The Open Shop Scheduling Problem

Author Gerhard J. Woeginger

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Gerhard J. Woeginger

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Gerhard J. Woeginger. The Open Shop Scheduling Problem. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We discuss the computational complexity, the approximability, the algorithmics and the combinatorics of the open shop scheduling problem. We summarize the most important results from the literature and explain their main ideas, we sketch the most beautiful proofs, and we also list a number of open problems.
  • Algorithms
  • Complexity
  • Scheduling
  • Approximation


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  1. V.A. Aksjonov. A polynomial-time algorithm for an approximate solution of a scheduling problem (in Russian). Upravlyaemye Sistemy, 28:8-11, 1988. Google Scholar
  2. W. Banaszczyk. The Steinitz constant of the plane. Journal für die Reine und Angewandte Mathematik, 373:218-220, 1987. Google Scholar
  3. I. Bárány and T. Fiala. Nearly optimum solution of multimachine scheduling problems (in Hungarian). Szigma Mathematika Közgazdasági Folyóirat, 15:177-191, 1982. Google Scholar
  4. I.S. Belov and Ya. N. Stolin. An algorithm for the single-route scheduling problem (in Russian). In Matematiceskaja ékonomika i funkcionalnyi analiz (Mathematical Economics and Functional Analysis), pages 248-257. Nauka, Moscow, 1974. Google Scholar
  5. V. Bergström. Zwei Sätze über ebene Vektorpolygone. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 8:148-152, 1931. Google Scholar
  6. B. Chen and V.A. Strusevich. Approximation algorithms for three-machine open shop scheduling. ORSA Journal on Computing, 5:321-326, 1993. Google Scholar
  7. B. Chen and W. Yu. How good is a dense shop schedule? Acta Mathematicae Applicatae Sinica, 17:121-128, 2001. Google Scholar
  8. T. Fiala. An algorithm for the open-shop problem. Mathematics of Operations Research, 8:100-109, 1983. Google Scholar
  9. M. R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. Google Scholar
  10. T. Gonzalez and S. Sahni. Open shop scheduling to minimize finish time. Journal of the Association for Computing Machinery, 25:92-101, 1976. Google Scholar
  11. V. Grinberg and S.V. Sevastianov. The value of the Steinitz constant (in Russian). Funktionalnyi Analiz i ego Prilozheniia (Functional Analysis and Its Applications), 14:125-126, 1980. Google Scholar
  12. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys. Sequencing and scheduling: Algorithms and complexity. In S.C. Graves, A.H.G. Rinnooy Kan, and P.H. Zipkin, editors, Logistics of Production and Inventory (Handbooks in Operations Research and Management Science), pages 445-522. North-Holland, Amsterdam, 1993. Google Scholar
  13. J.K. Lenstra. Strong NP-hardness of open shop scheduling. Unpublished manuscript, 1978. Google Scholar
  14. S. Sahni and Y. Cho. Complexity of scheduling shops with no wait in process. Mathematics of Operations Researc, 4:448-457, 1979. Google Scholar
  15. S.V. Sevastianov. Approximate solution of some problems in scheduling theory (in Russian). Metody Diskretnogo Analiza, 32:66-75, 1978. Google Scholar
  16. S.V. Sevastianov. A polynomially solvable case of the open shop problem with arbitrary number of machines (in Russian). Kibernetika i Systemnii Analiz, 6:135-154, 1992. Google Scholar
  17. S.V. Sevastianov. On some geometric methods in scheduling theory: a survey. Discrete Applied Mathematics, 55:59-82, 1994. Google Scholar
  18. S.V. Sevastianov. Vector summation in Banach space and polynomial algorithms for flow shops and open shops. Mathematics of Operations Research, 20:90-103, 1995. Google Scholar
  19. S.V. Sevastianov and I.D. Tchernykh. Computer-aided way to prove theorems in scheduling. In Proceedings of the 6th European Symposium on Algorithms (ESA'1998), LNCS 1461, pages 502-513. Springer, 1998. Google Scholar
  20. S.V. Sevastianov and G.J. Woeginger. Makespan minimization in open shops: A polynomial time approximation scheme. Mathematical Programming, 82:191-198, 1998. Google Scholar
  21. N.V. Shaklevich and V.A. Strusevich. Two machine open shop scheduling problem to minimize an arbitrary machine usage regular penalty function. European Journal of Operational Research, 70:391-404, 1993. Google Scholar
  22. E. Steinitz. Bedingt konvergente Reihen und konvexe Systeme. Journal für die Reine und Angewandte Mathematik, 143:128-176, 1913. Google Scholar
  23. M. van den Akker, J.A. Hoogeveen, and G.J. Woeginger. The two-machine open shop problem: to fit or not to fit, that is the question. Operations Research Letters, 31:219-224, 2003. Google Scholar
  24. D.P. Williamson, L.A. Hall, J.A. Hoogeveen, C.A.J. Hurkens, J.K. Lenstra, S.V. Sevastianov, and D.B. Shmoys. Short shop schedules. Operations Research, 45:288-294, 1997. Google Scholar