This document provides an overview of transportation models in linear programming. It discusses key concepts such as origins and destinations, unused and used squares, and opportunity costs. Transportation models aim to transport a homogeneous commodity from various origins to different destinations at minimum total cost. The document outlines the characteristics of transportation models and the two phases to solve them - obtaining an initial basic feasible solution using methods like the North-West Corner Rule or Least Cost Method, and then determining the optimal basic solution using techniques like the Stepping Stone Method or Modified Distribution Method.

1. Welcome everyone!

2. Linear programming:
Transportation model

3. 1.the Definition

4. What is Transportation model?
deals with a special class of linear programming
problem in which the objective is to transport a
homogenous commodity from various origins or
factories to different destinations or markets at a
total minimum cost.
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5. 2. concept

6. - addresses the concept of moving a thing
from one place to another, without change
- used to analyze transportation systems and
find the most efficient route
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7. 3. terminologies

8. ✘ Destination – a point of demand in
transportation problem
Terminologies used in transportation problem:
✘ Origin – the source or supply location
in transportation.
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9. Terminologies used in transportation problem:
✘ Unused Squares –
squares which
represents routes
where no quantity is
shipped between a
source and destination
✘ Stone Squares –
used squares in
transportation
problem.
✘ Opportunity Cost
– cost of the
opportunities that
are sacrificed in
order to take a
certain action.
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10. 4. characteristics

11. ✘ It has a minimum possible cost,
✘ Each source has a fixed number of units of the
product, and fixed demand for the product.
✘ The linear programming model has constraints
✘ All constraints are equalities in a balanced
transportation model where supply equals
demand.
✘ Constraints contain inequalities in unbalanced
models where supply is not equal to demand.
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Characteristics of transportation model:

12. 5. Two (2) phases of
solution using
transportation model

13. 1.1 North-West Corner Rule (NWCR)
The North-West Corner Rule is a method adopted to
compute the initial feasible solution of the transportation
problem. The name North-west corner is given to this method
because the basic variables are selected from the extreme
left corner.
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PHASE I: Initial Basic Feasible Solution

14. PHASE I: Initial Basic Feasible Solution
1.2 Least Cost Method (AKA Minimum Cost Method or Greedy
Method)
The Least Cost Method is another method used to obtain the initial
feasible solution for the transportation problem. Here, the allocation
begins with the cell which has the minimum cost. The lower cost cells
are chosen over the higher-cost cell with the objective to have the
least cost of transportation.
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15. PHASE I: Initial Basic Feasible Solution
1.3 Vogel’s Approximation Method (VAM)
The Vogel’s Approximation Method or VAM is an
iterative procedure calculated to find out the initial
feasible solution of the transportation problem. Like
Least cost Method, here also the shipping cost is taken
into consideration, but in a relative sense.
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16. PHASE II: Optimal Basic Solution
2.1 Stepping Stone Method
The Stepping Stone Method is used to check the optimality of the initial
feasible solution determined by using any of the method Viz. North-
West Corner, Least Cost Method or Vogel’s Approximation Method.
Thus, the stepping stone method is a procedure for finding the potential
of any non-basic variables (empty cells) in terms of the objective
function.
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17. PHASE II: Optimal Basic Solution
2.2 Modified Distribution Method (MODI)
The modified distribution method, is also known as
MODI method or (u - v) method provides a minimum cost
solution to the transportation problems. ... The objectives
are to develop and review an integral transportation
schedule that meets all demands from the inventory at a
minimum total transportation cost.
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19. Thank you so much for
listening! 
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