Q.1 What is an assignment problem in Quantitative Techniques?
A problem of assigning people to tasks
A problem of maximizing profit in transportation
A problem of inventory control
A problem of queuing management
Explanation - An assignment problem deals with optimally assigning resources such as people to tasks, minimizing cost or maximizing efficiency.
Correct answer is: A problem of assigning people to tasks
Q.2 The assignment problem is a special case of which problem?
Queuing problem
Transportation problem
Game theory problem
Inventory problem
Explanation - The assignment problem is a special case of the transportation problem with equal supply and demand (both equal to 1).
Correct answer is: Transportation problem
Q.3 What is the objective of solving an assignment problem?
To minimize or maximize total cost/profit
To calculate average waiting time
To forecast demand
To determine reorder levels
Explanation - Assignment problems are solved to optimize allocation by minimizing cost or maximizing profit.
Correct answer is: To minimize or maximize total cost/profit
Q.4 Which method is most commonly used to solve an assignment problem?
Hungarian method
North-West Corner method
Simplex method
Graphical method
Explanation - The Hungarian method is specifically designed to solve assignment problems efficiently.
Correct answer is: Hungarian method
Q.5 In an assignment problem, the number of workers and the number of jobs must be:
Equal
Greater
Smaller
Independent
Explanation - The assignment problem is defined for a square matrix where the number of jobs equals the number of workers.
Correct answer is: Equal
Q.6 What type of matrix is used in solving assignment problems?
Profit or Cost matrix
Frequency distribution table
Correlation matrix
Identity matrix
Explanation - Assignment problems are represented by a cost or profit matrix depending on whether minimization or maximization is required.
Correct answer is: Profit or Cost matrix
Q.7 If an assignment problem involves 4 workers and 4 jobs, how many possible assignments exist?
16
24
4
8
Explanation - The total possible assignments are n! (factorial). For 4 workers and 4 jobs, it is 4! = 24.
Correct answer is: 24
Q.8 The Hungarian method operates on which principle?
Opportunity cost minimization
Balancing supply and demand
Shortest path optimization
Game strategy equilibrium
Explanation - The Hungarian method minimizes opportunity costs through systematic reduction of rows and columns.
Correct answer is: Opportunity cost minimization
Q.9 Which of the following is true about assignment problems?
They always have a feasible solution
They may have no solution
They always maximize profit only
They always minimize waiting time
Explanation - Because the number of jobs equals the number of workers, there is always at least one feasible assignment.
Correct answer is: They always have a feasible solution
Q.10 What is the time complexity of the Hungarian method?
O(n)
O(n^2)
O(n^3)
O(n log n)
Explanation - The Hungarian method solves assignment problems in polynomial time with complexity O(n^3).
Correct answer is: O(n^3)
Q.11 Which operation is performed first in the Hungarian method?
Row reduction
Column reduction
Optimal assignment
Maximization conversion
Explanation - The Hungarian method begins with row reduction, subtracting the smallest value in each row.
Correct answer is: Row reduction
Q.12 In case of a maximization assignment problem, how is it solved?
Convert to minimization
Use queuing theory
Apply game theory directly
Simplex method only
Explanation - Maximization assignment problems are converted into minimization by subtracting each value from the maximum element in the matrix.
Correct answer is: Convert to minimization
Q.13 An unbalanced assignment problem occurs when:
Number of workers ≠ Number of jobs
Cost is too high
Demand is uncertain
Profits are negative
Explanation - An assignment problem is unbalanced when the number of workers and jobs differ. Dummy rows/columns are added to balance it.
Correct answer is: Number of workers ≠ Number of jobs
Q.14 Dummy rows or columns are introduced in assignment problems to:
Balance the problem
Reduce total cost
Increase accuracy
Improve speed
Explanation - Dummy rows or columns are added to make the assignment matrix square when jobs ≠ workers.
Correct answer is: Balance the problem
Q.15 If there are 5 workers and 5 jobs, the total possible assignments are:
10
15
25
120
Explanation - For n workers and n jobs, possible assignments = n!. For 5 workers and 5 jobs, it is 5! = 120.
Correct answer is: 120
Q.16 Which of the following is NOT true about the Hungarian method?
It finds the optimal solution
It is based on matrix reduction
It applies to balanced problems
It can only solve transportation problems
Explanation - Hungarian method is designed for assignment problems, not general transportation problems.
Correct answer is: It can only solve transportation problems
Q.17 When solving assignment problems, opportunity cost is shown as:
Zeros in the matrix
Maximum values
Negative values
Identity diagonal
Explanation - Zeros in the reduced matrix represent opportunities for cost-effective assignments.
Correct answer is: Zeros in the matrix
Q.18 Which step ensures that each worker gets exactly one job in the Hungarian method?
Optimal assignment step
Dummy balancing step
Row reduction step
Column reduction step
Explanation - The optimal assignment step ensures that exactly one job is allocated to each worker.
Correct answer is: Optimal assignment step
Q.19 If a worker cannot do a job, the cost is represented as:
Zero
Infinity or very high number
One
Negative value
Explanation - When a worker cannot perform a job, an infinite or very large cost is used to prevent assignment.
Correct answer is: Infinity or very high number
Q.20 What type of optimization problem is the assignment problem?
Linear programming
Non-linear programming
Dynamic programming
Stochastic programming
Explanation - The assignment problem is a special case of linear programming where constraints and objective function are linear.
Correct answer is: Linear programming
Q.21 Which of the following applications can be modeled as an assignment problem?
Assigning teachers to classes
Forecasting demand
Finding EOQ
Calculating correlation
Explanation - Assignment problems can model situations like assigning workers, teachers, or machines to tasks or jobs.
Correct answer is: Assigning teachers to classes
Q.22 In assignment problems, degeneracy occurs when:
More than one optimal solution exists
No feasible solution exists
Profit is negative
Costs are identical
Explanation - Degeneracy in assignment problems refers to multiple optimal solutions that provide the same cost or profit.
Correct answer is: More than one optimal solution exists
Q.23 What is the optimality condition in assignment problems?
Each job assigned once, each worker assigned once
Every worker gets multiple jobs
Each job assigned to all workers
Unbalanced solution exists
Explanation - Optimality requires one-to-one assignments: each worker gets one job, and each job is assigned to one worker.
Correct answer is: Each job assigned once, each worker assigned once
Q.24 The assignment problem is solved optimally when:
Minimum number of lines = matrix size
Row reduction completed
All costs minimized individually
All jobs unassigned
Explanation - In the Hungarian method, optimality is reached when the minimum number of lines covering all zeros equals the order of the matrix.
Correct answer is: Minimum number of lines = matrix size
Q.25 Which mathematical property ensures assignment problems can be solved using matrices?
Linearity
Convexity
Randomness
Independence
Explanation - Because both the objective function and constraints are linear, matrix methods like the Hungarian algorithm can be applied.
Correct answer is: Linearity