Q.1 In a transportation problem, what does the objective typically aim to minimize?
Profit
Cost
Supply
Demand
Explanation - The transportation problem seeks to minimize the total transportation cost of distributing goods from sources to destinations.
Correct answer is: Cost
Q.2 The transportation problem is a special case of which optimization technique?
Assignment problem
Linear programming
Game theory
Decision tree
Explanation - Transportation problems are a subset of linear programming problems where the decision variables represent shipment quantities.
Correct answer is: Linear programming
Q.3 In a balanced transportation problem, what condition must hold true?
Supply > Demand
Supply < Demand
Supply = Demand
No supply-demand relation
Explanation - A transportation problem is balanced if the total supply equals the total demand.
Correct answer is: Supply = Demand
Q.4 If total supply exceeds total demand, the transportation problem is called?
Balanced
Unbalanced
Degenerate
Infeasible
Explanation - When supply and demand are not equal, the problem is unbalanced and must be balanced by adding dummy rows or columns.
Correct answer is: Unbalanced
Q.5 What method is commonly used to find an initial feasible solution in transportation problems?
Simplex method
North-West Corner Rule
Hungarian Method
Graphical Method
Explanation - The North-West Corner Rule is one of the simplest methods to find an initial feasible solution in transportation problems.
Correct answer is: North-West Corner Rule
Q.6 Which method gives a better initial feasible solution compared to the North-West Corner Rule?
MODI Method
Stepping Stone Method
Vogel’s Approximation Method
Big M Method
Explanation - Vogel’s Approximation Method (VAM) usually provides a solution closer to optimal compared to the North-West Corner Rule.
Correct answer is: Vogel’s Approximation Method
Q.7 In the MODI method, what does MODI stand for?
Modified Distribution
Modern Distribution
Maximum Distribution
Minimum Distribution
Explanation - The MODI method stands for Modified Distribution method, used for testing the optimality of a transportation solution.
Correct answer is: Modified Distribution
Q.8 What type of problem does the transportation model solve?
Allocation problem
Routing problem
Scheduling problem
Inventory problem
Explanation - The transportation model is mainly used to allocate resources efficiently between different sources and destinations.
Correct answer is: Allocation problem
Q.9 In transportation problems, dummy sources or destinations are introduced to:
Reduce costs
Balance supply and demand
Increase profit
Avoid degeneracy
Explanation - Dummy rows or columns are added to balance supply and demand when the problem is unbalanced.
Correct answer is: Balance supply and demand
Q.10 The total number of basic variables in a balanced transportation problem is:
m+n-1
m×n
m+n
m−n
Explanation - In a balanced transportation problem with m sources and n destinations, the number of basic variables is always m+n-1.
Correct answer is: m+n-1
Q.11 If the number of allocations in an initial feasible solution is less than m+n-1, it is called:
Optimal solution
Degenerate solution
Infeasible solution
Balanced solution
Explanation - When allocations are fewer than m+n-1, the solution is degenerate, which requires special handling.
Correct answer is: Degenerate solution
Q.12 What does the cost matrix in transportation problem represent?
Supply values
Profit values
Transportation costs per unit
Demand values
Explanation - The cost matrix shows the cost of transporting one unit of goods from each source to each destination.
Correct answer is: Transportation costs per unit
Q.13 Which of the following is NOT a method for solving transportation problems?
North-West Corner Rule
Vogel’s Approximation
MODI Method
Hungarian Method
Explanation - The Hungarian Method is used for assignment problems, not for transportation problems.
Correct answer is: Hungarian Method
Q.14 The stepping stone method is used to:
Obtain initial feasible solution
Test for optimality
Balance supply and demand
Find degeneracy
Explanation - The stepping stone method is an optimality test for transportation problems.
Correct answer is: Test for optimality
Q.15 In the transportation problem, rows usually represent:
Demand centers
Supply sources
Profit centers
Warehouses only
Explanation - In transportation tables, rows usually represent supply sources, and columns represent demand destinations.
Correct answer is: Supply sources
Q.16 If supply is less than demand, what is added to balance the transportation problem?
Dummy source
Dummy destination
Dummy variable
Dummy cost
Explanation - When supply is less than demand, a dummy source is added with zero transportation cost to balance the problem.
Correct answer is: Dummy source
Q.17 Which of these is the fastest method for finding an initial feasible solution?
North-West Corner Rule
Vogel’s Approximation Method
Least Cost Method
MODI Method
Explanation - The North-West Corner Rule is computationally the fastest, though not necessarily the most efficient.
Correct answer is: North-West Corner Rule
Q.18 In Least Cost Method, allocations are made to:
Highest supply
Lowest demand
Lowest cost cell
Random cell
Explanation - In Least Cost Method, allocations are made to the cell with the lowest transportation cost first.
Correct answer is: Lowest cost cell
Q.19 The MODI method requires calculation of:
Row and column penalties
Dual variables (u and v)
Slack variables
Profit margins
Explanation - The MODI method uses u and v variables for rows and columns to calculate opportunity costs.
Correct answer is: Dual variables (u and v)
Q.20 What is the main difference between transportation and assignment problems?
Assignment deals with one-to-one allocation
Transportation deals with multiple allocations
Both A and B
Neither A nor B
Explanation - Assignment problems involve one-to-one allocations, while transportation problems involve distributing resources across multiple destinations.
Correct answer is: Both A and B
Q.21 Which of the following indicates an optimal solution in transportation problems?
All opportunity costs are non-negative
All opportunity costs are zero
Some opportunity costs are negative
No basic variables
Explanation - In the MODI or stepping stone method, an optimal solution exists when all opportunity costs are non-negative.
Correct answer is: All opportunity costs are non-negative
Q.22 The degeneracy problem occurs when:
Too many allocations
Too few allocations
Equal supply and demand
All costs are zero
Explanation - Degeneracy arises when the number of allocations is less than m+n-1, making solution unstable.
Correct answer is: Too few allocations
Q.23 The opportunity cost in stepping stone method represents:
Difference in supply and demand
Potential decrease in cost if a new route is used
Profit margin
Slack variable value
Explanation - Opportunity cost indicates how much the total cost would change if a unit is shipped through an unused route.
Correct answer is: Potential decrease in cost if a new route is used
Q.24 Which of the following methods is used after obtaining an initial feasible solution?
North-West Corner Rule
Vogel’s Approximation Method
MODI Method
Least Cost Method
Explanation - Once an initial feasible solution is obtained, MODI or Stepping Stone methods are used for optimality testing.
Correct answer is: MODI Method