Network analysis - directed networks, max-flow min-cut theorem, CPM, PERT, probabilistic network analysis - One Line Questions

1. What is the formula for calculating the 'expected time' (t_e) of an activity in PERT? — (t_o + 4*t_m + t_p) / 6
2. What is the formula for calculating the 'variance' (σ²) of an activity in PERT? — ((t_p - t_o) / 6)²
3. If an activity has an ES of 5, an EF of 12, an LS of 7, and an LF of 14, what is its slack? — 2 days
4. What is the variance of an activity in PERT if t_o=4, t_m=7, and t_p=16? — 1.44
5. In PERT, if the expected time (t_e) for an activity is 10 days, optimistic time (t_o) is 6 days, and pessimistic time (t_p) is 18 days, what is the most likely time (t_m)? — 9 days
6. In network analysis, what does a directed edge typically represent? — A dependency between tasks
7. In the context of max-flow min-cut, what is a 'sink' node? — A node where flow terminates.
8. In the context of max-flow min-cut, what is a 'source' node? — A node where flow originates.
9. In network analysis, what does a 'cut' refer to? — A set of edges whose removal disconnects the source from the sink.
10. What is an 'activity' in the context of CPM and PERT? — A task or operation that consumes time and resources.
11. What is an 'event' in the context of CPM and PERT? — A point in time marking the start or completion of an activity.
12. Which of the following is an activity on an arrow (AOA) representation in network diagrams? — Activities are represented by arrows.
13. Which of the following is a representation of dependencies between tasks where activities can have multiple predecessors and successors, and different types of relationships (FS, SS, FF, SF)? — Precedence Diagramming Method (PDM)
14. A network diagram where activities are represented by nodes and events by arrows is known as: — Precedence Diagramming Method (PDM)
15. What does 'probabilistic network analysis' imply? — Some network parameters, like activity durations, involve uncertainty and are modeled using probability distributions.
16. In a PERT network, if the project's expected completion time is 50 days and its standard deviation is 5 days, what is the probability of completing the project within 55 days? — Approximately 84.1%
17. What is the probability of completing a project by a certain date in PERT analysis based on the normal distribution? — Calculated using the Z-score derived from the expected project duration and the target date.
18. Which theorem establishes a direct relationship between the maximum flow and the minimum cut in a flow network? — Max-Flow Min-Cut Theorem
19. The concept of 'cut' in a flow network is analogous to which project management concept? — Bottleneck
20. What does CPM stand for in project management? — Critical Path Method
21. Which of the following is a probabilistic approach to network analysis? — Program Evaluation and Review Technique (PERT)
22. The Earliest Finish Time (EF) of an activity is calculated as: — ES + Duration
23. What does 'EF' stand for in CPM/PERT calculations? — Earliest Finish Time
24. What does 'ES' stand for in CPM/PERT calculations? — Earliest Start Time
25. Which of the following is NOT an activity on a node (AON) representation in network diagrams? — Activities are represented by arrows.
26. In the context of flow networks, the 'cut capacity' is the sum of capacities of edges that: — Go from the source side of the cut to the sink side.
27. What is the primary limitation of the basic CPM technique? — It assumes deterministic activity durations.
28. What does 'LF' stand for in CPM/PERT calculations? — Latest Finish Time
29. What does 'LS' stand for in CPM/PERT calculations? — Latest Start Time
30. The Latest Start Time (LS) of an activity is calculated as: — LF - Duration
31. Which technique is primarily used for project scheduling and management that focuses on identifying the critical path? — Critical Path Method (CPM)
32. In PERT analysis, how many time estimates are typically used for each activity? — Three (optimistic, most likely, and pessimistic time)
33. What is the primary advantage of using PERT over CPM? — PERT can handle uncertain activity durations, while CPM assumes fixed durations.
34. An activity is on the critical path if its slack is: — Zero
35. What does PERT stand for in project management? — Program Evaluation and Review Technique
36. In PERT, the standard deviation of the project completion time is calculated by: — Taking the square root of the sum of variances of activities on the critical path.
37. In a directed network, an edge with capacity 5 means: — A maximum of 5 units of flow can pass through this edge.
38. What is the 'slack' or 'float' of an activity? — The amount of time an activity can be delayed without delaying the project completion.
39. The Latest Finish Time (LF) of an activity is determined by: — The Latest Start Time of its succeeding activities.
40. The Earliest Start Time (ES) of an activity is determined by: — The Earliest Finish Time of its preceding activities.
41. What is the 'optimistic time' (t_o) estimate in PERT? — The shortest possible time to complete an activity, assuming ideal conditions.
42. What is the fundamental principle of the Max-Flow Min-Cut Theorem? — The maximum flow through a network is equal to the capacity of a minimum cut.
43. In a CPM network, what is the 'critical path'? — The sequence of activities that determines the minimum project completion time.
44. The Ford-Fulkerson algorithm is used to find: — The maximum flow in a network.
45. What is the 'pessimistic time' (t_p) estimate in PERT? — The longest possible time to complete an activity, assuming adverse conditions.
46. What is the 'most likely time' (t_m) estimate in PERT? — The time most likely to occur under normal conditions.
47. What is the 'capacity' of a cut in a network? — The sum of the capacities of the edges in the cut.
48. What is the primary goal of network analysis techniques like CPM and PERT? — To plan, schedule, and control projects to ensure timely completion.
49. What is the purpose of 'dummy activities' in AOA network diagrams? — To show dependencies correctly without consuming time or resources.
50. What is a 'residual graph' used for in max-flow algorithms? — To track the remaining capacity on edges after some flow has been sent.
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