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Analyzing a Transportation Problem with Reliability Under the Shadowed Environment

Author

Listed:
  • Raj Kumar Bera

    (Vidyasagar University)

  • Shyamal Kumar Mondal

    (Vidyasagar University)

Abstract

The concept of reliability is crucial in assessing the ability of a transportation network to provide the continuity in operation. Because of this, in the recent transportation business, sources are being pressurized to deliver items reliably and cost-effectively. In such a direction, a classical transportation problem has been modified to a reliable transportation problem by incorporating the transportation reliability along with cost. Also, the main objective of this study is to minimize the cost and maximize the reliability of the proposed problem simultaneously. Here, the transportation reliability has been considered based on the deterioration of items and failure of the transportation mode. It is noted that both the cost and reliability of each path are assigned through negotiation at the beginning of the business; therefore, both data are uncertain. Also, to properly cover the uncertainty, the model has been formulated under the shadowed environment. To solve the proposed model, various methodologies are developed such as a weighted-based de-shadowed procedure to convert the uncertain model into an equivalent deterministic model, a weighted sum method to convert the multi-objective model into a single objective model, the lingo solver to find the optimal result, and a method to find the most efficient pareto optimal result. To justify the impact and significance of the proposed model in the real world, some numerical studies have been done. The variation of results due to uncertainty has been presented. In addition, the effect of negotiation on the uncertainty has been discussed.

Suggested Citation

  • Raj Kumar Bera & Shyamal Kumar Mondal, 2025. "Analyzing a Transportation Problem with Reliability Under the Shadowed Environment," SN Operations Research Forum, Springer, vol. 6(2), pages 1-38, June.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:2:d:10.1007_s43069-025-00469-2
    DOI: 10.1007/s43069-025-00469-2
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    References listed on IDEAS

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    1. Bertazzi, Luca & Maggioni, Francesca, 2018. "A stochastic multi-stage fixed charge transportation problem: Worst-case analysis of the rolling horizon approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 555-569.
    2. S. Samanta & A. Ojha & B. Das & S. K. Mondal, 2021. "A Profit Maximisation Solid Transportation Problem Using Genetic Algorithm in Fuzzy Environment," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 13(1), pages 40-57, January.
    3. Raj Kumar Bera & Shyamal Kumar Mondal, 2023. "Analyzing the nature of a transportation problem before and during COVID-19 pandemic in multi-fuzzy environment," OPSEARCH, Springer;Operational Research Society of India, vol. 60(4), pages 1659-1702, December.
    4. Cavagnini, Rossana & Bertazzi, Luca & Maggioni, Francesca, 2022. "A rolling horizon approach for a multi-stage stochastic fixed-charge transportation problem with transshipment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 912-922.
    5. Zhu, Kai & Ji, Kaiyuan & Shen, Jiayu, 2021. "A fixed charge transportation problem with damageable items under uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    6. Anushri Maji & Asoke Kumar Bhunia & Shyamal Kumar Mondal, 2022. "A production-reliability-inventory model for a series-parallel system with mixed strategy considering shortage, warranty period, credit period in crisp and stochastic sense," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 862-907, September.
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