The transportation problems are special cases of the linear programming models. It deals with the situation in which a commodity / good is transported from Sources to Destinations.
The transportation problems are special cases of
the linear programming models. It deals with the situation in which a commodity
/ good is transported from Sources to Destinations.
Thus, obviously, the objective is to determine the amount of commodity to be
transported from each source to each destination in such a way that the total
transportation cost is lowest.
Transportation model problems play very significant
role in any country’s economy, particularly, in the business contexts. Since,
these kinds of problems are modelled with 1000s of constraints and assumptions,
we consider the problem usually involves the physical movement of goods and
services from various supply origins / sources /factories
to multiple demand destinations / markets / distribution centres within the
given constraints of supply and demand in such a way that the total
transportation cost is minimized.
Since, the transportation models are special types
of linear programming (LP) problems; they can also be solved by the Simplex
Algorithm. However, as a model developer, one will face severe issues of
handling huge number of variables and constraints. Even small transportation
problems such as 3X4 [3 origins & 4 destinations] requires 12 variables and
7 constraints. Thus, a direct application of the Simplex method may be a
cumbersome process and involve huge amount of calculations, solving them by
hands will be almost impossible and at times, even computers may not be useful.
However a transportation problem has a special mathematical structure which
permits it to be solved by a fairly efficient method known as Transportation
The basic transportation problem was originally
developed by F.L. Hitchcock (1941) in his study entitled “the distribution of a
product from several sources to numerous locations.” In the year, 1947, a
mathematician by name, T.C. Koopmans published a study on “optimum utilization
of the transportation system”. Later, Linear Programming formulation and the
associated systematic procedure for solution were developed by George B.
Tags : Operations Management - Transportation / Assignment & Inventory Management
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