Optimization Techniques Unit-4 Quiz

The transportation problem is indeed a special class of the linear programming problem. It involves determining the optimal way to transport goods from sources to destinations, while minimizing the total cost or maximizing the total profit. It can be solved using various mathematical techniques, such as the simplex method or the transportation simplex method. Therefore, the statement is true.

The statement is true because the MODI (Modified Distribution) Method is also known as the u-v Method. This method is used in linear programming to find the optimal solution of a transportation problem. It involves modifying the initial solution by evaluating the opportunity costs of reallocating units from one cell to another. Therefore, the alternative name for the MODI Method is u-v Method.

Here no. of rows, m = 3 and no. of columns , n = 4
No. of optimal cells = m + n – 1
= 3 + 4 – 1
∴ No. of optimal cells = 6

Since given transportation problem is said to be balance means
Sum of all supply costs = Sum of all Demand costs
300 + 400 + 500 = 250 + 350 + 400 + 200
1200 = 1200

Total Cost = (1*300)+(2*250)+(6*50)+(5*100)+(3*300)+(2*200)
= 300 + 500 + 300 + 500 + 900 + 400
∴ Total Cost = 2900

not-available-via-ai

not-available-via-ai

The three IBFS (Initial Basic Feasible Solution) methods of a transportation problem are the North-West Corner Method, the Least Cost Method, and Vogel's Approximation Method. The North-West Corner Method starts by allocating units from the top-left corner of the transportation table and gradually moves towards the bottom-right corner. The Least Cost Method selects the cell with the lowest cost to allocate units and repeats this process until all cells are filled. Vogel's Approximation Method considers the difference between the two lowest costs in each row and column to determine the best allocation.

The MODI method is a method used in transportation problems to find an optimal solution. It stands for Modified Distribution Method. This method involves calculating the opportunity costs for each empty cell in the transportation table and selecting the cell with the highest opportunity cost. It then performs a cycle test to check if the solution is optimal. If the solution is not optimal, the method adjusts the allocation of units in the transportation table and repeats the process until an optimal solution is reached.

North-West Corner Method

    Total Cost = (3*250)+(1*50)+(6*300)+(5*100)+(3*300)+(2*200)

                     = 750 + 50 + 1800 + 500 + 900 + 400

∴ Total Cost = 4400

Least Cost Method

     Total Cost = (1*300)+(2*250)+(6*50)+(5*100)+(3*300)+(2*200)

                       = 300 + 500 + 300 + 500 + 900 + 400

∴ Total Cost = 2900

Vogel's Approximation Method

   Total Cost = (1*300)+(2*250)+(5*150)+(3*50)+(3*250)+(2*200)

                     = 300 + 500 + 750 + 150 + 750 + 400

∴ Total Cost = 2850