Flashcards on Transportation Model

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What is the Transportation Model?

The Transportation Model is a linear programming model used for solving problems related to the transportation of goods or services from several supply sources to several demand destinations while minimizing the cost of transportation.

What are the assumptions of the Transportation Model?

1. Each demand destination must be supplied. 2. Each origin supplier must ship. 3. The supply and demand units are known and constant. 4. The unit transportation cost between each origin and destination is known and constant. 5. The transportation takes place along a single mode. 6. There are no capacity constraints for supplies or demand. 7. There are no intermediate transhipment points along the route. 8. The objective is to minimize total transportation cost.

What are the steps involved in solving a Transportation Model problem?

1. Formulate the linear programming model with the supply, demand, and cost data. 2. Solve the model using any of the available methods. 3. Verify the optimality and feasibility of the solution to ensure that it is the best possible solution. 4. Interpret the solution and recommend a transportation plan.

What is the Northwest Corner Method?

The Northwest Corner Method is a heuristic method used to find an initial feasible solution to the Transportation Model problem. It starts by allocating the maximum possible amount of supply at the upper left-hand corner of the table.

What is the Least Cost Method?

The Least Cost Method is a heuristic method used to find an initial feasible solution to the Transportation Model problem. It starts by allocating the maximum possible amount of supply at the lowest cost cell of the table.

What is the Vogel's Approximation Method?

The Vogel's Approximation Method is a heuristic method used to find an initial feasible solution to the Transportation Model problem. It considers the opportunity costs associated with each cell, which is the difference between the two lowest costs for each row and column.

What is the Optimality Test?

The Optimality Test is used to verify that the current solution to the Transportation Model problem is the best possible solution. It involves checking if the basic feasible solution is optimal by calculating the unit cost for each non-basic variable and comparing it with the corresponding dual variable. If there is any negative difference, the current solution is not optimal and another iteration is required.

What is the Modified Distribution Method?

The Modified Distribution Method is an iterative method used to obtain an optimal solution for the Transportation Model problem. It involves finding a basic feasible solution and then improving it using the stepping-stone method or the modified distribution method.

What is the Stepping-Stone Method?

The Stepping-Stone Method is an iterative method used to improve a basic feasible solution to the Transportation Model problem. It involves evaluating the opportunity cost for each empty cell of the table by creating a closed loop of occupied cells and then calculating the improvement in cost by moving along the loop.

What is the degeneracy in the Transportation Model?

Degeneracy in the Transportation Model occurs when one or more of the allocated variables assumes a value of zero in the optimal solution. It can cause certain algorithms, such as the simplex method, to fail or to require more iterations than usual.

What is the MODI method?

The MODI method is an iterative method used to calculate the optimal transportation plan and the corresponding value of the objective function in the Transportation Model problem. It is an improvement over the Stepping-Stone Method as it reduces the number of calculations required and handles degeneracy problems efficiently.

What is the Balanced Transportation Model?

The Balanced Transportation Model is a special case of the Transportation Model where the total supply is equal to the total demand. In this case, the model can be solved using any of the methods available and the solution obtained will be optimal and feasible.

What is the Unbalanced Transportation Model?

The Unbalanced Transportation Model is a special case of the Transportation Model where the total supply is not equal to the total demand. In this case, dummy variables are introduced to balance the model and make it solvable.

What is the Transshipment Model?

The Transshipment Model is an extension of the Transportation Model that allows for intermediate transshipment points to be included in the network. It is used to solve problems related to the transportation of goods or services through intermediate points while minimizing the cost of transportation.

What is the Capacitated Transport Model?

The Capacitated Transport Model is a variant of the Transportation Model that includes capacity constraints for supplies and/or demand. It is used to solve problems related to the transportation of goods or services under capacity restrictions while minimizing the cost of transportation.

What is the Transportation Model?

The Transportation Model is a linear programming model used for solving problems related to the transportation of goods or services from several supply sources to several demand destinations while minimizing the cost of transportation.

What are the assumptions of the Transportation Model?

1. Each demand destination must be supplied. 2. Each origin supplier must ship. 3. The supply and demand units are known and constant. 4. The unit transportation cost between each origin and destination is known and constant. 5. The transportation takes place along a single mode. 6. There are no capacity constraints for supplies or demand. 7. There are no intermediate transhipment points along the route. 8. The objective is to minimize total transportation cost.

What are the steps involved in solving a Transportation Model problem?

1. Formulate the linear programming model with the supply, demand, and cost data. 2. Solve the model using any of the available methods. 3. Verify the optimality and feasibility of the solution to ensure that it is the best possible solution. 4. Interpret the solution and recommend a transportation plan.

What is the Northwest Corner Method?

The Northwest Corner Method is a heuristic method used to find an initial feasible solution to the Transportation Model problem. It starts by allocating the maximum possible amount of supply at the upper left-hand corner of the table.

What is the Least Cost Method?

The Least Cost Method is a heuristic method used to find an initial feasible solution to the Transportation Model problem. It starts by allocating the maximum possible amount of supply at the lowest cost cell of the table.

What is the Vogel's Approximation Method?

The Vogel's Approximation Method is a heuristic method used to find an initial feasible solution to the Transportation Model problem. It considers the opportunity costs associated with each cell, which is the difference between the two lowest costs for each row and column.

What is the Optimality Test?

The Optimality Test is used to verify that the current solution to the Transportation Model problem is the best possible solution. It involves checking if the basic feasible solution is optimal by calculating the unit cost for each non-basic variable and comparing it with the corresponding dual variable. If there is any negative difference, the current solution is not optimal and another iteration is required.

What is the Modified Distribution Method?

The Modified Distribution Method is an iterative method used to obtain an optimal solution for the Transportation Model problem. It involves finding a basic feasible solution and then improving it using the stepping-stone method or the modified distribution method.

What is the Stepping-Stone Method?

The Stepping-Stone Method is an iterative method used to improve a basic feasible solution to the Transportation Model problem. It involves evaluating the opportunity cost for each empty cell of the table by creating a closed loop of occupied cells and then calculating the improvement in cost by moving along the loop.

What is the degeneracy in the Transportation Model?

Degeneracy in the Transportation Model occurs when one or more of the allocated variables assumes a value of zero in the optimal solution. It can cause certain algorithms, such as the simplex method, to fail or to require more iterations than usual.

What is the MODI method?

The MODI method is an iterative method used to calculate the optimal transportation plan and the corresponding value of the objective function in the Transportation Model problem. It is an improvement over the Stepping-Stone Method as it reduces the number of calculations required and handles degeneracy problems efficiently.

What is the Balanced Transportation Model?

The Balanced Transportation Model is a special case of the Transportation Model where the total supply is equal to the total demand. In this case, the model can be solved using any of the methods available and the solution obtained will be optimal and feasible.

What is the Unbalanced Transportation Model?

The Unbalanced Transportation Model is a special case of the Transportation Model where the total supply is not equal to the total demand. In this case, dummy variables are introduced to balance the model and make it solvable.

What is the Transshipment Model?

The Transshipment Model is an extension of the Transportation Model that allows for intermediate transshipment points to be included in the network. It is used to solve problems related to the transportation of goods or services through intermediate points while minimizing the cost of transportation.

What is the Capacitated Transport Model?

The Capacitated Transport Model is a variant of the Transportation Model that includes capacity constraints for supplies and/or demand. It is used to solve problems related to the transportation of goods or services under capacity restrictions while minimizing the cost of transportation.

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