Solving the multi-modal transportation problem via the rough interval approach

This research studies a transportation problem to minimize total transportation cost under the rough interval approximation by considering the multi-modal transport framework, referred to here as the rough Multi-Modal Transportation Problem (MMTP). The parameters of MMTP are rough intervals, because the problem is chosen from a real-life scenario. To solve MMTP under a rough environment, we employ rough chance-constrained programming and the expected value operator for the rough interval and then outline the main advantages of our suggested method over those existing methods. Next, we propose an algorithm to optimally solve the problem and present a numerical example to examine the proposed technique. Finally, the solution is analyzed by the proposed method with rough-chance constrained programming and expected value operator.