Transportation and Assignment

If you want this presentation just give me a mail to [email protected]

1. GYAN GANGA INSTITUTE OF TECHNOLOGY
AND MANAGEMENT, BHOPAL
GROUP NAME:- ELITE
Guided by:
Prof. Lokesh Payasi
Presented by:
Krati Barman
Poonam Patel
Nisha Johari
Tikaram Sahu
Ankit Jain
Prathrna
Yadav

2. CONCEPT
The Transportation problems are one of the type of
LPP.
The objective is to minimize the cost of distribution a
product from a no. of sources or origins to a number
of destinations in such a manner that the cost of
transportation is minimum.

3. DEFINITION
“The transportation problem is to transport various
amounts of a single homogenous commodity, which
are initially stored at various origins , to different
destinations in such a way that the total
transportation cost is a minimum”.

4. Terminology Used
Feasible Solution.
Basic Feasible Solution.
Optimal Feasible Solution.
Balanced Transportation Problem.
Unbalanced Transportation Problem.
Matrix Terminology.

5. Assumptions of the Model
Availability of the quantity.
Transportation of items.
Cost per unit.
Independent cost.
Objective.

6. Steps to solve a Transportation
Model
Formulate the problem and setup in the matrix form.
Obtain the Initial Basic Feasible solution.
Test the initial solution for optimality.
Updating the solution.

7. Methods of Transportation
North-West corner Method
Row Minima Method
Column Minima Method
Least-Cost Method
Vogel’s Approximation Method

8. North- West Corner Method (NWCM)
The simplest of the procedures, used to generate an
initial feasible solution is, NWCM. It is so called
because we begin with the North West or upper left
corner cell of our transportation table.

9. Row Minima Method
Row minima method consists in allocation as much as
possible in the lowest cost cell of the first row so that
either the capacity of the first plant is exhausted or
the requirement at distribution centre is satisfied or
both.

10. Column Minima Method
Column Minima Method consist in allocating as
much as possible in the lowest cost cell of the first
column so that either the demand of the first
distribution centre is satisfied or the capacity of the
plant is exhausted or both.

11. Least-Cost Method
Least-Cost Method consist in allocating as much as
possible in the lowest cost cell and then further
allocation is done in th cell with second lowest cost
cell and so on.

12. Vogel’s Approximation Method (VAM)
In this method, each allocation is made on the basis
of the opportunity (or penalty or extra) cost that
would have been incurred if allocations in certain
cells with minimum unit transportation cost were
missed. In this method allocations are made so thet
the penalty cost is minimized.

13. Meaning
The assignment problem which finds many
allocation in allocation and scheduling.
For example: In assigning salesman to different
regions vehicles and drives to different routes.
Products to bidders and research problem to
teams etc.

14. Assignment
The Name “assignment problem” originates from the
classical problem where the objective is to assign a
number of origins (Job) to the equal number of
destinations (Persons) at a minimum cast (or
maximum profit).

15. Application areas of Assignment Problem
In assignment machines to factory orders.
In assigning sales/marketing people to sales
territories.
In assignment contracts to bidders by systematic bid
evaluation.
In assignment teachers to classes.
In assigning accountants to account of the clients.
In assignment police vehicles to patrolling areas.

16. Method for solving assignment problem
 Enumeration Method
 Simplex Method
 Transportation Method
 Hungarian Method

17. Steps for Solving the problems
(By Hungarian method )
 Balancing the problem.
 Find the opportunity cost table.
 Make assignment in the opportunity cost matrix.
 Optimality criterion.
 Revise the opportunity cost table.
 Develop the new revised opportunity cost table.
 Repeat steps.

18. Difference Between Transportation problem and
Assignment problem
Transportation Problem Assignment Problem
Number of sources and
number of destinations need
not be equal. Hence, the cost
matrix is not necessarily a
square matrix.
The problem is unbalanced if
the total supply and total
demand are not equal.
Since assignment is done one
basis, the number of sources
and the number of
destinations are equal.
Hence, the cost matrix must
be a square matrix.
The problem is unbalanced if
the cost matrix is not a
square matrix.