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Summary
This paper is about solving transportation problem (shortest
path model) using Operation
Research (OR) approach in analysis. Transportation model is a
special type of networks
problems for shipping a commodity from source (e.g. branch
office) to destinations (e.g.,
main hub). Transportation model deal to get the minimum-cost,
time or distance plan to
transport a commodity from a number of sources. Using linear
programming method to solve
transportation problem, we determine the value of objective
function which minimize the
distance for transporting.
Background
About GATI
Gati Limited is a pioneer and leader in the Express Distribution
and Supply Chain Solutions
in India. It was the revolutionary approach adopted by Gati that
helped launch many path-breaking initiatives in the logistics
segment and many were the firsts for the Indian market. In
a span of 20 years, Gati has consistently explored various ways
to bring premium value to thecustomer, always setting benchmarks in
quality of service and customer satisfaction.
Having started as a cargo management company in 1989, Gati has
grown into an organization
with more than 3500 employees and a turnover of Rs 576 Crore
covering 603 out of 611
districts in India. Gati has over 4000 vehicles on road, fleet
of refrigerated trucks, container
vessels and world class mechantronic warehousing facilities
across India. Be it flexible point-
to-point distribution solutions or complex end-to-end integrated
logistics solutions or supply
chain management, Gati does it all with great effectiveness and
reliability, and enjoys the
trust of a large customer base.
The Gati advantage of seamless connectivity across air, road,
ocean and rail has resulted in a
plethora of offerings to the customer unmatched in the industry.
Besides having a strong
network in India, Gati has a strong market presence in the Asia
Pacific region and SAARC
countries. Today, Gati has offices in China, Singapore, Bhutan,
Dubai, Hong Kong, Thailand,
Nepal and Sri Lanka and has plans to foray into other
markets.
Gati's business model is well aligned with the customers need,
which is why the core
businesses have grown to meet the evolving needs of the
customer, and this has resulted in
consolidation of services and in the development of core and
critical infrastructure, thus
propelling Gati to the forefront in the logistics segment.
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Problem definition
Shortest path model
Cargo delivery is the transportation of packages or parcels from
a source point to a
destination point. Generally key success factors in cargo
delivery are speed and reliability.
During the journey from branch office to the main hub the
vehicles followed different routes
after it reaches to the main hub they send the cargo to their
main destination
Branch office Main hub
Customer either brings the cargo to the office or it is picked
up by the company vehicles.
Before being transported to the office cargos wait for other
cargo which has different origin
but same destination.
The branch office picks up the cargos and delivers cargos to the
main hub.
Shortest path model is to look the map and try to plan best
route to the destination. The
models main objective is to minimize the distance, time, or cost
from the starting point the
start node to the destination node terminal node.
GATI (south Bangalore branch) wants to determine the route to
minimum distance from
Singsandra office to Peenya main hub
METHODS FOR SOLVING TRANSPORTATION PROBLEM
There are five methods to determine the solution for balanced
transportation problem:
1. Northwest Corner method
2. Vogels approximation method(VAM)
3. Stepping stone method
4. Hungarian method
5. Linear programming.
The methods are as follows1. North-West corner method (NWCM)
The North West corner rule is a method for computing a basic
feasible solution of a
transportation problem where the basic variables are selected
from the North Westcorner (i.e., top left corner).
Steps
1. Select the North West (upper left-hand) corner cell of the
transportation table and
allocate as many units as possible equal to the minimum between
available supplies
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and demand requirements, i.e., min (s1, d1).
2. Adjust the supply and demand numbers in the respective rows
and columns
allocation.
3. If the supply for the first row is exhausted then move down
to the first cell in the
second row.
4. If the demand for the first cell is satisfied then move
horizontally to the next cell
in the second column.
5. If for any cell supply equals demand then the next allocation
can be made in cell
either in the next row or column.6. Continue the procedure until
the total available quantity is fully allocated to the
cells as required.
Vogels Approximation Method (VAM)
The Vogel approximation method is an iterative procedure for
computing a basic feasiblesolution of the transportation
problem.
Steps
1. Identify the boxes having minimum and next to minimum
transportation cost ineach row and write the difference (penalty)
along the side of the table against the
corresponding row.
2 Identify the boxes having minimum and next to minimum
transportation cost in
each column and write the difference (penalty) against the
corresponding column
3. Identify the maximum penalty. If it is along the side of the
table, make maximum
allotment to the box having minimum cost of transportation in
that row. If it is
below the table, make maximum allotment to the box having
minimum cost oftransportation in that column.
4. If the penalties corresponding to two or more rows or columns
are equal, select
the top most row and the extreme left column.
Linear Program Structure
Linear programming models consist of an objective function and
the constraints on thatfunction.
The problem is formulated from the problem statement as
follows:
1.Identify the objective of the problem; that is, which quantity
is to be optimized.
2.Identify the decision variables and the constraints on
them.
3. Write the objective function and constraints in terms of the
decision variables, using information
from the problem statement to determine the proper coefficient
for each term.
4. Add any implicit constraints, such as non-negative
restrictions.
5. Arrange the system of equations in a consistent form suitable
for solving by computer.
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Stepping stone method
TheStepping stone method is an iterative technique for moving
from an initial feasible solution
to an optimal solution.
It is used to evaluate the cost effectiveness of shipping goods
via transportation routes not
currently in the solution.
Rules of stepping stone method
1. Select an empty cell to evaluate.
2. Beginning at this cell, trace a closed path back to the cell,
turning corners only on filled cells. Only
horizontal & vertical moves are allowed. You may step over
any cell.
3. Place alternating +s and -s on this path, beginning with a +
on the empty cell being evaluated.
4. Calculate the change index by summing the unit costs, in the
tagged cells, accounting for the + & -
signs.
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DATA ANALY (Mathemati al Approach)
Deci i Variable: Xij
Objecti e functi n:
Mini i e t e di tance:
13.3X12
+11.7X13
+16.3X14
+12.6X16
+10.2X25
+5.5X26
+11.3X38
+3.6X47
+8.8X59
+8.5X65
+14.8X
68+16.6X69+11.2X78+7.1X89
Cons
nts:
X12+X13+X14+X16=1
X25+X26-X12=0
X38-X13=O
X47-X14=0
X59-X25-X65=0
X65+X68+X69-X16-X26=0
X78-X47=0
X89-X38=0
-X59-X69-X89=-1
XIJ=0 or1
V
ous outs
om Singasandra branc office to Peenya main hub
Figures are in kilometers
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Dec var x12 x13 x14 x16 x25 x26 x38 x47 x59 x65 x68 x69 x78
x89
2 1 -3 1 1 1 1 -3 2 1 3 -2 -3 1
13.3 11.7 16.3 12.6 10.2 5.5 11.3 3.6 8.8 8.5 14.8 16.6 11.2
7.1
constrain
1st 1 1 1 1
2nd -1 1 1
3rd -1 1
4th -1 1
5th -1 1 -1
6th -1 -1 1 1 1
7th -1 1
8th -1 1
9th -1 -1 -1
constrain
1st 1 1
2nd -1.1E-13 0
3rd 0 0
4th 0 0
5th 1.1E-13 0
6th -1.1E-13 0
7th 0 0
8th 0 0
9th -1 -1
obj.fn. 29
Shortest path: 1-3-8-9
