Transportation technique

1. Transportation Techniques By Group 1 Shreeya Sonia Shweta Shobha

2. Introduction A transportation problem basically deals with the problem, which aims to find the best way to fulfill the demand of n demand points using the capacities of m supply points

3. A Transportation Model Requires The origin points, and the capacity or supply per period at each The destination points and the demand per period at each The cost of shipping one unit from each origin to each destination

4. Terminology Balanced Transportation Problem Unbalanced Transportation Problem Transportation Table Dummy source or destination Initial feasible solution Optimum solution Objective function Constraint.

5. Transportation Problem Solutions steps Define problem Set up transportation table (matrix) Summarizes all data Keeps track of computations Develop initial solution Find optimal solution Assumption

6. Steps in Solving the Transportation Problem

7. Warehouse Source W 1 W 2 W 3 W 4 Supply Capacity F1 30 25 40 20 100 F2 29 26 35 40 250 F3 31 33 37 30 150 Demand 90 160 200 50 N = Total supply/ Demand Transportation Table

8. Special Issues in the Transportation Model Demand not equal to supply Called ‘unbalanced’ problem Add dummy source if demand > supply Add dummy destination if supply > demand

9. There are three basic methods: Minimum Cost Method Northwest Corner Method Vogel’s Method

10. Minimum Cost Method Here, we use the following steps: Step 1 Find the cell that has the least cost Step 2: Assign as much as allocation to this cell Step 3: Block those cells that cannot be allocated Step 4: Repeat above steps until all allocation have been assigned.

11. An example for Minimum Cost Method Step 1: Select the cell with minimum cost.

12. Step 2: Cross-out column 2

13. Step 3: Find the new cell with minimum shipping cost and cross-out row 2

14. Step 4: Find the new cell with minimum shipping cost and cross-out row 1

15. Step 5: Find the new cell with minimum shipping cost and cross-out column 1

16. Step 6: Find the new cell with minimum shipping cost and cross-out column 3

17. Step 7: Finally assign 6 to last cell. The bfs is found as: X 11 =5, X 21 =2, X 22 =8, X 31 =5, X 33 =4 and X 34 =6

18. Northwest corner method Steps: Assign largest possible allocation to the cell in the upper left-hand corner of the table Repeat step 1 until all allocations have been assigned Stop . Initial tableau is obtained 18

19. Vogel’s Approximation Method 1. Determine the penalty cost for each row and column. 2. Select the row or column with the highest penalty cost. 3. Allocate as much as possible to the feasible cell with the lowest transportation cost in the row or column with the highest penalty cost. 4. Repeat steps 1, 2, and 3 until all requirements have been met.

20. An example for Vogel’s Method Step 1: Compute the penalties.

21. Step 2: Identify the largest penalty and assign the highest possible value to the variable.

22. Step 3: Identify the largest penalty and assign the highest possible value to the variable.

23. Step 5: Finally the bfs is found as X 11 =0, X 12 =5, X 13 =5, and X 21 =15

24. Applications of Transportation Model Scheduling airlines, including both planes and crew Deciding the appropriate place to site new facilities such as a warehouse, factory or fire station Managing the flow of water from reservoirs Identifying possible future development paths for parts of the telecommunications industry Establishing the information needs and appropriate systems to supply them within the health service

25. 12 January 2014 W1 W2 W3 W4 SUPPLY S1 10 20 5 7 10 S2 13 9 12 8 20 S3 4 15 7 9 30 S4 14 7 1 40 S5 3 12 5 19 50 DEMAND 60 60 20 10

26. W1 W2 W3 W4 SUPPLY P1 190 300 500 100 70 P2 700 300 400 600 90 P3 400 100 400 200 180 DEMAND 50 80 70 140 340 12 January 2014