Operations Research — Transportation, queuing, decision theory, PERT-CPM. - Question Bank

1. The Expected Value of Perfect Information (EVPI) is the difference between:
A) The EMV with perfect information and the EMV without perfect information.
B) The maximum possible payoff and the minimum possible payoff.
C) The cost of information and the benefit of information.
D) The expected loss and the actual loss.
2. In the context of the Transportation Problem, what does 'destination' refer to?
A) A location where goods are produced.
B) A location where goods are demanded or received.
C) A route for transporting goods.
D) The cost per unit of transportation.
3. A system with infinite calling population, Poisson arrivals, and exponential service times, with an infinite queue capacity and a single server, is best represented by which model?
A) M/M/c
B) M/G/1
C) M/M/1
D) M/D/1
4. The project duration calculated using the critical path method (CPM) is:
A) The shortest possible project duration.
B) The longest possible project duration.
C) The average project duration.
D) The minimum time required if all activities start as early as possible.
5. In decision theory, 'states of nature' are:
A) The different decisions a decision-maker can make.
B) The possible outcomes that are beyond the decision-maker's control.
C) The payoffs associated with each decision.
D) The probabilities of success.
6. Which method is an iterative procedure to find the optimal solution for the Transportation Problem once an initial feasible solution is obtained?
A) North-West Corner Rule
B) Least Cost Method
C) MODI Method (Modified Distribution Method)
D) Vogel's Approximation Method
7. The 'waiting line' in a queuing system refers to:
A) The service facility itself.
B) Customers currently being served.
C) Customers who have arrived but are waiting for service.
D) Customers who have left the system.
8. A 'dummy activity' in CPM is used to:
A) Represent a task that takes no time or resources.
B) Show a dependency between two activities.
C) Indicate a milestone.
D) Reduce the project cost.
9. In PERT, the variance of an activity's duration is calculated as:
A) ((P - O) / 6)^2
B) ((P - O) / 3)^2
C) (P - O) / 6
D) (P - O) / 3
10. Which decision rule is most appropriate when the decision-maker has no information about the likelihood of different states of nature occurring?
A) Maximax
B) Maximin
C) Minimax Regret
D) Laplace
11. What does the 'rho' (ρ) represent in a queuing system, specifically for the M/M/1 model?
A) The probability that the system is empty.
B) The average number of customers in the queue.
C) The traffic intensity or server utilization, calculated as λ/μ.
D) The average waiting time in the queue.
12. In a transportation problem, the 'stepping stone method' is used for:
A) Finding the initial basic feasible solution.
B) Testing the optimality of a solution and improving it.
C) Balancing the problem.
D) Determining the demand at destinations.
13. What is the primary goal of the Minimax criterion in Decision Theory?
A) To maximize the minimum possible payoff.
B) To minimize the maximum possible regret.
C) To maximize the maximum possible payoff.
D) To minimize the minimum possible loss.
14. Which of the following is a limitation of PERT/CPM?
A) It cannot handle projects with uncertain activity times.
B) It assumes activities are independent.
C) It does not consider resource constraints explicitly.
D) It is only applicable to small projects.
15. In decision theory, a payoff matrix shows:
A) The costs associated with different decisions.
B) The probabilities of different states of nature.
C) The payoffs for each combination of decision alternative and state of nature.
D) The regret values for each decision.
16. What is the 'service rate' in a queuing system?
A) The rate at which customers arrive.
B) The rate at which customers are served by the server(s).
C) The maximum capacity of the queue.
D) The average time a customer spends in the system.
17. In a transportation problem, if the total supply exceeds the total demand, a dummy destination is added. What is the transportation cost associated with this dummy destination?
A) Very high cost
B) Zero cost
C) Average cost
D) Cost of the cheapest route
18. Which of the following is NOT a typical output of PERT/CPM analysis?
A) Project completion time
B) Identification of the critical path
C) Resource requirements for each activity
D) Activity float values
19. The 'earliest start time' (ES) of an activity is determined by:
A) The earliest finish time of the preceding activity.
B) The latest start time of the preceding activity.
C) The earliest start time of the preceding activity plus its duration.
D) The earliest finish time of the preceding activity.
20. The 'latest finish time' (LF) of an activity is determined by:
A) The earliest start time of the succeeding activity minus its duration.
B) The latest start time of the succeeding activity minus its duration.
C) The earliest finish time of the succeeding activity minus its duration.
D) The latest finish time of the succeeding activity minus its duration.
21. CPM typically uses a single, deterministic time estimate for each activity, while PERT uses probabilistic time estimates. This is a key difference.
A) True
B) False
C) Only for small projects
D) Only for large projects
22. PERT uses a three-time estimate (optimistic, most likely, pessimistic) to calculate the expected duration of an activity. The formula for expected duration (Te) is:
A) Te = (O + 4M + P) / 6
B) Te = (O + M + P) / 3
C) Te = O + M + P
D) Te = (O + P) / 2
23. What is 'float' or 'slack' in PERT/CPM?
A) The time an activity can be delayed without delaying the project completion.
B) The earliest start time of an activity.
C) The latest finish time of an activity.
D) The total duration of the project.
24. The 'Critical Path' in a project network is the sequence of activities that:
A) Has the shortest duration.
B) Has the most resources allocated.
C) Determines the shortest possible project duration and has zero float.
D) Represents the longest duration and must be completed on time.
25. What is an 'event' in PERT/CPM?
A) A task that takes time.
B) A point in time marking the start or completion of an activity.
C) The total duration of the project.
D) The critical path.
26. In PERT/CPM, what is an 'activity'?
A) A milestone or event.
B) A task or operation that consumes time and resources.
C) A dependency between tasks.
D) The start or end point of a project.
27. What does CPM stand for?
A) Critical Path Method
B) Cost Management Process
C) Continuous Project Management
D) Critical Performance Measurement
28. What does PERT stand for?
A) Program Evaluation and Review Technique
B) Project Execution and Review Tool
C) Process Engineering and Resource Tracking
D) Performance Evaluation and Reporting Technique
29. PERT and CPM are project management techniques used for:
A) Inventory control
B) Resource allocation
C) Planning, scheduling, and controlling projects
D) Quality assurance
30. Which decision criterion assumes that all states of nature are equally likely?
A) Maximin
B) Minimax
C) Maximax
D) Laplace
31. What is 'regret' or 'opportunity loss' in Decision Theory?
A) The actual payoff received.
B) The difference between the payoff of the best decision and the payoff of the chosen decision for a given state of nature.
C) The cost of making a decision.
D) The probability of a state of nature occurring.
32. The Expected Monetary Value (EMV) criterion is used when decisions are made under conditions of:
A) Uncertainty
B) Risk
C) Certainty
D) Ambiguity
33. What does the 'Minimax Regret' criterion aim to minimize?
A) The maximum possible loss.
B) The maximum possible regret (opportunity loss).
C) The minimum possible profit.
D) The average payoff.
34. The Maximin criterion is associated with which type of decision-maker?
A) Optimistic
B) Pessimistic
C) Risk-neutral
D) Risk-seeking
35. Which decision criterion is used when a decision-maker is optimistic about the future?
A) Maximin
B) Minimax
C) Maximax
D) Laplace
36. Decision Theory deals with making decisions under conditions of:
A) Certainty only
B) Risk and uncertainty
C) Perfect information only
D) No possible outcomes
37. What does the '1' in the M/M/1 notation represent?
A) The number of arrival streams.
B) The number of service channels.
C) The capacity of the queue.
D) The service time distribution.
38. Which queuing model assumes Poisson arrivals and exponential service times?
A) M/M/1
B) M/D/1
C) D/M/1
D) M/M/c
39. What is the 'busy period' in a queuing system?
A) The time between customer arrivals.
B) The time when the service facility is continuously occupied.
C) The time a customer spends waiting in the queue.
D) The total time the system operates.
40. Little's Law relates the average number of customers in the system (L) to the average arrival rate (λ) and the average time a customer spends in the system (W). The formula is:
A) L = λ / W
B) L = W / λ
C) L = λ * W
D) W = L * λ
41. What does 'μ' (mu) represent in queuing theory?
A) The average arrival rate of customers.
B) The average number of customers served per unit of time.
C) The maximum number of customers allowed in the system.
D) The probability of zero customers in the system.
42. In queuing theory, what does 'λ' (lambda) typically represent?
A) The average number of customers served per unit of time.
B) The average arrival rate of customers.
C) The capacity of the service facility.
D) The average waiting time in the queue.
43. Which of the following is a characteristic of a Queuing System?
A) Customers arrive and are served instantaneously.
B) There is a finite capacity for the waiting line.
C) There is a source of customers, a queue, and a service facility.
D) Service time is always constant.
44. If a Transportation Problem is unbalanced (total supply != total demand), how is it typically handled?
A) It cannot be solved.
B) A dummy origin or destination is added.
C) Some supply or demand is ignored.
D) The costs are adjusted.
45. What is a 'balanced' Transportation Problem?
A) When the total supply equals the total demand.
B) When all transportation costs are equal.
C) When the number of origins equals the number of destinations.
D) When the optimal solution is unique.
46. In a Transportation Problem, what does 'supply' represent?
A) The maximum demand at a destination.
B) The amount of product available at an origin.
C) The cost of transporting one unit of product.
D) The capacity of a transportation route.
47. The Hungarian Method is primarily used to solve which type of Operations Research problem?
A) Assignment Problem
B) Transportation Problem
C) Queuing Problem
D) Inventory Problem
48. Which method is commonly used to find an initial basic feasible solution for the Transportation Problem?
A) Simplex Method
B) North-West Corner Rule
C) Hungarian Method
D) Branch and Bound Method
49. What is the primary objective of the Transportation Problem in Operations Research?
A) To minimize the total cost of shipping goods from origins to destinations.
B) To maximize the profit from selling goods.
C) To determine the optimal production schedule.
D) To allocate resources to competing activities.
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