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A variable neighborhood search algorithm for a PET/CT examination scheduling problem considering multi-stage process and deteriorating effect

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Abstract

In this paper, a Positron Emission Tomography/Computed Tomography (PET/CT) examination scheduling problem considering multi-stage processes is studied. Before the actual examination process, imaging agents (a drug with radioactivity) need to be injected into patients. The radioactivity of the imaging agents continuously decays, which results in the required dose by patients increasing with time, i.e., the later the injection time, the more imaging agents need to be prepared for the patients at the beginning. Considering the imaging agents are expensive and non-storable, the studied problem is to determine the start time of the examination service and injection time for the patients, to minimize the total dose of purchased imaging agents. An integer programming model and a set partitioning model are formulated for this problem. A variable neighborhood search heuristic is proposed, in which a scheduling rule based on some derived optimal properties is embedded as one of the search operators. Computational experiments show that the proposed algorithm can obtain near-optimal solutions in a short time, and moreover find much better results than the commonly used First Come First Service (FCFS) rule in most medical institutions, i.e., our approach’s results need much fewer required dose of the imaging agents, and hence can save a lot of costs for the medical institutions.

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References

  1. Aristophanous, M., Berbeco, R.I., Killoran, J.H., Yap, J.T., Sher, D.J., Allen, A.M., Larson, E., Chen, A.B.: Clinical utility of 4D FDG-PET/CT scans in radiation treatment planning. Int. J. Radiat. Oncol. Biol. Phys. 82(1), 99–105 (2012). https://doi.org/10.1016/j.ijrobp.2010.12.060

    Article  Google Scholar 

  2. Arık, O.A.: Population-based Tabu search with evolutionary strategies for permutation flow shop scheduling problems under effects of position-dependent learning and linear deterioration. Soft. Comput. 25(2), 1501–1518 (2021). https://doi.org/10.1007/s00500-020-05234-7

    Article  Google Scholar 

  3. Bansal, J.C.: Particle swarm optimization. In: Bansal, J.C., Singh, P.K., Pal, N.R. (eds.) Evolutionary and Swarm Intelligence Algorithms, pp. 11–23. Springer, Cham (2019)

    Google Scholar 

  4. Bilge, Ü., Kiraç, F., Kurtulan, M., Pekgün, P.: A tabu search algorithm for parallel machine total tardiness problem. Comput. Oper. Res. 31(3), 397–414 (2004). https://doi.org/10.1016/S0305-0548(02)00198-3

    Article  MATH  Google Scholar 

  5. Cheng, T.C.E., Lee, W.C., Wu, C.C.: Single-machine scheduling with deteriorating jobs and past-sequence-dependent setup times. Appl. Math. Model. 35(4), 1861–1867 (2011). https://doi.org/10.1016/j.apm.2010.10.015

    Article  MathSciNet  MATH  Google Scholar 

  6. Cui, W.W., Lu, Z., Pan, E.: Integrated production scheduling and maintenance policy for robustness in a single machine. Comput. Oper. Res. 47, 81–91 (2014). https://doi.org/10.1016/j.cor.2014.02.006

    Article  MathSciNet  MATH  Google Scholar 

  7. Engin, O., Güçlü, A.: A new hybrid ant colony optimization algorithm for solving the no-wait flow shop scheduling problems. Appl. Soft Comput. J. 72, 166–176 (2018). https://doi.org/10.1016/j.asoc.2018.08.002

    Article  Google Scholar 

  8. Garey, M.R., Johnson, D.S., Sethi, R.: Complexity of flowshop and jobshop scheduling. Math. Oper. Res. 1(2), 117–129 (1976). https://doi.org/10.1287/moor.1.2.117

    Article  MathSciNet  MATH  Google Scholar 

  9. Hansen, P., Mladenović, N., Moreno Pérez, J.A.: Variable neighbourhood search: methods and applications. Ann. Oper. Res. 175(1), 367–407 (2010). https://doi.org/10.1007/s10479-009-0657-6

    Article  MathSciNet  MATH  Google Scholar 

  10. Hansen, P., Mladenović, N., Urošević, D.: Variable neighborhood search and local branching. Comput. Oper. Res. 33(10), 3034–3045 (2006). https://doi.org/10.1016/j.cor.2005.02.033

    Article  MATH  Google Scholar 

  11. Ji, M., Cheng, T.C.E.: Parallel-machine scheduling with simple linear deterioration to minimize total completion time. Eur. J. Oper. Res. 188(2), 342–347 (2008). https://doi.org/10.1016/j.ejor.2007.04.050

    Article  MathSciNet  MATH  Google Scholar 

  12. Johnson, S.M.: With setup times included. Naval Res. Logist. Q. 1, 61–68 (1954)

    Article  Google Scholar 

  13. Koulamas, C.: Common due date assignment with generalized earliness/tardiness penalties. Comput. Ind. Eng. 109, 79–83 (2017). https://doi.org/10.1016/j.cie.2017.04.040

    Article  Google Scholar 

  14. Li, S.S., Chen, R.X.: Scheduling with common due date assignment to minimize generalized weighted earliness–tardiness penalties. Optim. Lett. 14(7), 1681–1699 (2020). https://doi.org/10.1007/s11590-019-01462-5

    Article  MathSciNet  MATH  Google Scholar 

  15. Liu, S., Pei, J., Cheng, H., Liu, X., Pardalos, P.M.: Two-stage hybrid flow shop scheduling on parallel batching machines considering a job-dependent deteriorating effect and non-identical job sizes. Appl. Soft Comput. J. 84, 105701 (2019). https://doi.org/10.1016/j.asoc.2019.105701

    Article  Google Scholar 

  16. Mazdeh, M.M., Zaerpour, F., Zareei, A., Hajinezhad, A.: Parallel machines scheduling to minimize job tardiness and machine deteriorating cost with deteriorating jobs. Appl. Math. Model. 34(6), 1498–1510 (2010). https://doi.org/10.1016/j.apm.2009.08.023

    Article  MathSciNet  MATH  Google Scholar 

  17. Mirjalili, S.: Genetic algorithm. In: Mirjalili, S. (ed.) Evolutionary Algorithms and Neural Networks, pp. 43–55. Springer, Cham (2019a)

    Chapter  MATH  Google Scholar 

  18. Mirjalili, S.: Ant colony optimisation. In: Mirjalili, S. (ed.) Evolutionary Algorithms and Neural Networks, pp. 33–42. Springer, Cham (2019)

    Chapter  MATH  Google Scholar 

  19. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997). https://doi.org/10.1016/S0305-0548(97)00031-2

    Article  MathSciNet  MATH  Google Scholar 

  20. Pei, J., Liu, X., Fan, W., Pardalos, P.M., Lu, S.: A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers. Omega (UK) 82, 55–69 (2019). https://doi.org/10.1016/j.omega.2017.12.003

    Article  Google Scholar 

  21. Rosa, B.F., Souza, M.J.F., de Souza, S.R., de França Filho, M.F., Ales, Z., Michelon, P.Y.P.: Algorithms for job scheduling problems with distinct time windows and general earliness/tardiness penalties. Comput. Oper. Res. (2017). https://doi.org/10.1016/j.cor.2016.12.024

    Article  MathSciNet  MATH  Google Scholar 

  22. Rossit, D.A., Vásquez, Ó.C., Tohmé, F., Frutos, M., Safe, M.D.: A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems. Eur. J. Oper. Res. 289(3), 841–854 (2021). https://doi.org/10.1016/j.ejor.2019.07.055

    Article  MathSciNet  MATH  Google Scholar 

  23. Ruiz, R., Pan, Q.K., Naderi, B.: Iterated Greedy methods for the distributed permutation flowshop scheduling problem. Omega (UK) 83, 213–222 (2019). https://doi.org/10.1016/j.omega.2018.03.004

    Article  Google Scholar 

  24. Ruiz, R., Vázquez-Rodríguez, J.A.: The hybrid flow shop scheduling problem. Eur. J. Oper. Res. 205(1), 1–18 (2010). https://doi.org/10.1016/j.ejor.2009.09.024

    Article  MathSciNet  MATH  Google Scholar 

  25. Sánchez-Herrera, S., Montoya-Torres, J.R., Solano-Charris, E.L.: Flow shop scheduling problem with position-dependent processing times. Comput. Oper. Res. 111, 325–345 (2019). https://doi.org/10.1016/j.cor.2019.06.015

    Article  MathSciNet  MATH  Google Scholar 

  26. Steward, B.W., Wild, C.P.: World cancer report 2014. Technical report, World Health Organization, International Agency for Research on Cancer (2014)

  27. Tse, P.W., Atherton, D.P.: Prediction of machine deterioration using vibration based fault trends and recurrent neural networks. J. Vib. Acoust. (1999). https://doi.org/10.1115/1.2893988

    Article  Google Scholar 

  28. Wang, J.B., Cheng, T.E.: Scheduling problems with the effects of deterioration and learning. Asia-Pac. J. Oper. Res. 24(02), 245–261 (2007). https://doi.org/10.1142/S021759590700122X

    Article  MathSciNet  MATH  Google Scholar 

  29. Wang, J.B.: Single-machine scheduling problems with the effects of learning and deterioration. Omega 35(4), 397–402 (2007). https://doi.org/10.1016/j.omega.2005.07.008

    Article  Google Scholar 

  30. World Health Organization: GLOBOCAN 2018 (2018). http://globocan.iarc.fr/Default.aspx. Accessed 1 Oct 2020

  31. Wu, X., Shen, X., Li, C.: The flexible job-shop scheduling problem considering deterioration effect and energy consumption simultaneously. Comput. Ind. Eng. 135, 1004–1024 (2019). https://doi.org/10.1016/j.cie.2019.06.048

    Article  Google Scholar 

  32. Zhen, L., Liang, Z., Zhuge, D., Lee, L.H., Chew, E.P.: Daily berth planning in a tidal port with channel flow control. Transp. Res. Part B Methodol. 106, 193–217 (2017). https://doi.org/10.1016/j.trb.2017.10.008

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 72071057, 71922009, and 71690230), the Basic scientific research Projects in central colleges and Universities (JZ2018HGTB0232), and Innovative Research Groups of the National Natural Science Foundation of China (71521001). P.M. Pardalos is supported by a Humboldt Research Award (Germany).

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Authors and Affiliations

  1. School of Management, Hefei University of Technology, Hefei, China

    Kaining Shao, Wenjuan Fan & Shanlin Yang

  2. Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education, Hefei, China

    Kaining Shao, Wenjuan Fan & Shanlin Yang

  3. The Second Hospital of Anhui Medical University, Hefei, China

    Zishu Yang

  4. Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, Gainesville, USA

    Panos M. Pardalos

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  1. Kaining Shao
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Correspondence to Wenjuan Fan.

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Shao, K., Fan, W., Yang, Z. et al. A variable neighborhood search algorithm for a PET/CT examination scheduling problem considering multi-stage process and deteriorating effect. Optim Lett 17, 879–900 (2023). https://doi.org/10.1007/s11590-022-01915-4

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  • DOI: https://doi.org/10.1007/s11590-022-01915-4

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