4. Page 4
AgendaAgenda
Topics
Introduction
Concept of TP
History of TP
Application of TP
Process of TP
Methods/Techniques
NWCM
Types of TP
Steps
Problem Statement
Balanced Problem
Unbalanced Problem
Program
References
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Transportation Problem (TP)Transportation Problem (TP)
It deals with sources where a
supply of some commodity is
available and destinations where
the commodity is demanded. The
classic statement of the TP uses a
matrix with the rows representing
sources and columns representing
destinations.
IntroductionIntroduction
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Concept of TPConcept of TP
Transportation is a O.R technique intended to establish
the “least cost route” of transportation of goods from
the company’s factories to its warehouses at different
places.
It’s a special type of linear programming problem (LLP)
that involves transportation of goods from supply
points (factories) to the demand points (warehouses).
The problem involves determination of optimum routes
to minimize shipping route from supply to destinations.
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History of TPHistory of TP
“The Distribution of a Product from Several Sources of
Numerous Localities”
Study by: F.L. Hitchcock (1941)
“Optimum Utilization of the Transportation System”
Study by: T.C Koopmans (1947)
These two contribution are mainly responsible for the
development of Transportation Model.
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Application of TPApplication of TP
Minimize shipping costs
Determine low cost location
Find minimum cost production schedule
Military distribution system
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Process of TPProcess of TP
Standardization of problem
Check the nature of the problem
Check prohibited cell
Check balancing problem
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North West CornerNorth West Corner
“Most systematic and easiest method for
obtaining initial feasible basic solution”
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Types of TPTypes of TP
Balanced Transportation Problem (TP)
where the Total Supply = Total Demand
Unbalanced Transportation Problem (TP)
where the Total Supply ≠ Total Demand
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Steps to FollowSteps to Follow
Start with the NWC for the transportation tableau and
consider the cell in the first row and column.
Once in the next cell again compare the supply and
demand corresponding to the cell and assign lower of
two values.
Continue in zigzag manner until the last source and
destination is covered, so that south-east corner of the
tableau is reached.
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Problem StatementProblem Statement
A Medical Supply company produces catheters in packs
at three production facilities. The company ships the
packs from the production facilities to four warehouses.
The packs are distributed directly to hospitals from the
warehouses.
The table on the next slide shows the costs per pack to
ship to the four warehouses.
Medical SupplyMedical Supply
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Unbalanced ProblemUnbalanced Problem
If supply is less than demand then add dummy row
and if supply is greater than demand then add
dummy column and after adding dummy row or
column, same procedure will follow as it is followed
in Balanced problem.
Supply < Demand = Dummy Row Added
Supply > Demand = Dummy Column Added