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Approximation guarantees of algorithms for fractional optimization problems arising in dispatching rules for INDS problems

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Abstract

In this paper, we provide approximation guarantees of algorithms for the fractional optimization problems arising in the dispatching rules from recent literature for Integrated Network Design and Scheduling problems. These fractional optimization problem are proved to be NP-hard. The approximation guarantees are based both on the number of arcs in the network and on the number of machines in the scheduling environment. We further demonstrate, by example, the tightness of the factors for these approximation algorithms.

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References

  1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall Inc, New Jersey (1993)

    MATH  Google Scholar 

  2. Averbakh, I., Pereira, J.: The flowtime network construction problem. IIE Trans. 44, 681–694 (2012)

    Article  Google Scholar 

  3. Bajalinov, E.B.: Linear-Fractional Programming: Theory, Method, Applications and Software. Kluwer, Boston (2003)

    Book  MATH  Google Scholar 

  4. Baxter, M., Elgindy, T., Ernst, A.T., Kalinowski, T., Savelsbergh, M.W.P.: Incremental network design with shortest paths. Eur. J. Oper. Res. 238, 675–684 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Borrero, J.S., Gillen, C., Prokopyev, O.A.: Fractional 0–1 programing: applications and algorithms. J. Glob. Optim. (2016). doi:10.1007/s10898-016-0487-4

    Google Scholar 

  6. Borrero, J.S., Gillen, C., Prokopyev, O.A.: A simple technique to improve linearized reformulations of fractional (hyperbolic) 0–1 programming problems. Oper. Res. Lett. 44, 479–486 (2016)

    Article  MathSciNet  Google Scholar 

  7. DeBlasio, R., Tom, C.: standards for the smart grid. In: Proceedings of 2008 IEEE Energy 2030 Conference, pp. 1–7. Atlanta, GA (2008)

  8. Fang, S., Gao, D.Y., Sheu, R., Xing, W.: Global optimization for a class of fractional programming problems. J. Glob. Optim. 45, 337–353 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Farhangi, H.: The path of the smart grid. IEEE Power Energy Mag. 8, 18–28 (2010)

    Article  Google Scholar 

  10. Floudas, C.A., Gounaris, C.E.: A review of recent advances in global optimization. J. Glob. Optim. 45, 3–38 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kalinowski, T., Matsypura, D., Savelsbergh, M.W.P.: Incremental network design with maximum flows. Eur. J. Oper. Res. 242, 51–62 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lee, E.E., Mithchell, J.E., Wallace, W.A.: Restoration of services in interdependent infrastructure systems: a network flows approach. IEEE Trans. Syst. Man Cybern. C Appl. Rev. 37(6), 1303–1317 (2007)

    Article  Google Scholar 

  13. Mahmood, A., Aamir, M., Anis, M.I.: Design and implementation of AMR smart grid system. In: Proceedings of 2008 IEEE Electrical Power & Energy Conference, Vancouver, BC, pp. 1-6 (2008)

  14. Momoh, J.A.: Smart grid design for efficient and flexible power networks operation and control. In: Proceedings of 2009 IEEE/PES Power Syst Conference Exposition Seattle, WA, pp. 1–8 (2009)

  15. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, New York (1999)

    MATH  Google Scholar 

  16. Nurre, S.G., Cavdaroglu, B., Mitchell, J.E., Sharkey, T.C., Wallace, W.A.: Restoring infrastructure systems: an integrated network design and scheduling problem. Eur. J. Oper. Res. 223(3), 794–806 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Nurre, S.G., Sharkey, T.C.: Integrated network design and scheduling problems with parallel identical machines: complexity results and dispatching rules. Networks 63(4), 306–326 (2014)

    Article  MathSciNet  Google Scholar 

  18. Ouyang, M.: Review on modeling and simulation of interdependent critical infrastructure systems. Reliab. Eng. Syst. Saf. 121, 43–60 (2014)

    Article  Google Scholar 

  19. Pardalos, P.M., Phillips, A.T.: Global optimization of fractional programs. J. Glob. Optim. 1, 173–182 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pinedo, M.L.: Scheduling: Theory, Algorithms, and Systems, 4th edn. Springer, New York (2012)

    Book  MATH  Google Scholar 

  21. Pochet, Y., Warichet, F.: A tighter continuous time formulation for the cyclic scheduling of a mixed plant. Comput. Chem. Eng. 32(11), 2723–2744 (2008)

    Article  Google Scholar 

  22. Sauter, T., Lobashov, M.: End to end communication architecture for smart grids. IEEE Trans. Ind. Electron. 58(4), 1218–1228 (2011)

    Article  Google Scholar 

  23. Ursulenko, O., Butenko, S., Prokopyev, O.A.: A global optimization algorithm for solving the minimum multiple ratio spanning tree problem. J. Glob. Optim. 56, 1029–1043 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang, Y.J., Shen, P.P., Liang, Z.: A branch-and-bound algorithm to globally solve the sum of several linear ratios. Appl. Math. Comput. 168(1), 89–101 (2005)

    MathSciNet  MATH  Google Scholar 

  25. Warichet, F.: Scheduling of mixed batch-continuous production lines. PhD thesis, Université Catholique de Louvain, Belguim (2007)

  26. Yue, D., Guilén-Gasálbez, G., You, F.: Global optimization of large-scale mixed-integer linear fractional programming problems: a reformulation-linearization method and process scheduling applications. AIChE J. 59, 4255–4272 (2013)

    Article  Google Scholar 

  27. You, F., Castro, P.M., Grossmann, I.E.: Dinkelbach’s algorithm as an efficient method to solve a class of MINLP models for large-scale cyclic scheduling problems. Comput. Chem. Eng. 33, 1879–1889 (2009)

    Article  Google Scholar 

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Acknowledgements

The work of Thomas C. Sharkey was supported in part by the U.S. National Science Foundation under Grant Number CMMI-1254258.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180, USA

    Hongtan Sun & Thomas C. Sharkey

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  1. Hongtan Sun
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Correspondence to Hongtan Sun.

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Sun, H., Sharkey, T.C. Approximation guarantees of algorithms for fractional optimization problems arising in dispatching rules for INDS problems. J Glob Optim 68, 623–640 (2017). https://doi.org/10.1007/s10898-017-0498-9

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  • DOI: https://doi.org/10.1007/s10898-017-0498-9

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