Analyzing a transportation problem with reliability under the shadowed environment

Abstract

In today's market, sources are being pressurized to deliver the product in a reliable and cost effective manner. From this perspective, the aim of the present work is to model a transportation problem to transport items from some sources to various destinations by minimizing the cost with maximum reliability. Here, the considered reliability is called 'transportation reliability' and it refers to the probability of successfully transporting items over different routes. Also, system reliability has been for different type transportation problems. Due to the imprecise nature of unit transportation cost and transportation reliability, the model has been formulated in shadowed environment. To convert the uncertain model into a deterministic form, a weighted-based de-shadowed procedure has been established. Further, to find the most efficient pareto optimal solution, an algorithm has been developed. Finally, Some numerical examples are considered to illustrate the models in both crisp and shadowed environments numerically.