Multi-Objective Green 4-Dimensional Transportation Problem for Incompatible Damageable Items with Optimum Use of Transport Vehicles’ Space

Md Samim Aktar, Chaitali Kar (), Manoranjan De (), Sanat Kumar Mazumder (), Manoranjan Maiti () and Laxmi Rathour ()
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Md Samim Aktar: Department of Mathematics, Indian Institute of Engineering, Science and Technology, Howrah, West Bengal, India
Chaitali Kar: Department of Mathematics, Indian Institute of Engineering, Science and Technology, Howrah, West Bengal, India
Manoranjan De: Department of Mathematics, Mugberia Gangadhar, Mahavidyalaya, West Bengal, India
Sanat Kumar Mazumder: Department of Mathematics, Indian Institute of Engineering, Science and Technology, Howrah, West Bengal, India
Manoranjan Maiti: Department of Mathematics, Vidyasagar University, Midnapore, West Bengal, India
Laxmi Rathour: Department of Mathematics, National Institute of Technology, Aizawl, Mizoram, India

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 01, 245-279

Abstract: In the transportation system, an item is transported from sources to destinations. In this process, as well as the weight of the items volume of the items also plays a crucial role in obtaining minimum objectives. In general, one of these constraints becomes binding. Few transportation problems (TPs) have been formulated with the restriction on vehicle volume capacity. Surface transport is one of the most powerful carbon emitters, which leads to global climate change. Thus, in addition to the usual travel cost and time minimization, carbon emission (CE) minimization and maximum vehicle space utilization should also be considered. A TP for damageable and incompatible items in a multi-objective green 4-dimensional environment is presented in this paper. The model is developed with four objectives: minimizing transportation cost, transportation time, vehicles’ vacant space, and carbon emission amount. The model is solved by six multi-objective optimization methods, and their results are compared. A multi-criteria decision-making method, “MetaRanking,†is used to compare the results of the different multi-objective methods. The model is illustrated with some numerical data using the Generalized Reduced Gradient method through Lingo 11.0. A real-life example is also presented. Several particular models are deduced. The numerical results demonstrate the importance of each objective. Pareto fronts represent that each objective is conflicting with the other.

Keywords: Multi-objective; 4D transportation problem; vacant space; carbon emission; multi-objective methods; MetaRanking (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500140

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