothing: shift within TF → keep original finish date. 🔍 Key Comparisons Critical Path vs. Resource‑Critical Path Critical Path: longest duration ignoring resources. Resource‑Critical Path: longest duration after resource leveling. Fast‑Tracking vs. Crashing Fast‑Tracking: adds parallelism, may increase risk. Crashing: adds resources, raises cost, reduces duration directly. Total Float vs. Free Float Total Float: impacts project finish. Free Float: impacts only immediate successors. ⚠️ Common Misunderstandings “All long activities are critical.” → Only those on the longest continuous path with zero float are critical. “Float is the same for every activity on a path.” → Float varies per activity based on successors. “Resource leveling never changes the critical path.” – It can create a new, longer resource‑critical path. “Crashing always saves time.” – Only activities with positive drag and feasible crash duration yield savings. 🧠 Mental Models / Intuition “Longest chain = project clock.” Visualize the schedule as a rope; the tightest (longest) segment sets the overall time. “Float is slack in a shoe lace.” Zero slack = you can’t pull; any slack lets you adjust without tripping the schedule. “Drag = weight you’re dragging behind.” The heavier the drag, the more pulling (time) you feel; lighten the heaviest drags first. 🚩 Exceptions & Edge Cases Parallel activities with zero float can exist if they share the same start and finish dates; they are still critical. Negative float indicates an impossible schedule or missed dependencies – requires re‑evaluation. Step‑function crash curves: not always linear; some activities can’t be crashed beyond a certain point regardless of cost. 📍 When to Use Which Choose Fast‑Tracking when schedule pressure is high and the risk of rework is acceptable. Choose Crashing when additional cost is justified and the activity has high drag with a clear linear (or known) cost‑time relationship. Apply Resource Smoothing when resource limits exist but the project finish date must stay unchanged. Apply Resource Leveling when resource constraints are hard (e.g., limited crew) and schedule flexibility is available. 👀 Patterns to Recognize Sudden appearance of zero‑float activities after a minor duration change → likely a new critical path. Multiple activities with identical EF/LF values → potential parallel critical activities. High total float on a long‑duration activity → not on the critical path; may be a candidate for delay without impact. Increasing drag values as project progresses → indicates bottleneck activities becoming more limiting. 🗂️ Exam Traps Distractor: “All activities on the longest path have zero float.” – Only the critical activities (where ES = LS) have zero; a long path can contain non‑critical activities if there’s parallel slack. Distractor: “Resource leveling always reduces total float.” – It usually reduces total float by extending the schedule, not by increasing slack. Distractor: “Crashing any activity reduces project duration.” – Only activities on the critical path (or near‑critical with sufficient drag) affect the overall finish. Distractor: “Free float can be larger than total float.” – By definition, FF ≤ TF; a larger FF would contradict the definitions. --- Use this guide to quickly recall the “what, why, and how” of CPM right before the exam. Good luck!