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<p>Reducing unrestricted carbon emissions presents a significant challenge for the pharmaceutical industry, crucial for avoiding governmental penalties and meeting social responsibility standards. Again, risk factors within pharmaceutical supply chains (PSC) not only lead to economic losses but also disrupt product flows. In response to these challenges about different conflicting objectives, this research provides an innovative approach to tackle a multi-objective multi-route fixed-charge solid transportation problem within PSC by incorporating carbon emissions and risk mitigation. The trapezoidal Pythagorean fuzzy numbers are chosen to tackle the impreciseness of the proposed PSC model. This study specifically focuses on minimizing carbon emissions throughout PSC while concurrently addressing the risk factors contributing to breakdowns in the supply chain. The inclusion of various risk mitigation policies within the PSC framework underscores the comprehensive nature of the proposed solution. To solve the proposed model, we employ intuitionistic fuzzy programming and hybrid programming (HP) techniques, aiming to extract Pareto-optimal solutions. HP addresses weighting features for decision maker to specify objective functions based on priorities, and uses the criteria of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10886_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon\)</EquationSource> </InlineEquation>-constraint method to generate Pareto optimal solutions. The effectiveness and potential of the proposed model are demonstrated through a real case study within an industrial context. Finally, we compare the efficiency of the proposed approach not only by comparative analysis but also statistical hypothesis testing and sensitivity analysis.</p>

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Pythagorean fuzzy multi-objective optimization with risk mitigation: A case study on pharmaceutical green supply chain

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Sudipta Midya,
  • Sankar Kumar Roy,
  • Binoy Krishna Giri

摘要

Reducing unrestricted carbon emissions presents a significant challenge for the pharmaceutical industry, crucial for avoiding governmental penalties and meeting social responsibility standards. Again, risk factors within pharmaceutical supply chains (PSC) not only lead to economic losses but also disrupt product flows. In response to these challenges about different conflicting objectives, this research provides an innovative approach to tackle a multi-objective multi-route fixed-charge solid transportation problem within PSC by incorporating carbon emissions and risk mitigation. The trapezoidal Pythagorean fuzzy numbers are chosen to tackle the impreciseness of the proposed PSC model. This study specifically focuses on minimizing carbon emissions throughout PSC while concurrently addressing the risk factors contributing to breakdowns in the supply chain. The inclusion of various risk mitigation policies within the PSC framework underscores the comprehensive nature of the proposed solution. To solve the proposed model, we employ intuitionistic fuzzy programming and hybrid programming (HP) techniques, aiming to extract Pareto-optimal solutions. HP addresses weighting features for decision maker to specify objective functions based on priorities, and uses the criteria of \(\epsilon\) -constraint method to generate Pareto optimal solutions. The effectiveness and potential of the proposed model are demonstrated through a real case study within an industrial context. Finally, we compare the efficiency of the proposed approach not only by comparative analysis but also statistical hypothesis testing and sensitivity analysis.