Network analysis - directed networks, max-flow min-cut theorem, CPM, PERT, probabilistic network analysis - Question Bank

1. In the context of flow networks, the 'cut capacity' is the sum of capacities of edges that:
A) Form the critical path.
B) Connect nodes within the same partition of the cut.
C) Go from the source side of the cut to the sink side.
D) Go from the sink side of the cut to the source side.
2. What is the primary goal of network analysis techniques like CPM and PERT?
A) To optimize resource allocation.
B) To determine the minimum cost of a project.
C) To plan, schedule, and control projects to ensure timely completion.
D) To forecast market demand.
3. 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)?
A) Activity on Arrow (AOA)
B) Activity on Node (AON)
C) Precedence Diagramming Method (PDM)
D) Gantt Chart
4. 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?
A) Approximately 68.3%
B) Approximately 84.1%
C) Approximately 97.7%
D) Approximately 50%
5. What does 'probabilistic network analysis' imply?
A) All network parameters are known with certainty.
B) Some network parameters, like activity durations, involve uncertainty and are modeled using probability distributions.
C) The network analysis is performed using statistical methods only.
D) The focus is on deterministic relationships between activities.
6. What is the variance of an activity in PERT if t_o=4, t_m=7, and t_p=16?
A) 1.44
B) 1.2
C) 1.0
D) 0.8
7. Which theorem establishes a direct relationship between the maximum flow and the minimum cut in a flow network?
A) Central Limit Theorem
B) Bayes' Theorem
C) Max-Flow Min-Cut Theorem
D) Law of Large Numbers
8. In a directed network, an edge with capacity 5 means:
A) The activity takes 5 units of time.
B) The activity requires 5 units of a resource.
C) A maximum of 5 units of flow can pass through this edge.
D) The activity must be completed within 5 days.
9. What is the primary limitation of the basic CPM technique?
A) It cannot handle complex networks.
B) It assumes activity durations are uncertain.
C) It requires probabilistic time estimates.
D) It assumes deterministic activity durations.
10. The concept of 'cut' in a flow network is analogous to which project management concept?
A) Critical path
B) Bottleneck
C) Milestone
D) Resource allocation
11. 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?
A) 0 days
B) 1 day
C) 2 days
D) 3 days
12. 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)?
A) 8 days
B) 9 days
C) 10 days
D) 12 days
13. A network diagram where activities are represented by nodes and events by arrows is known as:
A) Activity on Node (AON)
B) Activity on Arrow (AOA)
C) Precedence Diagramming Method (PDM)
D) Event on Node (EON)
14. What is the probability of completing a project by a certain date in PERT analysis based on the normal distribution?
A) Calculated using the Z-score derived from the expected project duration and the target date.
B) Always 50% if the target date is the expected duration.
C) Determined by the number of critical activities.
D) Equal to the sum of probabilities of individual activities.
15. In PERT, the standard deviation of the project completion time is calculated by:
A) Summing the standard deviations of all activities.
B) Taking the square root of the sum of variances of activities on the critical path.
C) Summing the variances of all activities on the critical path.
D) Taking the square root of the sum of standard deviations of activities on the critical path.
16. Which of the following is a probabilistic approach to network analysis?
A) Critical Path Method (CPM)
B) Program Evaluation and Review Technique (PERT)
C) Max-Flow Min-Cut Theorem
D) Gantt Chart
17. What is a 'residual graph' used for in max-flow algorithms?
A) To represent the original network capacities.
B) To track the remaining capacity on edges after some flow has been sent.
C) To visualize the critical path.
D) To show the total flow in the network.
18. The Ford-Fulkerson algorithm is used to find:
A) The shortest path in a network.
B) The minimum spanning tree.
C) The maximum flow in a network.
D) The critical path of a project.
19. In the context of max-flow min-cut, what is a 'sink' node?
A) A node where flow originates.
B) A node where flow terminates.
C) A node with minimum capacity.
D) A node with zero flow.
20. In the context of max-flow min-cut, what is a 'source' node?
A) A node where flow terminates.
B) A node where flow originates.
C) A node with no incoming or outgoing edges.
D) A node on the critical path.
21. What is the purpose of 'dummy activities' in AOA network diagrams?
A) To represent resources.
B) To show dependencies correctly without consuming time or resources.
C) To indicate critical activities.
D) To represent parallel activities.
22. An activity is on the critical path if its slack is:
A) Positive
B) Negative
C) Zero
D) Equal to its duration
23. What is the 'slack' or 'float' of an activity?
A) The difference between ES and LS.
B) The difference between LF and EF.
C) The amount of time an activity can be delayed without delaying the project completion.
D) The duration of the activity.
24. The Latest Start Time (LS) of an activity is calculated as:
A) LF - Duration
B) ES + Duration
C) LF + Duration
D) ES - Duration
25. The Latest Finish Time (LF) of an activity is determined by:
A) The Earliest Start Time of its succeeding activities.
B) The Latest Start Time of its succeeding activities.
C) The Earliest Finish Time of its succeeding activities.
D) The Latest Finish Time of its succeeding activities.
26. The Earliest Finish Time (EF) of an activity is calculated as:
A) ES + Duration
B) LS + Duration
C) LF - Duration
D) ES - Duration
27. The Earliest Start Time (ES) of an activity is determined by:
A) The Latest Finish Time of its preceding activities.
B) The Earliest Finish Time of its preceding activities.
C) The Latest Start Time of its succeeding activities.
D) The Earliest Start Time of its succeeding activities.
28. What does 'LF' stand for in CPM/PERT calculations?
A) Latest Finish Time
B) Limited Finish Time
C) Last Finish Time
D) Longest Finish Time
29. What does 'LS' stand for in CPM/PERT calculations?
A) Latest Start Time
B) Limited Start Time
C) Last Start Time
D) Longest Start Time
30. What does 'EF' stand for in CPM/PERT calculations?
A) Estimated Finish Time
B) Earliest Finish Time
C) Effective Finish Time
D) Expected Finish Time
31. What does 'ES' stand for in CPM/PERT calculations?
A) Estimated Start Time
B) Earliest Start Time
C) Effective Start Time
D) Expected Start Time
32. What is an 'activity' in the context of CPM and PERT?
A) A point in time.
B) A task or operation that consumes time and resources.
C) A milestone in the project.
D) The end of the project.
33. What is an 'event' in the context of CPM and PERT?
A) A task that takes time to complete.
B) A point in time marking the start or completion of an activity.
C) A resource required for an activity.
D) The total duration of the project.
34. Which of the following is an activity on an arrow (AOA) representation in network diagrams?
A) Activities are represented by nodes.
B) Events are represented by arrows.
C) Activities are represented by arrows.
D) Dependencies are shown by nodes.
35. Which of the following is NOT an activity on a node (AON) representation in network diagrams?
A) Events are represented by nodes.
B) Activities are represented by nodes.
C) Activities are represented by arrows.
D) Dependencies are shown by the sequence of nodes.
36. What is the 'capacity' of a cut in a network?
A) The sum of the lengths of the edges in the cut.
B) The sum of the capacities of the edges in the cut.
C) The maximum flow that can pass through the cut.
D) The minimum number of edges in the cut.
37. In network analysis, what does a 'cut' refer to?
A) A path from the source to the sink.
B) A set of edges whose removal disconnects the source from the sink.
C) The total capacity of the network.
D) The critical path of the project.
38. What is the formula for calculating the 'variance' (σ²) of an activity in PERT?
A) (t_p - t_o) / 6
B) ((t_p - t_o) / 6)²
C) (t_p - t_o)² / 4
D) (t_o + 4*t_m + t_p) / 6
39. What is the formula for calculating the 'expected time' (t_e) of an activity in PERT?
A) (t_o + t_p) / 2
B) (t_o + 4*t_m + t_p) / 6
C) (t_o + t_m + t_p) / 3
D) t_m
40. What is the 'most likely time' (t_m) estimate in PERT?
A) The shortest possible time to complete an activity.
B) The time most likely to occur under normal conditions.
C) The longest possible time to complete an activity.
D) The average of optimistic and pessimistic times.
41. What is the 'pessimistic time' (t_p) estimate in PERT?
A) The shortest possible time to complete an activity.
B) The most probable time to complete an activity.
C) The longest possible time to complete an activity, assuming adverse conditions.
D) The expected time to complete an activity.
42. What is the 'optimistic time' (t_o) estimate in PERT?
A) The longest possible time to complete an activity.
B) The most probable time to complete an activity.
C) The shortest possible time to complete an activity, assuming ideal conditions.
D) The average time to complete an activity.
43. In PERT analysis, how many time estimates are typically used for each activity?
A) One (most likely time)
B) Two (optimistic and pessimistic time)
C) Three (optimistic, most likely, and pessimistic time)
D) Four (optimistic, most likely, pessimistic, and expected time)
44. What does PERT stand for in project management?
A) Program Evaluation and Review Technique
B) Project Estimation and Resource Tracking
C) Performance Evaluation and Reporting Tool
D) Process Engineering and Resource Technology
45. What is the primary advantage of using PERT over CPM?
A) PERT is deterministic, while CPM is probabilistic.
B) PERT can handle uncertain activity durations, while CPM assumes fixed durations.
C) CPM is better for very large projects than PERT.
D) PERT focuses on cost optimization, while CPM focuses on time.
46. In a CPM network, what is the 'critical path'?
A) The sequence of activities with the longest duration.
B) The sequence of activities with the shortest duration.
C) The sequence of activities that determines the minimum project completion time.
D) The sequence of activities with the most resources allocated.
47. What does CPM stand for in project management?
A) Critical Path Method
B) Continuous Project Management
C) Complete Project Milestones
D) Critical Performance Measurement
48. Which technique is primarily used for project scheduling and management that focuses on identifying the critical path?
A) Linear Programming
B) Queuing Theory
C) Critical Path Method (CPM)
D) Game Theory
49. What is the fundamental principle of the Max-Flow Min-Cut Theorem?
A) The maximum flow through a network is equal to the capacity of a minimum cut.
B) The minimum cut in a network is always greater than the maximum flow.
C) The maximum flow is achieved when all paths are saturated.
D) The minimum cut determines the shortest path in the network.
50. In network analysis, what does a directed edge typically represent?
A) A dependency between tasks
B) A resource constraint
C) A specific duration for an activity
D) The start or end of a project
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