Uncertain 4D-transportation problem with maximum profit and minimum carbon emission

Abstract

The impact of transportation on greenhouse gas emissions is significant. Effective transportation planning can help in achieving maximum profit and minimum carbon emission by considering the appropriate route and conveyance. The formulation and resolution of an uncertain multi-objective multi-item 4D-transportation problem with the objectives of maximum profit and minimum carbon emissions is the main focus of this study. Two different models are considered under different conditions, one assuming breakable or damageable items and other assuming non-breakable or non-damageable items. The uniqueness comes in modeling the green 4D-transportation problem with different purchasing price discounts under uncertain environment. Due to insufficient data or due to the complex situation at the time of the transportation activities, several parameters are considered as uncertain variables to attain real-life situations. Here, multi-objective problems are reduced to single-objective problems using uncertain goal programming and uncertain convex combination method. The models are converted into respective crisp equivalents with the help of certain features of uncertainty theory. Some real-life examples are used to demonstrate the models and subsequently to tackle these issues, the Generalized Reduced Gradient method is utilised (using LINGO 14.0 solver). By adjusting various confidence levels in the context of chance constraints, different optimal values are achieved. Additionally, compromise solutions for various weights of the two objectives are found using the convex combination approach. A few sensitivity analyses are also offered. The use of this study will assist managers in determining the necessary transported amount, the appropriate supplier with discount offers, the vehicles and routes to be employed in the transportation activity by balancing the economic and environmental hazards.