North West Corner Method

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TransporTaTion problem

“North West Corner Method”

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Group Members:Muhammad Daniyal Ashfaq (051)Muhammad Waleed Aslam (014)Javeria Khalid Hassan (047)Shahrukh Hussain (032)

Course Instructor:Ms. Faiza Shahid

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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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Methods/TechniquesMethods/Techniques

North West Corner Method (NWCM)

Least Cost Method (LCM)

Vogel’s Approximation Method (VAM)

Methods AvailableMethods Available

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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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Problem StatementProblem Statement

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Balanced ProblemBalanced Problem

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Balanced ProblemBalanced Problem

= 19 (100) + 15 (50) + 21(100) + 18 (150) + 15(50) + 22(150)

= 1900 + 750 + 2100 + 750 + 3300

= 11,500

Cost/Feasible Solution:Cost/Feasible Solution:

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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

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ProgramProgram

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ReferencesReferences

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