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Declarative approach to cyclic steady state space refinement: periodic process scheduling

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Problems of cyclic scheduling are usually observed in flexible manufacturing systems which produce multitype parts where the automated guided vehicle system plays the role of a material handling system, as well as in various other multimodal transportation systems where goods and/or passenger itinerary planning plays a pivotal role. The schedulability analysis of the processes executed in the so-called systems of concurrent cyclic processes (SCCPs) can be executed within a declarative modeling framework. Consequently, the considered SCCP scheduling problem can be seen as a constraint satisfaction problem. Such a representation provides a unified way for evaluating the performance of local cyclic processes as well as of multimodal processes supported by them. Here, the crucial issue is that of a control procedure (e.g., a set of dispatching rules), which would guarantee the cyclic behavior of the SCCP. In this context, we discuss the sufficient conditions guaranteeing the schedulability of both local and multimodal cyclic processes, and we propose a recursive approach in designing them.


  1. 1.

    Bocewicz G, Wójcik R, Banaszak Z (2009) On undecidability of cyclic scheduling problems. In: Mapping relational databases to the semantic web with original meaning, lecture notes in computer science, vol. 5914. Springer, Berlin, pp 310321

  2. 2.

    Bocewicz G, Bach I, Banaszak Z (2009) Logic-algebraic method based and constraints programming driven approach to AGVs scheduling. Int J Intel Inf Database Syst 3(1):56–74

  3. 3.

    Bocewicz G, Wójcik R, Banaszak Z (2011) Toward cycling scheduling of concurrent multimodal processes. In: Jedrzejowicz P, Nguyen NT, Hoang K (eds) Computational collective intelligence: technologies and applications, lecture notes in artificial intelligence, LNAI, vol. 6922. Springer, Berlin, pp 448–457

  4. 4.

    Bocewicz G, Wójcik R, Banaszak Z (2011) Cyclic steady state refinement. In: Abraham A, Corchado JM, Rodríguez González S, de Paz Santana JF (eds) International symposium on distributed computing and artificial intelligence, series: advances in intelligent and soft computing, vol. 91. Springer, Berlin, pp 191–198

  5. 5.

    Bocewicz G, Banaszak Z (2013) Declarative approach to cyclic scheduling of multimodal processes. In: Golińska P (ed) EcoProduction and Logistics, emerging trends and business practices, series: EcoProduction, vol. 1. Springer, Heidelberg, pp 203–238

  6. 6.

    Cai X, Li KN (2000) A genetic algorithm for scheduling staff of mixed skills under multi-criteria. Eur J Oper Res 125:359–369

  7. 7.

    Gaujal B, Jafari M, Baykal-Gursoy M, Alpan G (1995) Allocation sequences of two processes sharing a resource. IEEE Trans Robot Autom 11(5):748–353

  8. 8.

    Guan X, Dai X (2009) Deadlock-free multi-attribute dispatching method for AGV systems. Int J Adv Manuf Technol 45:603–615

  9. 9.

    Guy RK (1994) Diophantine equations. Ch. D in unsolved problems in number theory, 2nd edn. Springer, New York, pp 139–198

  10. 10.

    Jamili A, Ali Shafia M, Tavakkoli-Moghaddam R (2011) A hybrid algorithm based on particle swarm optimization and simulated annealing for a periodic job shop scheduling problem. Int J Adv Manuf Technol 54:309–322

  11. 11.

    Korytkowski P, Wisniewski T, Zaikin O (2010) Multi-criteria approach to comparison of inspection allocation for multi-product manufacturing systems in make-to-order sector. Control Cybern 39(1):97–116

  12. 12.

    Lawley MA, Reveliotis SA, Ferreira PM (1998) A correct and scalable deadlock avoidance policy for flexible manufacturing systems. IEEE Trans Robot Autom 14(5):796–809

  13. 13.

    Levner E, Kats V, Alcaide D, Pablo L, Cheng TCE (2010) Complexity of cyclic scheduling problems: a state-of-the-art survey. Comput Ind Eng 59(2):352–361

  14. 14.

    Liebchen C, Möhring RH (2002) A case study in periodic timetabling. Electronic Notes Theor Comput Sci 66(6):21–34

  15. 15.

    Pinedo ML (2005) Planning and scheduling in manufacturing and services. Springer, New York

  16. 16.

    Polak M, Majdzik P, Banaszak Z, Wójcik R (2004) The performance evaluation tool for automated prototyping of concurrent cyclic processes. Fundamenta Informaticae 60(1–4):269–289

  17. 17.

    Schulte CH, Smolka G, Wurtz J (1998) Finite domain constraint programming in Oz, DFKI OZ documentation series. German Research Center for Artificial Intelligence, Saarbrucken, Germany

  18. 18.

    Smart Nigiel P (1998) The algorithmic resolution of Diophantine equations. London Mathematical Society Student Text, vol 41. Cambridge University, Cambridge

  19. 19.

    Song J-S, Lee T-E (1998) Petri net modeling and scheduling for cyclic job shops with blocking. Comput Ind Eng 34(2):281–295

  20. 20.

    Heo S-K, Lee K-H, Lee H-K, Lee I-B, Park JH (2003) A new algorithm for cyclic scheduling and design of multipurpose batch plants. Ind Eng Chem Res 42(4):836–846

  21. 21.

    Trouillet B, Korbaa O, Gentina J-CK (2007) Formal approach for FMS cyclic scheduling. IEEE SMC Trans, Part C 37(1):126–137

  22. 22.

    Wójcik R (2007) Constraint programming approach to designing conflict-free schedules for repetitive manufacturing processes. In: Cunha PF, Maropoulos PG (eds) Digital enterprise technology. Perspectives and future challenges. Springer, New York, pp 267–274

  23. 23.

    Wang B, Yang H, Zhang Z-H (2007) Research on the train operation plan of the Beijing-Tianjin inter-city railway based on periodic train diagrams. Tiedao Xuebao/J China Railway Soc 29(2):8–13

  24. 24.

    Von Kampmeyer T (2006) Cyclic scheduling problems, Ph.D. Dissertation, Fachbereich Mathematik/Informatik, Universität Osnabrück

  25. 25.

    Zandong H, Lee G (2005) Application of Petri nets for deadlock analysis and avoidance in flexible manufacturing systems. Int J Adv Manuf Technol 25:735–742

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Correspondence to Grzegorz Bocewicz.

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Bocewicz, G., Banaszak, Z.A. Declarative approach to cyclic steady state space refinement: periodic process scheduling. Int J Adv Manuf Technol 67, 137–155 (2013).

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  • Cyclic processes
  • Declarative modeling
  • Constraint programming
  • State space
  • Periodicity
  • Dispatching rules