A study of uncertain 4D transportation problems with rough interval parameters and additional real-life factors

Abstract

In developing countries like India and Nepal, a vehicle document verification system is implicated at the checkpoints and border crossings that allows users to authenticate and verify the validity of vehicle related documents such as registration certificates, driving licenses, pollution under control certificates, and insurance policies. This results in the formation of long queues of the vehicles and hence a significant time wastage. These vehicles waiting in the long queues, continue to emit carbon dioxide and other greenhouse gases into the atmosphere. To address these issues, the government has introduced the Automated Number Plate Recognition (ANPR) technology which plays a significant role in the efficient and accurate document verification by identifying and validating vehicle registration details. It also automates toll collection by capturing the vehicle’s number plate, reducing waiting times and congestion at toll barriers. To analyze all these benefits, in this study, for the first time, ANPR technology has been introduced in the multi-objective model of transportation problem and its impact on various objectives has been observed. Also, real-life factors: fixed-charge cost, carbon emission, multiple routes have been considered in the proposed model and the problem is named as multi-objective fixed-charge four dimensional green transportation problem. Rough set theory has been employed as a tool for effectively addressing the indeterminacy and facilitating the modeling of real-life transportation problems. Two methods: the expected value method and the rough chance constrained programming method, are proposed to transform the suggested model of multi-objective transportation problem into a deterministic form. To solve these transformed models, a new multi-objective optimization approach based on the neutrosophic theory, named as neutrosophic goal programming has been introduced. To further demonstrate the practicality of the proposed study, an application for the apple fruit transportation has been solved. Detailed comparisons between obtained results are done on the basis of different modeling perspectives, different solution techniques and also with/and without ANPR technology. Based on the outcomes, the suggested neutrosophic goal programming technique proved to be superior to the existing techniques in the literature.