transport model

The transportation model is a special class of linear programs that deals with shipping a commodity from sources to destinations . The objective is to determine the shipping schedule that minimizes the total shipping cost while satisfying supply and demand limits. The application of the transportation model can be extended to other areas of operation, including inventory control, employment scheduling, and personnel assignment.transportation problem is represented by the network, there are m sources and n destinations, each represented by a node. the arcs represent the routes linking the sources and the destinations. arc (i, j) joining source i to destination j carries two pieces of information: the transportation cost per unit, cij and the amount shipped, xij the amount of supply at source i is ai and the amount of demand at destination j is bj . the objective of the model is to determine the unknowns xij that will minimize the total transportation cost while satisfying all the supply and demand restrictions.