2. INTRODUCTION
It is a one Method of Optimization
Techniques
Introduce about
transportation model
methods of solving transportation
problem to its optimistic solution stage.
2
3. What Is Optimization ?
Transportation Model
Applications of Transportation Model…
Phases of Solution
Obtains the Initial Basic Feasible Solution
Obtains the Optimal Basic Solution
Actual model
Conclusion
Use of this technique
CONTENTS
4. What Is Optimization ?
Optimization problem :
Maximizing or minimizing some function
• Common
applications:
Minimal cost,
maximal profit,
minimal error,
optimal design,
optimal
management,
variation principles
5. Transportation Model
The transportation problem is a special type
of LPP
The objective is to minimize the cost of
distributing a product
Because of its special structure the usual
simplex method is not suitable
require special method of solution.
Aim : find out optimum transportation
schedule keeping in mind cost of
transportation to be minimized
6. Assumptions in the transportation
Model :
1. Total qty of the item available at different sources
is equal to the total requirement at different
destinations.
2. Item can be transported conveniently from all
sources to destinations.
3. The unit transportation cost of the item from all
sources to destinations is certainly & precisely
known.
4. The transportation cost on given route is directly
proportional to the no. of units shipped on that
route.
5. The objective is to minimize the total
transportation cost for the organization as a
whole & not for individual supply & distribution
centre.
7. Application of Transportation
Model
Minimize shipping costs
Determine low cost location
Find minimum cost production
schedule
Military distribution system
8. Phases of Solution of Transportation
Problem :-
Phase I- obtains the initial basic feasible
solution
◦ North West Corner Method (NWC)
◦ Row Minima Method
◦ Column Minima Method
◦ Least Cost Method
◦ Vogel's Approximation Method (VAM)
Phase II-obtains the optimal basic solution
◦ Stepping Stone Method
◦ Modified Distribution Method a.k.a. MODI
Method
9. Example.
Factory takes 16 Rs/km transport cost per truck
for supply of bricks.
Following is requirement of bricks on various
sites with respective distances(km) from
warehouses
Available Single truck contains 7000 bricksSites
warehouse
s
Karad Saidapur Masur
Agashiv
Nagar
Available
Bricks
Tasavde 2 3 11 7 42,000
Tembhu 1 0 6 1 7,000
Koparde 5 8 15 9 70,000
Required
Bricks
49,000 35,000 21,000 14,000 1,19,000
10. Solution
Unit cost of single tuck transport =17x travelling
distance(km)
Sites
warehouses
Karad Saidapur Masur
Agashiv
Nagar
Available
Bricks
(trucks)
Tasavde 2 3 11 7 6
Tembhu 1 0 6 1 1
Koparde 5 8 15 9 10
Required
Bricks (trucks)
7 5 3 2 17*
18. Use of This Technique :-
This model can be used for a wide variety
of situations such as
scheduling, production, investment, mix
problems & many other, so that the model
is really not confined to transportation or
distribution only.
The objective is to minimize the cost of
transportation while meeting the
requirements at the destinations.