By the end of this chapter, you will be able to:
Mastering these skills will help you plan and manage projects efficiently, ensuring successful and timely completion in your future trade work.
Project networks are essential quantitative tools that enable accountancy professionals to plan, schedule, and control projects effectively, especially in environments where multiple interdependent activities must be coordinated. In Kenya, where diverse projects from financial audits to system implementations require precise time and resource management, mastering project network analysis enhances decision-making and optimises project outcomes. This chapter focuses on the fundamental terms used in project networks, laying the groundwork for understanding complex project scheduling and control techniques.
Project networks rely on a set of core terms and concepts that describe the structure, timing, and dependencies of project activities. Understanding these terms is critical for accountants tasked with budgeting, forecasting, and monitoring project progress to ensure timely delivery within cost constraints.
An activity in project networks represents a distinct task or work element that must be completed as part of the overall project. Activities consume time and resources and are the building blocks of the project schedule.
Example 1: A bank plans to implement a new accounting software system. One activity is "Data Migration" estimated to take 5 days.
Given: Duration = 5 days
Calculate the time required to complete the activity:
Answer: The activity "Data Migration" requires 5 days.
Example 2: In a retail business expansion, the activity "Inventory Setup" takes 3 days, followed by "Staff Training" which takes 4 days. Both are sequential.
Calculate the total duration for both activities.
Step 1: Add durations: 3 days + 4 days
Step 2: Total duration = 7 days
Answer: Total duration for both activities is 7 days.
Example 3: For a cooperative's financial audit, activities "Document Collection" and "Preliminary Review" are done in parallel, taking 2 and 3 days respectively.
Calculate the project duration for these parallel activities.
Step 1: Identify the longer duration: max(2,3) = 3 days
Answer: The parallel activities take 3 days to complete.
An event or node in project networks signifies a point in time marking the start or completion of one or more activities. Events themselves consume no time or resources but represent milestones in the project timeline.
Example 1: In a SACCO loan processing project, event 1 marks the start of "Application Verification" and event 2 marks its completion.
Given: Activity duration between event 1 and 2 is 4 days.
Calculate the duration between events.
Answer: Duration between event 1 and 2 is 4 days.
Example 2: A county government office project has event 3 as the completion of "Budget Approval" and event 4 as the start of "Procurement".
Given: No activity duration between event 3 and 4 (events occur consecutively).
Calculate activity duration.
Step 1: Duration = 0 (events only mark milestones)
Answer: No duration; events mark transition points.
Example 3: In a hotel renovation, event 5 marks start of "Electrical Works" and event 6 marks start of "Interior Painting". If "Electrical Works" takes 6 days, find the duration between events 5 and 6.
Given: Activity duration = 6 days
Answer: Duration between event 5 and 6 is 6 days.
The critical path is the longest sequence of activities in a project network that determines the shortest possible project duration. Delays on the critical path directly delay the entire project.
Example 1: A retail store refurbishment has activities with durations: A=4 days, B=3 days, C=5 days. Paths: A-B (7 days), C alone (5 days).
Find the critical path.
Step 1: Calculate path durations: A + B = 4 + 3 = 7 days; C = 5 days
Step 2: Critical path = longest path = 7 days (A-B)
Answer: Critical path is A-B with 7 days duration.
Example 2: In a university audit project, paths are:
Path 1: Activities D (3 days), E (4 days), F (2 days) total 9 days
Path 2: Activities G (5 days), H (3 days) total 8 days
Determine the critical path.
Step 1: Sum durations:
Path 1 = 3 + 4 + 2 = 9 days
Path 2 = 5 + 3 = 8 days
Step 2: Critical path = Path 1
Answer: Critical path is Path 1 with 9 days.
Example 3: For a bank's system upgrade:
Path 1: Activities I (2), J (3), K (6) = 11 days
Path 2: Activities L (5), M (7) = 12 days
Find critical path and project duration.
Step 1: Calculate path durations:
Path 1 = 2 + 3 + 6 = 11 days
Path 2 = 5 + 7 = 12 days
Step 2: Critical path = Path 2
Answer: Critical path is Path 2 with 12 days duration.
Float or slack is the amount of time an activity can be delayed without affecting the overall project completion time. It provides flexibility in scheduling non-critical activities.
Example 1: A farm project has activity N with duration 4 days, earliest start day 3, latest start day 7.
Calculate total float.
Step 1: Total float = Latest start - Earliest start = 7 - 3 = 4 days
Answer: Total float for activity N is 4 days.
Example 2: In a retail expansion, activity O has earliest finish at day 10 and latest finish at day 12.
Calculate total float.
Step 1: Total float = Latest finish - Earliest finish = 12 - 10 = 2 days
Answer: Total float for activity O is 2 days.
Example 3: A county office project activity P has earliest start 5, earliest finish 9, latest start 5, latest finish 9.
Calculate float.
Step 1: Total float = Latest start - Earliest start = 5 - 5 = 0 days
Answer: Activity P has zero float and is critical.
A cooperative project has activities with durations: A=3 days, B=5 days, C=4 days. The paths are A-B and C alone. Determine the critical path and project duration. (5 marks)
In a SACCO loan processing, activity "Verification" has earliest start day 2 and latest start day 6. Calculate the total float for the activity. (4 marks)
For an audit project, event 1 marks the start of "Data Collection" and event 2 marks its completion after 7 days. Event 2 leads immediately to "Data Analysis". What is the duration between event 1 and event 2? (3 marks)
A bank's system upgrade project has two paths: Path 1 with activities of 4, 5, and 3 days; Path 2 with activities of 6 and 7 days. Identify the critical path and total project duration. (5 marks)
An activity in a hotel refurbishment project has an earliest finish time of day 12 and a latest finish time of day 15. Calculate its total float. (3 marks)
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Create a free accountThis chapter began by defining essential terms used in project network analysis, establishing a clear foundation for understanding the concepts involved. It then outlined the fundamental rules that must be followed when drawing project networks to ensure accuracy and logical sequencing of activities. The construction of project networks was explored in detail, demonstrating how to represent project activities and their dependencies graphically. The chapter explained how to identify the critical path, which determines the minimum project duration and highlights activities that directly affect the completion time. Techniques for calculating project duration were presented, emphasizing the importance of timely project completion. Finally, the chapter discussed practical applications of network analysis in project management and introduced the use of calculus to optimize project scheduling and resource allocation. Together, these topics provide a comprehensive overview of analyzing project networks for effective project control.
A project consists of three activities A, B, and C. Activity A takes 5 days, B takes 8 days, and C takes 6 days. Activity B and C cannot start until A is complete. Calculate the total project duration. (2 marks)
Activity D takes 7 days and must be completed before activities E and F can start. Activity E takes 4 days and activity F takes 5 days. Calculate the critical path and the project duration. (3 marks)
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