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A fuzzy approach to multicriteria assignment problem using exponential membership functions

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Abstract

In this paper, we extend the classical assignment problem to the multicriteria assignment problem by considering three criteria: cost, time and quality subject to many realistic constraints including multi-job assignment and a knapsack-type resource constraint. The paper addresses the uncertainty of the real-life assignment problem by formulating a fuzzy cost–time–quality assignment problem using exponential membership functions. We define fuzzy goal for each criterion as per the preferences of the decision-maker and aggregate the fuzzy goals using product operator. In order to obtain optimal assignment plans, the resultant nonlinear 0-1 optimization problem is solved using genetic algorithm for different choices of the shape parameters in the exponential membership functions. As an illustrative example, we consider a fuzzy manpower planning problem.

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Acknowledgments

We are thankful to the Editor-in-Chief Professor Xi-Zhao Wang and the anonymous referees for their valuable comments and suggestions to improve presentation of the paper.

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Authors and Affiliations

  1. Department of Operational Research, University of Delhi, Delhi, India

    Pankaj Gupta & Garima Mittal

  2. Flat No.-01, Kamayani Kunj, Plot No. 69, Indraprastha Extension, Delhi, 110092, India

    Pankaj Gupta

  3. Department of Decision Sciences, Apeejay School of Management, Dwarka, New Delhi, India

    Mukesh K. Mehlawat

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  1. Pankaj Gupta
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  2. Mukesh K. Mehlawat
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  3. Garima Mittal
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Correspondence to Pankaj Gupta.

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Gupta, P., Mehlawat, M.K. & Mittal, G. A fuzzy approach to multicriteria assignment problem using exponential membership functions. Int. J. Mach. Learn. & Cyber. 4, 647–657 (2013). https://doi.org/10.1007/s13042-012-0122-8

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  • DOI: https://doi.org/10.1007/s13042-012-0122-8

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