✅ MCQ QUESTIONS: Assignment Problem (Management Science)
Here are 50 Multiple Choice Questions (MCQs) related to the Assignment Problem topic in Management Science. These are useful for exams, quizzes, or practice sets.
The assignment problem is a special case of the:
A) Linear Programming Problem
B) Transportation Problem
C) Game Theory
D) Network Analysis
The objective of an assignment problem is to:
A) Maximize time
B) Minimize total cost or time
C) Maximize tasks
D) None of the above
The Hungarian method is used to:
A) Solve linear equations
B) Solve assignment problems
C) Solve dual problems
D) Solve game theory problems
In assignment problems, agents are assigned to:
A) Multiple tasks
B) No tasks
C) Exactly one task
D) At least two tasks
If the cost matrix is not square, we must:
A) Solve using simplex
B) Add dummy rows or columns
C) Multiply the matrix
D) Ignore the extra values
A dummy row/column is added to:
A) Increase costs
B) Create a square matrix
C) Reduce complexity
D) Avoid zero costs
In the Hungarian method, the first step is:
A) Assign zeros
B) Column reduction
C) Row reduction
D) Test optimality
Row reduction means:
A) Subtracting the smallest value from each row
B) Eliminating a row
C) Doubling the row values
D) Converting rows to columns
Column reduction is done:
A) Before row reduction
B) After row reduction
C) Randomly
D) Never
Assignment problem solutions must:
A) Maximize costs
B) Be partial
C) Cover all tasks and agents
D) Ignore feasibility
The total number of possible assignments for 4 workers and 4 jobs is:
A) 8
B) 16
C) 24
D) 256
In a cost matrix, zero values suggest:
A) Infeasibility
B) No cost
C) High cost
D) Delay
In a maximization assignment problem, we convert it to minimization by:
A) Using duality
B) Subtracting values from maximum
C) Adding constants
D) Doubling the values
Assignment problems help in:
A) Queue management
B) Job allocation
C) Inventory control
D) Cost accounting
Which of the following is NOT true for assignment problems?
A) One-to-one assignment
B) Costs are known
C) Tasks can be split
D) Square cost matrix
The assignment model is useful in:
A) Scheduling
B) Machine loading
C) Personnel assignment
D) All of the above
The Hungarian method provides:
A) Approximate solution
B) Optimal solution
C) Random solution
D) Greedy solution
Assignment problem assumes:
A) One task per agent
B) Multiple tasks per agent
C) Zero costs
D) Random preferences
If more than one solution exists, it is called:
A) Degeneracy
B) Redundancy
C) Optimality
D) Duality
In the assignment matrix, diagonal elements indicate:
A) Cost of unassigned tasks
B) Self-assignment costs
C) Maximum benefit
D) Constraint levels
Assignment problem constraints are:
A) Linear equalities
B) Nonlinear equations
C) Inequalities
D) Random variables
Which of the following is a valid objective of assignment models?
A) Maximize profit
B) Minimize total cost
C) Minimize time
D) All of the above
A balanced assignment problem has:
A) Equal number of jobs and agents
B) Unequal size matrix
C) No optimal solution
D) Dummy agents
Assignment problem is applicable in:
A) Crew assignment
B) Class scheduling
C) Salesman route planning
D) Both A and B
Which technique is used for balancing the assignment problem?
A) Adding dummy row/column
B) Row swapping
C) Reducing rows
D) Recalculating costs
The assignment problem is a form of:
A) Quadratic programming
B) Linear programming
C) Dynamic programming
D) Goal programming
In assignment problems, decision variables are:
A) Continuous
B) Binary
C) Integer
D) Random
Total opportunity cost is minimized in:
A) Assignment method
B) Simplex method
C) Transportation method
D) North-West method
Assignment problem always has:
A) One solution
B) No solution
C) At least one feasible solution
D) Multiple infeasible solutions
The optimal solution is reached in the Hungarian method by:
A) Maximizing zeros
B) Minimizing the diagonal
C) Assigning all rows
D) Covering all zeros with lines
If all costs are the same, the number of optimal solutions is:
A) One
B) Two
C) Infinite
D) None
A feasible solution satisfies:
A) One constraint
B) Some constraints
C) All constraints
D) No constraints
Assignment problem is not suitable for:
A) One-to-one assignments
B) Multiple-task assignment
C) Cost-based allocation
D) Job scheduling
Which of the following ensures balanced problem?
A) Equal rows and columns
B) Equal costs
C) Zero diagonals
D) Same objective
A non-zero cost means:
A) Infeasibility
B) Penalty
C) Valid cost
D) Dual value
Which of the following is TRUE?
A) Assignment problem uses duality
B) Assignment problem uses binary variables
C) Assignment problem uses probability
D) Assignment problem uses graphs
Degeneracy in assignment problem means:
A) No zeros
B) More than one solution
C) Lack of square matrix
D) Inconsistent costs
The optimal assignment minimizes:
A) Delay
B) Time
C) Cost
D) All of the above
Maximization problems in assignment are converted to minimization by:
A) Adding zeros
B) Subtracting from highest value
C) Eliminating rows
D) Increasing penalties
The maximum number of lines needed to cover all zeros is:
A) Equal to the number of rows
B) Equal to number of zeros
C) Equal to size of matrix
D) Half of matrix size
The step after covering all zeros in Hungarian method is:
A) Row swapping
B) Checking assignment
C) Drawing more lines
D) Reducing uncovered elements
The cost of dummy assignments is:
A) 1
B) Negative
C) 0
D) Infinity
What happens if fewer lines than matrix size are used to cover zeros?
A) Repeat assignments
B) Subtract minimum uncovered value
C) Recalculate diagonals
D) Stop process
Which type of matrix is used in Hungarian method?
A) Cost matrix
B) Profit matrix
C) Probability matrix
D) Transition matrix
Which of the following statements is FALSE?
A) Each agent is assigned one task
B) The matrix must be square
C) Assignment problem maximizes cost
D) Zeros help in optimal assignments
Which technique is not applicable to assignment problem?
A) Hungarian method
B) Branch and bound
C) North-West corner
D) Dual simplex
In practical use, assignment problems are applied in:
A) Airline crew scheduling
B) Production planning
C) Job allocation
D) All of the above
Cost reduction in assignment is mainly due to:
A) Increased demand
B) Efficient allocation
C) Lower supply
D) Random choices
Assignments are made where cost is:
A) Maximum
B) Minimum
C) Constant
D) Negative
Which is the final step in solving assignment problems?
A) Maximizing zeros
B) Reassigning rows
C) Making optimal assignments
D) Minimizing penalties
The assignment problem is a special case of the:
A) Linear Programming Problem
B) Transportation Problem
C) Game Theory
D) Network Analysis
The objective of an assignment problem is to:
A) Maximize time
B) Minimize total cost or time
C) Maximize tasks
D) None of the above
The Hungarian method is used to:
A) Solve linear equations
B) Solve assignment problems
C) Solve dual problems
D) Solve game theory problems
In assignment problems, agents are assigned to:
A) Multiple tasks
B) No tasks
C) Exactly one task
D) At least two tasks
If the cost matrix is not square, we must:
A) Solve using simplex
B) Add dummy rows or columns
C) Multiply the matrix
D) Ignore the extra values
A dummy row/column is added to:
A) Increase costs
B) Create a square matrix
C) Reduce complexity
D) Avoid zero costs
In the Hungarian method, the first step is:
A) Assign zeros
B) Column reduction
C) Row reduction
D) Test optimality
Row reduction means:
A) Subtracting the smallest value from each row
B) Eliminating a row
C) Doubling the row values
D) Converting rows to columns
Column reduction is done:
A) Before row reduction
B) After row reduction
C) Randomly
D) Never
Assignment problem solutions must:
A) Maximize costs
B) Be partial
C) Cover all tasks and agents
D) Ignore feasibility
The total number of possible assignments for 4 workers and 4 jobs is:
A) 8
B) 16
C) 24
D) 256
In a cost matrix, zero values suggest:
A) Infeasibility
B) No cost
C) High cost
D) Delay
In a maximization assignment problem, we convert it to minimization by:
A) Using duality
B) Subtracting values from maximum
C) Adding constants
D) Doubling the values
Assignment problems help in:
A) Queue management
B) Job allocation
C) Inventory control
D) Cost accounting
Which of the following is NOT true for assignment problems?
A) One-to-one assignment
B) Costs are known
C) Tasks can be split
D) Square cost matrix
The assignment model is useful in:
A) Scheduling
B) Machine loading
C) Personnel assignment
D) All of the above
The Hungarian method provides:
A) Approximate solution
B) Optimal solution
C) Random solution
D) Greedy solution
Assignment problem assumes:
A) One task per agent
B) Multiple tasks per agent
C) Zero costs
D) Random preferences
If more than one solution exists, it is called:
A) Degeneracy
B) Redundancy
C) Optimality
D) Duality
In the assignment matrix, diagonal elements indicate:
A) Cost of unassigned tasks
B) Self-assignment costs
C) Maximum benefit
D) Constraint levels
Assignment problem constraints are:
A) Linear equalities
B) Nonlinear equations
C) Inequalities
D) Random variables
Which of the following is a valid objective of assignment models?
A) Maximize profit
B) Minimize total cost
C) Minimize time
D) All of the above
A balanced assignment problem has:
A) Equal number of jobs and agents
B) Unequal size matrix
C) No optimal solution
D) Dummy agents
Assignment problem is applicable in:
A) Crew assignment
B) Class scheduling
C) Salesman route planning
D) Both A and B
Which technique is used for balancing the assignment problem?
A) Adding dummy row/column
B) Row swapping
C) Reducing rows
D) Recalculating costs
The assignment problem is a form of:
A) Quadratic programming
B) Linear programming
C) Dynamic programming
D) Goal programming
In assignment problems, decision variables are:
A) Continuous
B) Binary
C) Integer
D) Random
Total opportunity cost is minimized in:
A) Assignment method
B) Simplex method
C) Transportation method
D) North-West method
Assignment problem always has:
A) One solution
B) No solution
C) At least one feasible solution
D) Multiple infeasible solutions
The optimal solution is reached in the Hungarian method by:
A) Maximizing zeros
B) Minimizing the diagonal
C) Assigning all rows
D) Covering all zeros with lines
If all costs are the same, the number of optimal solutions is:
A) One
B) Two
C) Infinite
D) None
A feasible solution satisfies:
A) One constraint
B) Some constraints
C) All constraints
D) No constraints
Assignment problem is not suitable for:
A) One-to-one assignments
B) Multiple-task assignment
C) Cost-based allocation
D) Job scheduling
Which of the following ensures balanced problem?
A) Equal rows and columns
B) Equal costs
C) Zero diagonals
D) Same objective
A non-zero cost means:
A) Infeasibility
B) Penalty
C) Valid cost
D) Dual value
Which of the following is TRUE?
A) Assignment problem uses duality
B) Assignment problem uses binary variables
C) Assignment problem uses probability
D) Assignment problem uses graphs
Degeneracy in assignment problem means:
A) No zeros
B) More than one solution
C) Lack of square matrix
D) Inconsistent costs
The optimal assignment minimizes:
A) Delay
B) Time
C) Cost
D) All of the above
Maximization problems in assignment are converted to minimization by:
A) Adding zeros
B) Subtracting from highest value
C) Eliminating rows
D) Increasing penalties
The maximum number of lines needed to cover all zeros is:
A) Equal to the number of rows
B) Equal to number of zeros
C) Equal to size of matrix
D) Half of matrix size
The step after covering all zeros in Hungarian method is:
A) Row swapping
B) Checking assignment
C) Drawing more lines
D) Reducing uncovered elements
The cost of dummy assignments is:
A) 1
B) Negative
C) 0
D) Infinity
What happens if fewer lines than matrix size are used to cover zeros?
A) Repeat assignments
B) Subtract minimum uncovered value
C) Recalculate diagonals
D) Stop process
Which type of matrix is used in Hungarian method?
A) Cost matrix
B) Profit matrix
C) Probability matrix
D) Transition matrix
Which of the following statements is FALSE?
A) Each agent is assigned one task
B) The matrix must be square
C) Assignment problem maximizes cost
D) Zeros help in optimal assignments
Which technique is not applicable to assignment problem?
A) Hungarian method
B) Branch and bound
C) North-West corner
D) Dual simplex
In practical use, assignment problems are applied in:
A) Airline crew scheduling
B) Production planning
C) Job allocation
D) All of the above
Cost reduction in assignment is mainly due to:
A) Increased demand
B) Efficient allocation
C) Lower supply
D) Random choices
Assignments are made where cost is:
A) Maximum
B) Minimum
C) Constant
D) Negative
Which is the final step in solving assignment problems?
A) Maximizing zeros
B) Reassigning rows
C) Making optimal assignments
D) Minimizing penalties
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