Question 1

Independent float formula with clear event times For an activity i→j of duration t, let L_i be the latest event time at its start (tail) and E_j be the earliest event time at its finish (head). If we denote t1 = L_i and t2 = E_j, what is the indepen…

Accepted Answer

Introduction / Context: Float measures scheduling flexibility. Several flavors exist: total float, free float, and independent float. Independent float represents the amount of delay available to an activity without affecting either the earliest start of its successor or the latest finish of its predecessor—making it a conservative, “independent” buffer. Given Data / Assumptions: Activity i→j with duration t. L_i = latest permissible time of event i (latest finish of preceding event), denoted t1. E_j = earliest permissible time of event j (earliest start for successors), denoted t2. Concept / Approach: The well-known expression for independent float is IF = E_j - L_i - t. With t1 = L_i and t2 = E_j, this becomes IF = (t2 - t1) - t. If the result is negative, independent float is taken as zero in practical scheduling, because negative float indicates infeasibility under current constraints. Step-by-Step Solution: Start with definition: IF = earliest at head − latest at tail − duration.Substitute symbols: IF = E_j − L_i − t.Map to problem notation: t2 = E_j, t1 = L_i → IF = (t2 − t1) − t.Hence, the correct choice is (t2 − t1) − t. Verification / Alternative check: Testing on a simple network confirms that delaying the activity by at most IF neither pushes the successor’s earliest start nor encroaches on the predecessor’s latest finish. Why Other Options Are Wrong: (t1 − t2) − t: Sign reversed; would suggest negative float for normal schedules.t − (t2 − t1): Rearrangement that does not match the definition; equals t1 − t2 + t.(t1 + t2) − t and t + (t1 − t2): Not dimensionally meaningful per the independent float definition. Common Pitfalls: Confusing independent float with free float (which uses earliest times only). Using negative independent float directly; in practice, it is set to zero and highlights a tight network. Final Answer: (t2 - t1) - t

Question 2

Scheduling a project by CPM: What are the essential steps? When preparing a CPM schedule for an engineering project, which set of actions correctly describes the overall process?

Accepted Answer

Introduction / Context: CPM (Critical Path Method) is a deterministic scheduling technique used to plan, monitor, and control project timelines. It relies on a clear breakdown of work, time estimates, precedence logic, and a network representation from which critical paths and floats are computed. Given Data / Assumptions: The project is suited to CPM (deterministic activity durations). All activities can be identified and sequenced logically. Accurate time estimates are available or can be developed. Concept / Approach: The CPM workflow includes: breaking the project into discrete activities; establishing logical relationships among them; estimating durations; and drawing the network (AOA or AON). This allows a forward and backward pass to compute earliest and latest times, floats, and identify the critical path. Step-by-Step Solution: Identify activities and milestones.Sequence activities using precedence logic.Estimate durations based on productivity data and resource plans.Draw the network and run time analysis to find the critical path and floats. Verification / Alternative check: Any CPM tutorial or worked example follows these steps, confirming that all listed points collectively form the correct process rather than any single step alone. Why Other Options Are Wrong: Options a–c each capture only a fragment. CPM requires all steps to work together. Common Pitfalls: Skipping proper activity definition, leading to overlaps or gaps. Ignoring precedence constraints while estimating durations, causing unrealistic schedules. Final Answer: All the above (activities defined, durations estimated, logical sequence set, and the network drawn)

Question 3

Project classification: How are power stations generally treated? Considering typical scope (civil, structural, mechanical, electrical, and control systems), a power station falls under which class of construction project?

Accepted Answer

Introduction / Context: Power stations combine substantial civil works with complex process systems (boilers, turbines, generators, cooling systems). Such projects are distinguished not only by structural scale but also by the depth of mechanical, electrical, and control integration—hallmarks of industrial construction. Given Data / Assumptions: Scope includes process plants, heavy MEP (mechanical, electrical, plumbing), and controls. Commissioning and performance testing are critical deliverables. Safety and reliability requirements are stringent. Concept / Approach: Industrial construction describes facilities centered on production or energy conversion. While heavy civil elements may be present (foundations, cooling towers), the dominant characteristic is the integration of process systems—placing power stations firmly in the industrial category. Step-by-Step Solution: Assess project nature: a process-driven facility.Consider systems integration: extensive MEP and control systems.Map to category: “industrial construction.” Verification / Alternative check: Industry classifications group refineries, chemical plants, and power stations together as industrial projects due to process-centric scope and specialized commissioning. Why Other Options Are Wrong: Light construction: Suits dwellings and small buildings.Heavy construction: Emphasizes linear or massive civil works (dams, highways); power plants are process facilities.Electrical construction: A discipline, not a project class. Common Pitfalls: Equating presence of heavy civil elements with classification as “heavy construction.” Ignoring the defining process/commissioning focus of industrial projects. Final Answer: industrial construction

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