Transportation Techniques By Group 1 Shreeya Sonia Shweta Shobha
Jul 15, 2015
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
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
Terminology
• Balanced Transportation Problem
• Unbalanced Transportation Problem
• Transportation Table
• Dummy source or destination
• Initial feasible solution
• Optimum solution
• Objective function
• Constraint.
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
Warehouse
Source W1 W2 W3 W4 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
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
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.
An example for Minimum Cost MethodStep 1: Select the cell with minimum cost.
2 3 5 6
2 1 3 5
3 8 4 6
5
10
15
12 8 4 6
Step 3: Find the new cell with minimum shipping cost and cross-out row 2
2 3 5 6
2 1 3 5
2 8
3 8 4 6
5
X
15
10 X 4 6
Step 4: Find the new cell with minimum shipping cost and cross-out row 1
2 3 5 6
5
2 1 3 5
2 8
3 8 4 6
X
X
15
5 X 4 6
Step 5: Find the new cell with minimum shipping cost and cross-out column 1
2 3 5 6
5
2 1 3 5
2 8
3 8 4 6
5
X
X
10
X X 4 6
Step 6: Find the new cell with minimum shipping cost and cross-out column 3
2 3 5 6
5
2 1 3 5
2 8
3 8 4 6
5 4
X
X
6
X X X 6
Step 7: Finally assign 6 to last cell. The bfs is found as: X11=5, X21=2, X22=8, X31=5, X33=4 and X34=6
2 3 5 6
5
2 1 3 5
2 8
3 8 4 6
5 4 6
X
X
X
X X X X
Northwest corner method
Steps:
1. Assign largest possible allocation to the cell in the upper left-hand corner of the table
2. Repeat step 1 until all allocations have been assigned
3. Stop. Initial tableau is obtained
18
Vogel’s Approximation Method
• 1. Determine the penalty cost for each row andcolumn.
• 2. Select the row or column with the highestpenalty cost.
• 3. Allocate as much as possible to the feasiblecell with the lowest transportation cost in the rowor column with the highest penalty cost.
• 4. Repeat steps 1, 2, and 3 until all requirementshave been met.
An example for Vogel’s MethodStep 1: Compute the penalties.
Supply Row Penalty
6 7 8
15 80 78
Demand
Column Penalty 15-6=9 80-7=73 78-8=70
7-6=1
78-15=63
15 5 5
10
15
Step 2: Identify the largest penalty and assign the highest possible value to the variable.
Supply Row Penalty
6 7 8
5
15 80 78
Demand
Column Penalty 15-6=9 _ 78-8=70
8-6=2
78-15=63
15 X 5
5
15
Step 3: Identify the largest penalty and assign the highest possible value to the variable.
Supply Row Penalty
6 7 8
5 5
15 80 78
Demand
Column Penalty 15-6=9 _ _
_
_
15 X X
0
15
Step 5: Finally the bfs is found as X11=0, X12=5, X13=5, and X21=15
Supply Row Penalty
6 7 8
0 5 5
15 80 78
15
Demand
Column Penalty _ _ _
_
_
X X X
X
X
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
2 February 2015
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 0 40
S5 3 12 5 19 50
DEMAND 60 60 20 10