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# Transportation Problem

Posted On :  23.06.2018 12:20 am

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.

Transportation Problem

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 Models.

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. Dantzig (1951).
Tags : Operations Management - Transportation / Assignment & Inventory Management
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