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A novel approach for solving rough multi-objective transportation problem: development and prospects

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Abstract

Transportation problem is the prominent class of mathematical programming problems that has a significant role in many practical transportation fields. Naturally, the transportation parameters inherently involve uncertainty in real life caused by lacking of information, imprecision in judgment, environmental factors, and etc. Therefore, it is very valuable to handle transportation problem under uncertainty aspect. The aim of this paper is to study the solution of the rough multi-objective transportation problem by supposing that the decision makers realize the transportation cost, availability and demand of the product as rough interval coefficients. The proposed approach exploits the merits of the weighted sum method to find the non-inferior solutions and it has two distinguishing features. Firstly, the proposed approach characterizes the surely Pareto optimal solution through converting the lower interval into two crisp transportation problems. Secondly, the proposed approach characterizes the possibly Pareto optimal solution through decomposing the upper interval into two crisp transportation problems. Furthermore, the expected nondominated value is applied to obtain the optimal compromise solutions of multi-objective transportation problem in rough environment. The presented approach is showed with rough multi-objective optimization problem as numerical illustration, where a wide set of the expected compromise solution ranged from 15.75 to 25.8 can be obtained. Furthermore, the investigation on the rough multi-objective transportation problem is conducted a real thought-provoking case study, where the optimal rough interval of transportation cost ranged from 97 to 314 can be achieved. With the adoption of rough environment modeling, a wide variate of optimal solutions can be achieved that can help the decision maker to extract the best compromise alternative according to practical situations. This represents a novel contribution to the decision making field and profit satisfaction models.

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Authors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala, 147004, Punjab, India

    Harish Garg

  2. Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom, Egypt

    Rizk M. Rizk-Allah

Authors
  1. Harish Garg
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  2. Rizk M. Rizk-Allah
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Correspondence to Harish Garg.

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Communicated by Marcos Eduardo Valle.

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Garg, H., Rizk-Allah, R.M. A novel approach for solving rough multi-objective transportation problem: development and prospects. Comp. Appl. Math. 40, 149 (2021). https://doi.org/10.1007/s40314-021-01507-5

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