SYBSc B Session 2.pdf - Operations Research | Richa Saxena...

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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.