Bipolar neutrosophic multi-item four-dimensional transportation problem with variable routes for breakable items

Sarbari Samanta (), Dipankar Chakraborty () and Dipak Kumar Jana ()
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Sarbari Samanta: Haldia Institute of Technology
Dipankar Chakraborty: Heritage Institute of Technology
Dipak Kumar Jana: Gangarampur College

Computational Management Science, 2025, vol. 22, issue 1, No 7, 38 pages

Abstract: Abstract Generally, in case of transportation problem, mathematical frameworks predominantly focus on positive beliefs to manage uncertain and vague information, often overlooking the negative perspectives in decision-making. To address this gap, we introduce a four-dimensional transportation problem (4D-TP) model within a bipolar neutrosophic environment, which incorporates both positive and negative aspects of human cognition. The proposed model is formulated as a multi-item 4D-TP with breakability, aimed at maximizing profit by considering key parameters such as costs, accessibility, demands, and transportation capacities, all represented using single-valued triangular bipolar neutrosophic numbers. Unlike traditional approaches that assume uniformity in the number of routes for each origin-destination pair, our model accommodates varying numbers of routes, reflecting more realistic transportation scenarios. Furthermore, this is the first attempt to solve the 4D-TP using possibility measure associated with single-valued triangular bipolar neutrosophic number, which includes truth, indeterminacy, and falsity membership functions to capture both positive and negative dimensions. To validate the model, we provide a numerical example and solve it using the Generalized Reduced Gradient method, implemented in the LINGO-14.0 solver. Some managerial implications are also included at the end.

Keywords: 4D-transportation problem; Breakability; Bipolar single-valued neutrosophic numbers; Possibility measure (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10287-025-00531-8

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