Journal of Combinatorial Optimization

, Volume 37, Issue 1, pp 363–374 | Cite as

Two-machine flowshop scheduling in a physical examination center

  • Yadong Wang
  • Baoqiang FanEmail author
  • Jingang Zhai
  • Wei Xiong


In this paper, we formulate two important operational processes of the physical examination center as a group scheduling problem in two-machine flowshop. The objective is to minimize the makespan. We first analyze the complexity of the problem with a fixed number of release dates and present a pseudo-polynomial-time algorithm. Then we provide an approximation algorithm and analyze its worst-case error bounds for the problem with two release dates and an optimal algorithm for a very practical special case of the problem.


Physical examination Scheduling Flowshop Complexity Algorithm 



This research was supported by the Shandong Province Natural Science Foundation under Grant Nos. ZR2015AM005 and ZR2014FM029. In addition, the third author was also supported by the Shandong Province Higher Educational Science and Technology Program under Grant No. J14L106.


  1. Ahmadi R, Bagchi U (1990) Scheduling of multi-job customer orders in multi-machine environments. ORSA/TIMS PhiladelphiaGoogle Scholar
  2. Fan B, Cheng T (2016) Two-agent scheduling in a flowshop. Eur J Oper Res 252:376–384MathSciNetCrossRefzbMATHGoogle Scholar
  3. Garey M, Johnson D (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San FranciscozbMATHGoogle Scholar
  4. Hall L (1994) A polynomial approximation scheme for a constrained flow-shop scheduling problem. Math Oper Res 19(1):68–85MathSciNetCrossRefzbMATHGoogle Scholar
  5. Johnson S (1954) Optimal two- and three-stage production schedules with setup times included. Nav Res Logist Q 1:61–68CrossRefzbMATHGoogle Scholar
  6. Jia Y, Guo R (2013) Optimal management of hospital physical examination process. Chin Med Rec 14(3):27–28Google Scholar
  7. Kashyrskikh K, Potts C, Sevastianoy S (2001) A 3/2-approximation algorithm for two-machine flow-shop sequencing subject to release dates. Discrete Appl Math 114:255–271MathSciNetCrossRefzbMATHGoogle Scholar
  8. Lee C (1997) Minimizing the makespan in the two-machine flowshop scheduling problem with an availability constraint. Oper Res Lett 20:129–139MathSciNetCrossRefzbMATHGoogle Scholar
  9. Lin B, Cheng T (2011) Scheduling with centralized and decentralized batching policies in concurrent open shops. Nav Res Logist 58:17–27MathSciNetCrossRefzbMATHGoogle Scholar
  10. Lee C, Cheng T, Lin B (1993) Minimizing the makespan in three-machine assembly type flow shop problem. Manag Sci 39:616–625CrossRefzbMATHGoogle Scholar
  11. Leung J, Li H, Pinedo M (2006) Scheduling orders for multiple product types with duedate related objectives. Eur J Oper Res 168:370–389CrossRefzbMATHGoogle Scholar
  12. Lenstra J, Rinnooy Kan A, Brucker P (1977) Complexity of machine scheduling problems. Ann Discrete Math 1:343–362MathSciNetCrossRefzbMATHGoogle Scholar
  13. Ng C, Cheng T, Yuan J (2003) Concurrent open shop scheduling to minimize the weighted number of tardy jobs. J Sched 6:405–412MathSciNetCrossRefzbMATHGoogle Scholar
  14. Pan J, Shan J, Li G, Wu Z (2016) Report on urban development of China No.9: the road to healthy city. Social Sciences Academic Press, ChinaGoogle Scholar
  15. Potts C (1985) Analysis of heuristics for two-machine flow-shop sequencing subject to release dates. Math Oper Res 10(4):576–584MathSciNetCrossRefzbMATHGoogle Scholar
  16. Potts C, Sevastyanov S, Strusevich V, Van Wassenhove L, Zwaneveld C (1995) The two-stage assembly scheduling problem: complexity and approximation. Oper Res 43:346–355MathSciNetCrossRefzbMATHGoogle Scholar
  17. Su Q, Yao X, Jiang Z, Zhang G (2006) Process reengineering and information system design for physical examination center. IFAC Proc 39(3):689–693CrossRefGoogle Scholar
  18. Wang D, Liu F, Yin Y, Wang J, Wang Y (2015) Prioritized surgery scheduling in face of surgeon tiredness and fixed off-duty period. J Comb Optim 30(4):967–981MathSciNetCrossRefzbMATHGoogle Scholar
  19. Yang J (2011) Customer order scheduling in a two machine flowshop. Int J Manag Sci 17:95–116Google Scholar
  20. Yan Y, Wang Y, Zheng W, Xu J (2016) Construction of physical examination self service information management system and its application effect. Hosp Admin J PLA 23(4):336–338Google Scholar
  21. Zhong L, Luo S, Wu L, Xu L, Yang J, Tang G (2014) A two-stage approach for surgery scheduling. J Comb Optim 27(3):545–556MathSciNetCrossRefzbMATHGoogle Scholar
  22. Zhang X, Wang H, Wang X (2015) Patients scheduling problems with deferred deteriorated functions. J Comb Optim 30(4):1027–1041MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Statistic ScienceLudong UniversityYantaiPeople’s Republic of China
  2. 2.Department of Spinal SurgeryYantai Affiliated Hospital of Binzhou Medical UniversityYantaiPeople’s Republic of China

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