Analyzing a Transportation Problem with Reliability Under the Shadowed Environment

The concept of reliability is crucial in assessing the ability of a transportation network to provide the continuity in operation. Because of this, in the recent transportation business, sources are being pressurized to deliver items reliably and cost-effectively. In such a direction, a classical transportation problem has been modified to a reliable transportation problem by incorporating the transportation reliability along with cost. Also, the main objective of this study is to minimize the cost and maximize the reliability of the proposed problem simultaneously. Here, the transportation reliability has been considered based on the deterioration of items and failure of the transportation mode. It is noted that both the cost and reliability of each path are assigned through negotiation at the beginning of the business; therefore, both data are uncertain. Also, to properly cover the uncertainty, the model has been formulated under the shadowed environment. To solve the proposed model, various methodologies are developed such as a weighted-based de-shadowed procedure to convert the uncertain model into an equivalent deterministic model, a weighted sum method to convert the multi-objective model into a single objective model, the lingo solver to find the optimal result, and a method to find the most efficient pareto optimal result. To justify the impact and significance of the proposed model in the real world, some numerical studies have been done. The variation of results due to uncertainty has been presented. In addition, the effect of negotiation on the uncertainty has been discussed.