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

Abstract

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 our proposed method with rough-chance constrained programming and expected value operator.

An approach for unbalanced fully rough interval transportation problem

“…Currently, a number of researchers [9,14,25,26,32,33] have given their consideration on various properties of rough interval to solve the transportation problem such as Bera et al [9] investigated the model of 4D transportation problem with rough intervals to maximize the profit. Garg and Allah [14] proposed a novel approach to solve the rough interval multi-objective transportation problems.…”

Profit maximization multi-item Just-in-Time solid transportation problem with budget constraints based on carbon emission

“…Jiménez and Verdegay [24] utilized an evolutionary algorithm-based parametric approach to effectively solve the fuzzy STP. More recently, Mardanya et al [36] successfully addressed the multi-objective multi-item just-in-time TP. Furthermore, Ghosh et al [16] introduced a carbon mechanism for managing waste in a sustainable multi-objective STP, considering the Pythagorean hesitant fuzzy environment.…”