Operations Research
| Richa Saxena
Transportation Problems
1
SYBSc Finance B Session 2
TRANSPORTATION
PROBLEM - 1
Some of the early work in the development of the theory of transportation has come from Charles
Babbage. Popularly known as the father of computers, Charles Babbage did a research on
transportation costs and sorting of mails for the Uniform Penny Post in England in 1840
(“History
of Operations Research,” 2006). In 1930, A.N Tolstoi published a paper titled “Methods of finding
the minimal total kilometrage in cargo-
transportation planning in space”. This pap
er was published
in a book issed by National Commissariat of Soviet Union (Schrijver, 2002). The credit of formulated
transportation problem is attributed to F. L. Hitchcock. In 1941, Hitchcock also gave the
computational procedure for solving the problem. Independently, during the WWII, T. C. Koopmans,
during his tenure in Joint Shipping Board, invented a similar type of problem. The problem was
frequently referred to as Hitchcock-Koopmans problem (Fulkerson, 1966).
Nature of Transportation Problem
The distribution of goods produced by a factory from various warehouses (or sources) to different
markets (or destinations) where they are required, causes problems to almost every business. The
transportation method deals with the transportation of goods from different destinations. Relevant
data regarding available quantities at various sources, demand at each of the destinations, the cost
of shipping along each route, and non-availability of certain routes; if any.
A typical transportation problem is like this. A matrix is given where sources are given row-wise,
destinations are indicated column-wise, and unit cost of transportation from each source to each
destination is provided. Also mentioned is the supply at each source and demand at every market.
(Vohra, 2010)
Plant
Market
Supply
Demand
Balanced and Unbalanced Problems
If aggregate demand (AD) is equal to aggregate supply (AS), the problem is called a balanced
transportation problem, and if the two do not match, it is called unbalanced. An unbalanced problem

Operations Research
| Richa Saxena
Transportation Problems
2
is balanced first by introducing a dummy source (if AS<AD) or a dummy destination (if AD>AS).
The cost elements of the dummy row/column are taken to be zero. If, however, penalties for not
satisfying demand are given, they should be taken instead of zeros. In any case, the solution to a
problem begins when it is a balanced one.