Soft Computing

, Volume 21, Issue 8, pp 2015–2033 | Cite as

A two-agent single-machine scheduling problem with late work criteria

  • Du-Juan Wang
  • Chao-Chung Kang
  • Yau-Ren Shiau
  • Chin-Chia Wu
  • Peng-Hsiang Hsu
Methodologies and Application

Abstract

This paper addresses a two-agent scheduling problem where the objective is to minimize the total late work of the first agent, with the restriction that the maximum lateness of the second agent cannot exceed a given value. Two pseudo-polynomial dynamic programming algorithms are presented to find the optimal solutions for small-scale problem instances. For medium- to large-scale problem instances, a branch-and-bound algorithm incorporating the implementation of a lower bounding procedure, some dominance rules and a Tabu Search-based solution initialization, is developed to yield the optimal solution. Computational experiments are designed to examine the efficiency of the proposed algorithms and the impacts of all the relative parameters.

Keywords

Scheduling Two agent Dynamic programming Branch-and-bound algorithm 

References

  1. Agnetis A, Mirchandani PB, Pacciarelli D, Pacifici A (2004) Scheduling problems with two competing agents. Oper Res 52:229–242MathSciNetCrossRefMATHGoogle Scholar
  2. Agnetis A, Pascale G, Pacciarelli D (2009) A Lagrangian approach to single-machine scheduling problems with two competing agents. J Sched 12:401–415MathSciNetCrossRefMATHGoogle Scholar
  3. Baker KR, Smith JC (2003) A multiple criterion model for machine scheduling. J Sched 6:7–16MathSciNetCrossRefMATHGoogle Scholar
  4. Blazewicz J (1984) Scheduling preemptible tasks on parallel processors with information loss. Tech Sci Inform 3(6):415–420MathSciNetMATHGoogle Scholar
  5. Blazewicz J, Pesch E, Sterna M, Werner F (1999) Total late work criteria for shop scheduling problems. In: Inderfurth K, Schwödiauer G, Domschke W, Juhnke F, Kleinschmidt P, Waescher G (eds) Operations research proceedings. Springer, Berlin, pp 354–359Google Scholar
  6. Blazewicz J, Pesch E, Sterna M, Werner F (2004) Open shop scheduling problems with late work criteria. Discret Appl Math 134:1–24MathSciNetCrossRefMATHGoogle Scholar
  7. Cheng TCE, Cheng SR, Wu WH, Hsu PH, Wu CC (2011) A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations. Comput Ind Eng 60:534–541CrossRefGoogle Scholar
  8. Gerstl E, Mosheiov G (2012) Scheduling problems with two competing agents to minimize weighted earliness-tardiness. Comput Oper Res 40:109–116CrossRefMATHGoogle Scholar
  9. Guo P, Cheng W, Wang Y (2014) A general variable neighborhood search for single-machine total tardiness scheduling problem with step-deteriorating jobs. J Ind Manag Optim 10(4):1071–1090MathSciNetCrossRefMATHGoogle Scholar
  10. Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(1):156–166CrossRefGoogle Scholar
  11. Glover F (1989) Tabu search—part I. INFORMS J Comput 1(3):190–206MathSciNetCrossRefMATHGoogle Scholar
  12. Hall NG, Posner ME (2001) Generating experimental data for computation testing with machine scheduling applications. Oper Res 8:54–865MATHGoogle Scholar
  13. Ke H, Ma J (2014) Modeling project time-cost trade-off in fuzzy random environment. Appl Soft Comput 19:80–85CrossRefGoogle Scholar
  14. Lee WC, Chen SK, Chen WC, Wu CC (2011) A two-machine flowshop problem with two agents. Comput Oper Res 38:98–104MathSciNetCrossRefMATHGoogle Scholar
  15. Lee K, Choi BC, Leung JYT, Pinedo ML (2009) Approximation algorithms for multi-agent scheduling to minimize total weighted completion time. Inf Process Lett 109:913–917MathSciNetCrossRefMATHGoogle Scholar
  16. Leung JYT, Pinedo M, Wan G (2010) Competitive two-agent scheduling and its applications. Oper Res 58:458–469MathSciNetCrossRefMATHGoogle Scholar
  17. Li S, Yuan J (2012) Unbounded parallel-batching scheduling with two competitive agents. J Sched 15:629–640MathSciNetCrossRefMATHGoogle Scholar
  18. Liao LM, Huang CJ (2011) Tabu search heuristic for two-machine flowshop with batch processing machines. Comput Ind Eng 60:426–432CrossRefGoogle Scholar
  19. Lin BMT, Hsu SW (2005) Minimizing total late work on a single machine with release and due dates, In: SIAM conference on computational science and engineering, OrlandoGoogle Scholar
  20. Liu P, Yi N, Zhou XY (2011) Two-agent single-machine scheduling problems under increasing linear deterioration. Appl Math Model 35:2290–2296MathSciNetCrossRefMATHGoogle Scholar
  21. Li J, Pan Q, Wang F (2014) A hybrid variable neighborhood search for solving the hybrid flow shop scheduling problem. Appl Soft Comput 24:63–77CrossRefGoogle Scholar
  22. Li G, Lu X (2015) Two-machine scheduling with periodic availability constraints to minimize makespan. J Ind Manag Optim 11(2):685–700MathSciNetCrossRefMATHGoogle Scholar
  23. Mor B, Mosheiov G (2010) Scheduling problems with two competing agents to minimize minmax and minsum earliness measures. Eur J Oper Res 206:540–546MathSciNetCrossRefMATHGoogle Scholar
  24. Mor B, Mosheiov G (2011) Single machine batch scheduling with two competing agents to minimize total flowtime. Eur J Oper Res 215:524–531MathSciNetCrossRefMATHGoogle Scholar
  25. Ng CT, Cheng TCE, Yuan JJ (2006) A note on the complexity of the two-agent scheduling on a single machine. J Comb Optim 12:387–394MathSciNetCrossRefMATHGoogle Scholar
  26. Potts CN, Van Wassenhove LN (1991a) Single machine scheduling to minimize total late work. Oper Res 40:586–595Google Scholar
  27. Potts CN, Van Wassenhove LN (1991b) Approximation algorithms for scheduling a single machine to minimize total late work. Oper Res Lett 11:261–266Google Scholar
  28. Pei J, Pardalos PM, Liu X, Fan W, Yang S, Wang L (2015) Coordination of production and transportation in supply chain scheduling. J Ind Manag Optim 11(2):399–419MathSciNetMATHGoogle Scholar
  29. Ren J, Zhang Y, Sun G (2009) The NP-hardness of minimizing the total late work on an unbounded batch machine. Asia-Pac J Oper Res 26(3):351–363MathSciNetCrossRefMATHGoogle Scholar
  30. Roy PK, Bhui S, Paul C (2014) Solution of economic load dispatch using hybrid chemical reaction optimization approach. Appl Soft Comput 24:109–125CrossRefGoogle Scholar
  31. Sterna M (2007) Dominance relations for two-machine flow shop problem with late work criterion. Bull Pol Acad Sci 55:59–69MATHGoogle Scholar
  32. Sterna M (2011) A survey of scheduling problems with late work criteria. Omega 39:120–129CrossRefGoogle Scholar
  33. Tuong NH, Soukhal A, Billaut JC (2012) Single-machine multi-agent scheduling problems with a global objective function. J Sched 15:311–332MathSciNetCrossRefMATHGoogle Scholar
  34. Wan G, Vakati RS, Leung JYT, Pinedo M (2010) Scheduling two agents with controllable processing times. Eur J Oper Res 205:528–539MathSciNetCrossRefMATHGoogle Scholar
  35. Wu W-H, Yin Y, Wu W-H, Wu C-C, Hsu P-H (2014) A time-dependent scheduling problem to minimize the sum of the total weighted tardiness among two agents. J Ind Manag Optim 10(2):591–611MathSciNetCrossRefMATHGoogle Scholar
  36. Yin Y, Cheng SR, Cheng TCE, Wu CC, Wu WH (2012a) Two-agent single-machine scheduling with assignable due dates. Appl Math Comput 219:1674–1685Google Scholar
  37. Yin Y, Cheng SR, Cheng TCE, Wu WH, Wu CC (2013a) Two-agent single-machine scheduling with release times and deadlines. Int J Shipp Transp Logist 5:75–94Google Scholar
  38. Yin Y, Cheng SR, Wu CC (2012b) Scheduling problems with two agents and a linear non-increasing deterioration to minimize earliness penalties. Inf Sci 189:282–292Google Scholar
  39. Yin Y, Wu C-C, Wu W-H, Hsu C-J, Wu W-H (2013b) A branch-and-bound procedure for a single-machine earliness scheduling problem with two agents. Appl Soft Comput 13(2):1042–1054Google Scholar
  40. Yuan X, Ji B, Zhang S, Tian H, Hou Y (2014) A new approach for unit commitment problem via binary gravitational search algorithm. Appl Soft Comput 22:249–260CrossRefGoogle Scholar
  41. Zhao K, Lu X (2013) Approximation schemes for two-agent scheduling on parallel machines. Theor Comput Sci 468:114–121MathSciNetCrossRefMATHGoogle Scholar
  42. Zhao CL, Yin Y, Cheng TCE, Wu C-C (2014) Single-machine scheduling and due date assignment with rejection and position-dependent processing times. J Ind Manag Optim 10(3):691–700MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Du-Juan Wang
    • 1
  • Chao-Chung Kang
    • 2
  • Yau-Ren Shiau
    • 3
  • Chin-Chia Wu
    • 4
  • Peng-Hsiang Hsu
    • 5
  1. 1.School of Management Science and EngineeringDalian University of TechnologyDalianChina
  2. 2.Department of Business Administration, Graduate Institute of ManagementProvidence UniversityTaichungTaiwan
  3. 3.Department of Industrial Engineering and System ManagementFeng-Chia UniversityTaichungTaiwan
  4. 4.Department of StatisticsFeng Chia UniversityTaichungTaiwan
  5. 5.Department of Business AdministrationKang Ning UniversityTaipeiTaiwan

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