CPM Fundamentals - Worked Examples

A canal excavation activity has an Early Start ($ES$) of day $4.00$ and a duration of $6.00$ days. Calculate the Early Finish ($EF$) of the excavation.

A canal turnover sequence requires the following dependent activities:

• Activity F (Concrete Lining) finishes on day $30.0$.
• Activity G (Concrete Curing) requires $14.0$ days and must finish before any testing can occur. It depends directly on Activity F.
• Activity H (Water Delivery Testing) requires $5.00$ days and depends directly on Activity G.
• Activity I (Final Turnover Inspection) depends on Activity H and requires $2.00$ days.

Calculate the Early Finish ($EF$) of the Final Turnover Inspection.

A lateral canal excavation (Activity C) requires Right-of-Way (ROW) clearing (Activity A) to be finished. The clearing finishes on day $12.0$. However, due to local community access constraints, the equipment cannot mobilize to the site until day $15.0$ (Activity B). If Activity C requires both Activity A and Activity B to be completed before it can start, calculate the Early Start of the lateral canal excavation.

A $500 \text{ m}$ canal section requires $2500 \text{ m}^3$ of excavation. A backhoe and dump truck crew has a verified daily output of $250 \text{ m}^3\text{/day}$. Calculate the planned duration for the canal excavation activity, assuming a $0.80$ efficiency factor due to limited site access.

Concrete lining can begin only after canal excavation, subgrade preparation, and formwork are completely finished. Their Early Finishes are day $8.00$, day $10.0$, and day $9.00$, respectively. Calculate the Early Start for the concrete lining activity.

A structure installation activity has an Early Start ($ES$) of day $12.0$, Early Finish ($EF$) of day $17.0$, Late Start ($LS$) of day $15.0$, and Late Finish ($LF$) of day $20.0$. Calculate the Total Float.

A simplified irrigation project network has three continuous paths from start to finish:

• Path A: Site Survey, Canal Excavation, Concreting, Concrete Curing = $18.0$ days
• Path B: Site Survey, Material Delivery, Structure Installation = $14.0$ days
• Path C: Site Survey, Final Inspection, Project Turnover = $12.0$ days

Identify the critical path and determine the minimum project completion time.

A material delivery activity finishes on day $7.00$ ($EF = 7.00$). Its immediate and only successor, structure installation, has an Early Start ($ES$) of day $11.0$. Calculate the free float of the delivery activity.

An activity sequence consists of Canal Excavation (Task A) followed by Subgrade Preparation (Task B). Task A has an Early Start ($ES$) of $0$ and a duration of $6.00$ days. Task B has a duration of $4.00$ days. Calculate the Early Start and Early Finish for both tasks.

Concrete Curing (Task C) has a duration of $5.00$ days and precedes Water Delivery Testing (Task D), which has a Late Start ($LS$) of $12.0$ days. If Task D is the only immediate successor of Task C, calculate the Late Finish ($LF$) and Late Start ($LS$) of Task C.

Procurement of steel gates (Activity E) has a duration of $8.00$ days, with $ES = 4.00$ days and $LS = 8.00$ days. Its immediate successors are Gate Installation (Activity F, which has $ES = 15.0$ days) and Electrical Wiring (Activity G, which has $ES = 16.0$ days). Assume one calendar, finish-to-start zero-lag relationships, and consistent backward-pass data without an earlier imposed deadline. Calculate the Total Float and Free Float of Activity E.

A project network diagram for an irrigation dam has three parallel paths with expected durations:

• Path 1: Cofferdam Construction $\rightarrow$ River Diversion $\rightarrow$ Core Trench Excavation with duration $18.5$ days
• Path 2: Foundation Grouting $\rightarrow$ Embankment Fill $\rightarrow$ Spillway Concreting with duration $22.0$ days
• Path 3: Access Road Grading $\rightarrow$ Temporary Facilities Setup with duration $15.0$ days

Identify the critical path and the total project duration.