A solid transportation model with product blending and parameters as rough variables

A Multiobjective Multi-Product Solid Transportation Model with Rough Fuzzy Coefficients

Transportation management is one of the key success factors to keep an organization competitive, sustain its growth pace, and raise profits not only at a local but also a global scale. Therefore, planning and designing a transport system are prerequisite and vital topics for achieving these goals. In this paper, a multiobjective multi-product solid transportation problem (MOMPSTP) under uncertainty is formulated and solved by two different methods of multiobjective optimization problems (MOPs). The system parameters namely unit transportation cost, availability of products at source points, demands of products at destinations and the capacity of transportation mode all are taken as rough fuzzy variables (RFVs). A chance constraint programming model for MOP with RFVs is developed in order to obtain satisfactory solutions when decision makers (DMs) aim to optimize multiple objectives (cost, time, profit, etc.) simultaneously. For given credibility (Cr) and trust (Tr) levels of RFVs, Cr-Tr constraint programming technique is used to reduce the uncertain transportation problem into equivalent deterministic form. Two classical solution techniques-weighted sum method (WSM) and ideal point method (IPM) are utilized to solve the problem. Finally, a numerical example is provided to illustrate the usefulness of our proposed model and then a sensitivity analysis is performed to verify different solutions due to different level of satisfaction.