Operations Research

2. • The Transportation models were originated in
1941, when F.L. Hitchcock presented a study
entitled “The Distribution of product from
several sources to Numerous Localities.”
• This presentation is thought to be the first
important contribution to the solution of
Transportation problems

3. • Transportation problem is a particular class of
LPP.
• It deals with the situation in which a product
is shipped from sources to destinations.
• This model deals with the determination of a
minimum cost plan for transporting a single
commodity from a number of sources to a
number of destinations.

4. • The transportation problems can be extended
in a direct manner to cover practical situations
in the areas of :
1. inventory control,
2. employment scheduling,
3. personnel assignment,
4. scheduling dam reservoir levels,
5. and many others.

6. Objective
• The Transportation Problem is one of the sub-
classes of L.P.Ps. in which the objective is to
transport various quantities of a single
homogeneous commodity, that are initially
stored at various origins, to different
destinations in such a way that the total
transportation cost is minimum.

7. • To achieve this objective we must know the
amount and location of available supplies and
the quantities demanded.
• In addition, we must know the costs that
result from transporting one unit of
commodity from various origins to various
destinations.

8. MATHEMATICAL FORMULATION OF THE PROBLEM:
Transportation Tableau :

9. STEPS TO SOLVE TRANSPORTATION
PROBLEM
• Step 1: FORMULATE THE PROBLEM IN
STANDARD FORMAT
• Step 2: GET THE INITIAL FEASABLE SOLUTION
1. North West Corner Method
2. Least Cost Entry Method
3. Vogel’s Approximation Method

10. • Step 3: Test the Optimality of the Initial Feasible
Solution using :
1. Stepping Stone Method
2. Modified Distribution Method (MODI)
3. If the solution is optimal stop
• Step 4 Revise the solution if not optimal
• Test again its optimality till we get the optimal
solution

11. Model 1. (Cost Matrix or
Minimisation Problem]