BSIE Operations Research & Linear Programming 2 — Questions and Answers
Question 1: What is the assignment problem in operations research primarily used for?
- Minimizing inventory costs
- Optimally matching n workers to n jobs (Correct answer)
- Scheduling production runs
- Balancing assembly lines
Correct answer: Optimally matching n workers to n jobs
The assignment problem seeks to optimally assign n agents to n tasks to minimize total cost or maximize total profit.
Question 2: In the critical path method (CPM), the critical path is defined as:
- The path with the fewest activities
- The shortest path through the project network
- The longest path through the project network determining project duration (Correct answer)
- The path with the highest resource usage
Correct answer: The longest path through the project network determining project duration
The critical path is the longest sequence of dependent activities and determines the minimum project completion time.
Question 3: Which inventory model assumes constant demand and instantaneous replenishment?
- Wagner-Whitin model
- Economic Order Quantity (EOQ) model (Correct answer)
- Silver-Meal heuristic
- Newsvendor model
Correct answer: Economic Order Quantity (EOQ) model
The classic EOQ model assumes deterministic constant demand and instantaneous lead time to derive the optimal order quantity.
Question 4: In PERT, what probability distribution is used to model activity durations?
- Normal distribution
- Exponential distribution
- Beta distribution (Correct answer)
- Uniform distribution
Correct answer: Beta distribution
PERT uses the beta distribution to model uncertain activity durations based on optimistic, most likely, and pessimistic time estimates.
Question 5: What is the purpose of sensitivity analysis in linear programming?
- To detect infeasible solutions
- To determine how optimal solution changes with parameter variations (Correct answer)
- To convert a maximization to a minimization problem
- To identify redundant constraints
Correct answer: To determine how optimal solution changes with parameter variations
Sensitivity analysis examines the range over which objective coefficients or right-hand-side values can change without altering the optimal basis.
Question 6: In a network flow problem, what does the max-flow min-cut theorem state?
- Maximum flow equals the capacity of the minimum cut (Correct answer)
- Minimum cost flow equals minimum cut capacity
- Maximum flow equals minimum path length
- Flow conservation must hold at all nodes
Correct answer: Maximum flow equals the capacity of the minimum cut
The max-flow min-cut theorem states that the maximum flow through a network equals the capacity of its minimum cut separating source from sink.
BSIE Operations Research & Linear Programming 2
What is the assignment problem in operations research primarily used for?