Chance constrained programming for sustainable four dimensional fuzzy-rough transportation problem with rest period of drivers and time window constraints

The rest period of driver plays a critical role in ensuring both safety and efficiency, and hence the success rate of a transportation system. Fatigued drivers are more prone to accidents and errors, making it essential to incorporate their rest time into the transportation planning. Additionally, time window constraints, which define specific time frames for deliveries, play a significant role in the efficiency of transportation systems. Despite their importance, existing research has yet to integrate both driver’s rest period and time window constraints into transportation models. To address these gaps and improve operational performance, this study introduces a novel multi-objective, multi-item four-dimensional green transportation model that incorporates both driver’s rest period and time window constraints. Given the complexities of predicting market demand and other transportation-related parameters within specific time frames, the model’s parameters are represented as trapezoidal fuzzy-rough numbers. A new methodology, “Neutrosophic Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)”, based on neutrosophic programming, is proposed to find an optimal compromise solution. The practicality of this approach is demonstrated by solving a real-world industrial problem. A comparative analysis shows that the Neutrosophic TOPSIS method yields the most effective Pareto-optimal solution. The results reveal a reduction of 10.85 h in transportation time and 21.36 kg in carbon emissions compared to existing methods. Additionally, the findings reveal that excluding the driver’s rest period reduces transportation time by 15.9 h but increases carbon emissions by 591 kg. Lastly, the possible avenues for future research are outlined.