Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint

Modeling of real-world problems requires data as input parameter which include information represented in the state of indeterminacy. To deal with such indeterminacy, use of uncertainty theory (Liu in Uncertainty theory, Springer, Berlin, 2007) has become an important tool for modeling real-life decision-making problems. This study presents a profit maximization and time minimization scheme which considers the existence of possible indeterminacy by designing an uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint (UMMFSTPwB) at each destination. Here, items are purchased at different source points with different prices and are accordingly transported to different destinations using different types of vehicles. The items are sold to the customers at different selling prices. In the proposed model, unit transportation costs, fixed charges, transportation times, supplies at origins, demands at destinations, conveyance capacities and budget at destinations are assumed to be uncertain variables. To model the proposed UMMFSTPwB, we have developed three different models: (1) expected value model, (2) chance-constrained model and (3) dependent chance-constrained model using uncertain programming techniques. These models are formulated under the framework of uncertainty theory. Subsequently, the equivalent deterministic transformations of these models are formulated and are solved using three different methods: (1) linear weighted method, (2) global criterion method and (3) fuzzy programming method. Finally, numerical examples are presented to illustrate the models.