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Multi-objective mixed integer programming and an application in a pharmaceutical supply chain

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  • Sujeet Kumar Singh
  • Mark Goh

Abstract

Multi-objective integer linear and/or mixed integer linear programming (MOILP/MOMILP) are very useful for many areas of application as any model that incorporates discrete phenomena requires the consideration of integer variables. However, the research on the methods for the general multi-objective integer/mixed integer model has been scant when compared to multi-objective linear programming with continuous variables. In this paper, an MOMILP is proposed, which integrates various conflicting objectives. We give importance to the imprecise nature of some of the critical factors used in the modelling that can influence the effectiveness of the model. The uncertainty and the hesitation arising from estimating such imprecise parameters are represented by intuitionistic fuzzy numbers. The MOMILP model with intuitionistic fuzzy parameters is first converted into a crisp MOMILP model, using appropriate defuzzification strategies. Thereafter, the MOMILP is transformed into a single objective problem to yield a compromise solution with an acceptable degree of satisfaction, using suitable scalarisation techniques such as the gamma-connective technique and the minimum bounded sum operator technique. The proposed solution method is applied to several test problems and a multi-objective pharmaceutical supply chain management model with self generated random data.

Suggested Citation

  • Sujeet Kumar Singh & Mark Goh, 2019. "Multi-objective mixed integer programming and an application in a pharmaceutical supply chain," International Journal of Production Research, Taylor & Francis Journals, vol. 57(4), pages 1214-1237, February.
    • Handle: RePEc:taf:tprsxx:v:57:y:2019:i:4:p:1214-1237
    DOI: 10.1080/00207543.2018.1504172
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    Cited by:

    1. Ronaldo Brito da Silva & Claudia Aparecida de Mattos, 2019. "Critical Success Factors of a Drug Traceability System for Creating Value in a Pharmaceutical Supply Chain (PSC)," IJERPH, MDPI, vol. 16(11), pages 1-18, June.
    2. Firoz Ahmad, 2022. "Interactive neutrosophic optimization technique for multiobjective programming problems: an application to pharmaceutical supply chain management," Annals of Operations Research, Springer, vol. 311(2), pages 551-585, April.
    3. Georgiou, Giorgos S. & Rouvas, Constantinos & Nathanael, Demetris, 2022. "Enhancing expansion of rooftop PV systems through Mixed Integer Linear Programming and Public Tender Procedures," Renewable Energy, Elsevier, vol. 187(C), pages 347-361.
    4. Ieva Meidute-Kavaliauskiene & Figen Yıldırım & Shahryar Ghorbani & Renata Činčikaitė, 2022. "The Design of a Multi-Period and Multi-Echelon Perishable Goods Supply Network under Uncertainty," Sustainability, MDPI, vol. 14(4), pages 1-18, February.
    5. Ahmad, Firoz & Alnowibet, Khalid A. & Alrasheedi, Adel F. & Adhami, Ahmad Yusuf, 2022. "A multi-objective model for optimizing the socio-economic performance of a pharmaceutical supply chain," Socio-Economic Planning Sciences, Elsevier, vol. 79(C).
    6. Ieva Meidute-Kavaliauskiene & Halil Ibrahim Cebeci & Shahryar Ghorbani & Renata Činčikaitė, 2021. "An Integrated Approach for Evaluating Lean Innovation Practices in the Pharmaceutical Supply Chain," Logistics, MDPI, vol. 5(4), pages 1-17, October.

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