DTB_Manya Jain PPT.pptxhjggdgjdjjdjgdjdjdjdg

khfkdfkfkfiyiyiydid

1. Decision Making TECHNIQUES IN BUSINESS Submitted by: MANYA JAIN 71815601723 BBA (1 ST YEAR) II SEM Submitted to: DR. SURYYA FARHAT

2. INDEX Transportation Problem Introduction Balanced problem Unbalanced problem Methods to solve problems North- West Corner Rule Least Cost Method Vogel’s Approximation

3. Transportation problem

4. Introduction… Transportation problem is a special kind of Linear Programming Problem (LPP) in which goods are transported from a set of sources to a set of destinations subject to the supply and demand of the sources and destination respectively such that the total cost of transportation is minimized. It is also sometimes called as Hitchcock problem. Types of Transportation Problem: Balanced: When both the supplies and demand equal then the problem then the problem is said to be balanced. Unbalanced: When the supply and demand are not equal then the problem is said to be unbalance. In this type of problem, either a dummy row or a dummy column is added according to the requirement to make it a balanced problem. Then it can be solved similar to a balanced problem.

5. (solution) Warehouse 1 Warehouse 2 Warehouse 3 Supply Factory A 25 10 5 40 Factory B 20 20 Demand 25 10 25 Balanced Transportation Problem

6. ($cost) Dest X Dest Y Dest Z Supply Site A 460 350 640 8 Site B 510 420 690 12 Site C 650 680 490 10 Demand 9 7 11 Unbalanced Transportation Problem

7. Methods to solve Transportation Problem (North-West corner Method) Step 1:  Select the upper-left cell, i.e., the north-west corner cell of the transportation matrix and assign the minimum value of supply or demand, i.e., min(supply, demand). Step 2:  Subtract the above minimum value from Oi and Di of the corresponding row and column. Here, we may get three possibilities, as given below. If the supply is equal to 0, strike that row and move down to the next cell. If the demand equals 0, strike that column and move right to the next cell. If supply and demand are 0, then strike both row and column and move diagonally to the next cell. Step 3:  Repeat these steps until all the supply and demand values are 0.

8. Least Cost Method Step 1: Balance the problem Step 2: Select the lowest cost from the entire matrix and allocate the minimum of supply or demand. Step 3: Remove the row or column whose supply or demand is fulfilled and prepare a new matrix Step 4: Repeat the procedure until all the allocations are over Step 5: After all the allocations are over, write the allocations and calculate the transportation cost

9. Least Cost Method

10. Vogel’s Approximation Method Step 1:  Identify the two lowest costs in each row and column of the given cost matrix and then write the absolute row and column difference. These differences are called penalties Step 2:  Identify the row or column with the maximum penalty and assign the corresponding cell’s min(supply, demand). If two or more columns or rows have the same maximum penalty, then we can choose one among them as per our convenience Step 3:  If the assignment in the previous satisfies the supply at the origin, delete the corresponding row. If it satisfies the demand at that destination, delete the corresponding column. Step 4:  Stop the procedure if supply at each origin is 0, i.e., every supply is exhausted, and demand at each destination is 0, i.e., every demand is satisfying. If not, repeat the above steps, i.e., from step 1.

11. Vogel’s Approximation Method

12. THANKS FOR YOUR TIME You are a great audience!