Uncertain transportation model with rough unit cost, demand and supply

Abstract

In a transportation problem, the parameters like unit cost of transportation of goods or services from source to destination, supplies from the sources and demands at destinations depend on many factors which may not be deterministic in nature. To deal with the uncertainty of the parameters, random variables and fuzzy variables were used previously. Sometimes, in absence of sufficient sample observations, the uncertain parameters are estimated by the belief degree of the experts. In this paper, the aim is to investigate the transportation problem where the unit cost of transportation, supplies, demands are initially taken as rough variables based on subjective estimation of experts. Further, these rough estimates are suitably approximated as uncertain normal variables and the conceptual uncertain programming model has been developed. The model is then transformed to a deterministic linear programming model by minimizing the expected value of the uncertain objective function under the constraints at certain confidence level.