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🚚 Transportation Problem MCQ Test

Test your knowledge with 25 comprehensive questions on Transportation Problems

1. What is the primary objective of the Transportation Problem?

• a) Maximize profit
• b) Minimize transportation cost
• c) Maximize supply
• d) Minimize demand

2. In a balanced transportation problem, what condition must be satisfied?

• a) Supply > Demand
• b) Supply = Demand
• c) Supply < Demand
• d) Supply ≠ Demand

3. Which method is used to find the initial basic feasible solution in transportation problem?

• a) North-West Corner Method
• b) Least Cost Method
• c) Vogel's Approximation Method
• d) All of the above

4. What is a degenerate solution in transportation problem?

• a) When number of basic variables = m + n - 1
• b) When number of basic variables < m + n - 1
• c) When number of basic variables > m + n - 1
• d) When all variables are zero

5. The MODI method is used for:

• a) Finding initial solution
• b) Testing optimality
• c) Finding maximum cost
• d) Balancing the problem

6. In Vogel's Approximation Method, what do we calculate first?

• a) Opportunity cost
• b) Penalty cost
• c) Transportation cost
• d) Total cost

7. What is the stepping stone method used for?

• a) Finding initial solution
• b) Improving the solution
• c) Checking feasibility
• d) Balancing supply and demand

8. A dummy source is added when:

• a) Total supply > Total demand
• b) Total supply < Total demand
• c) Total supply = Total demand
• d) Never added

9. The transportation cost from dummy source is always:

• a) Maximum
• b) Zero
• c) Minimum
• d) Infinite

10. Which of the following is NOT a characteristic of transportation problem?

• a) Linear objective function
• b) Linear constraints
• c) Non-negativity constraints
• d) Quadratic objective function

11. In North-West Corner Method, allocation starts from:

• a) Lowest cost cell
• b) Highest cost cell
• c) Top-left corner cell
• d) Bottom-right corner cell

12. The optimal solution of a transportation problem is always:

• a) Unique
• b) Multiple
• c) May be unique or multiple
• d) Does not exist

13. The transportation tableau is also known as:

• a) Cost matrix
• b) Distribution matrix
• c) Transportation matrix
• d) All of the above

14. What does ui + vj represent in MODI method?

• a) Transportation cost
• b) Shadow price
• c) Opportunity cost
• d) Penalty cost

15. When is a transportation problem said to have alternative optimal solutions?

• a) When all opportunity costs are positive
• b) When at least one opportunity cost is zero
• c) When all opportunity costs are negative
• d) When the problem is degenerate

16. The Hungarian method is used to solve:

• a) Transportation problem
• b) Assignment problem
• c) Linear programming problem
• d) Network flow problem

17. In transportation problem, each constraint equation has:

• a) All coefficients as 1
• b) At least one coefficient as 0
• c) All coefficients as 0 or 1
• d) Mixed coefficients

18. The number of basic variables in a transportation problem with m sources and n destinations is:

• a) m + n
• b) m × n
• c) m + n - 1
• d) m - n + 1

19. What is the main advantage of Vogel's Approximation Method over other methods?

• a) Simplicity
• b) Gives solution closer to optimal
• c) Requires less computation
• d) Always gives optimal solution

20. The transportation problem is a special case of:

• a) Assignment problem
• b) Linear Programming Problem
• c) Integer Programming Problem
• d) Dynamic Programming Problem

21. To resolve degeneracy in transportation problem, we:

• a) Add a dummy variable
• b) Allocate a very small amount (ε)
• c) Remove a constraint
• d) Start over with new method

22. In Least Cost Method, allocation is made to:

• a) First available cell
• b) Cell with minimum cost
• c) Cell with maximum cost
• d) Last available cell

23. The dual of a transportation problem is:

• a) Another transportation problem
• b) An assignment problem
• c) A maximization problem
• d) Always infeasible

24. A transportation problem is said to be unbalanced when:

• a) Total supply = Total demand
• b) Total supply ≠ Total demand
• c) All supplies are equal
• d) All demands are equal

25. The feasible region of a transportation problem is:

• a) Always empty
• b) Always unbounded
• c) Always bounded and non-empty
• d) May be empty

Demand

🎉 Your Results 🎉

📚 Correct Answers & Explanations

Q1: b) Minimize transportation cost
The primary objective is to minimize the total cost of transporting goods from sources to destinations.

Q2: b) Supply = Demand
A balanced transportation problem has total supply equal to total demand.

Q3: d) All of the above
North-West Corner, Least Cost, and Vogel's methods are all used for finding initial basic feasible solutions.

Q4: b) When number of basic variables < m + n - 1
Degeneracy occurs when the number of basic variables is less than m + n - 1.

Q5: b) Testing optimality
MODI (Modified Distribution) method is used to test if the current solution is optimal.

Q6: b) Penalty cost
VAM calculates penalty costs (difference between two smallest costs) for each row and column.

Q7: b) Improving the solution
Stepping stone method is used to improve a given basic feasible solution.

Q8: b) Total supply < Total demand
A dummy source with zero cost is added when total supply is less than total demand.

Q9: b) Zero
Transportation cost from dummy source is always zero as it represents unmet demand.

Q10: d) Quadratic objective function
Transportation problem has linear objective function, not quadratic.

Q11: c) Top-left corner cell
North-West Corner method starts allocation from the top-left corner of the transportation table.

Q12: c) May be unique or multiple
Optimal solution can be unique or there may be multiple optimal solutions.

Q13: d) All of the above
The transportation tableau is known by all these names.

Q14: b) Shadow price
ui + vj represents the shadow price or dual variables in MODI method.

Q15: b) When at least one opportunity cost is zero
Alternative optimal solutions exist when at least one non-basic variable has zero opportunity cost.

Q16: b) Assignment problem
Hungarian method is specifically used to solve assignment problems.

Q17: c) All coefficients as 0 or 1
Each constraint in transportation problem has coefficients of either 0 or 1.

Q18: c) m + n - 1
The number of basic variables in a non-degenerate solution is m + n - 1.

Q19: b) Gives solution closer to optimal
VAM typically provides an initial solution that is closer to the optimal solution.

Q20: b) Linear Programming Problem
Transportation problem is a special case of Linear Programming Problem.

Q21: b) Allocate a very small amount (ε)
Degeneracy is resolved by allocating a very small quantity ε to make m + n - 1 basic variables.

Q22: b) Cell with minimum cost
Least Cost Method allocates to the cell with minimum transportation cost.

Q23: c) A maximization problem
The dual of a transportation minimization problem is a maximization problem.

Q24: b) Total supply ≠ Total demand
Unbalanced transportation problem has total supply not equal to total demand.

Q25: c) Always bounded and non-empty
The feasible region of a transportation problem is always bounded and non-empty due to its structure.