Transportation Problem with Uncertain Cost, Rough Demand and Supply

Abstract

In a transportation problem, the cost of transportation from source to destination depends on many factors which may not be deterministic in nature. In this work, the unit cost of transportation is considered to be imprecise and the trapezoidal fuzzy cost is assigned to the model. Further the demand and supply are considered as uncertain due to lack of proper information. So the demand and supply are considered as rough variable in this proposed model. In the solution process of such a model, two solutions as pessimistic and optimistic solutions are obtained at certain trust level which suggests a range for the actual solution. Further, suitably converting the fuzzy cost as rough, the solution is obtained and comparison of results in both cases is made by taking one numerical example.

Keywords

• Generalized trapezoidal fuzzy number
• Rough variable
• Pessimistic value
• Optimistic value
• Transportation problem
• Optimistic value