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Transportation problem decides the transportation routes for allocating production of various plants to several warehouses with an objective to satisfy the demands of the warehouses, taking into consideration the supply constraints of the plants at minimum possible transportation cost. In case of a transportation model, the parameters of the system are assumed to be deterministic in nature. But in real life situation, parameters are random in nature. In this study, a case of distribution of coal from collieries to washeries of a coal producing company has been undertaken. The outputs of collieries as well as the demand of washeries were random in nature. Chance constrained programming technique, a technique of stochastic programming approach, has been used to solve this transportation problem and to obtain the optimum transportation routes for supplying coal from collieries to washeries. The results obtained from this study will help the organization to decide the optimum routes for transporting its coal from collieries to washeries.
Transportation problem is associated with solving problems of distribution of resources from one place to another. The goods are transported from a set of sources (e.g., plants) to a set of destinations (e.g., warehouses) to meet the specific requirements. The objective of the transportation problem is to satisfy the demand at destinations subject to supply constraints of the sources at minimum possible transportation cost (Mitra, 2006). Transportation problem is one of the subclasses of linear programming problem and it deals with the transportation of various quantities of a single homogenous commodity from various origins to different destinations so that the total transportation cost is minimum (Kalavathy, 2005). The transportation problem is useful for making strategic decisions involved in selecting optimum transportation routes for allocating production of various plants to several warehouses (Jaishankar, 2005).
In case of a transportation problem, the parameters of the system are assumed to be deterministic. But in real life problems, it is very difficult to determine the exact values of the parameters. Stochastic programming is used to solve the problem, where some or all of the parameters are described by random variables. Stochastic programming converts the probabilistic nature of the problem into an equivalent deterministic model and appropriate solution technique is used to solve the problem (Taha, 2001). |
