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Chapter 3 Parallel machines — Linear programming and enumerative algorithms

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References

  1. E. Balas, Machine sequencing via disjunctive graphs: an implicit enumeration algorithm, Operations Research 17 No. 6 (1969).

    Google Scholar 

  2. J. Błaźewicz, W. Cellary, R. Slowiński and J. Węglarz, Deterministic problems of scheduling tasks on parallel processors (in Polish), Podstawy sterowania 6 (1976) Part I, No. 2, pp. 155–178, Part II, No. 3, pp. 297–320.

    Google Scholar 

  3. M. Cochand, D. de Werra and R. Słowiński, Preemptive scheduling with staircase and piecewise linear resource availability. O.R. Working Paper 85/1, Ecole Polytechnique Fédérale de Lausanne, Dép. de Mathématiques, Lausanne 1985.

  4. E.W. Davis and G.E. Heidorn, An algorithm for optimal project scheduling under multiple resource constraints, Management Science 17, No. 12B(1971)803–816.

    Google Scholar 

  5. D.R. Fulkerson and O.A. Gross, Incidence matrices and interval graphs, Pacific Journal of Mathematics 15, No. 3 (1965)835–855.

    Google Scholar 

  6. N. Karmarkhar, A new polynomial-time algorithm for linear programming, Combinatorica 4, No. 4 (1984)373–395.

    Google Scholar 

  7. F.L. Lawer and J. Labetoulle, On preemptive scheduling of unrelated processors by linear programming, Journal of the ACM 25, No. 4 (1978)612–619.

    Article  Google Scholar 

  8. S. Lin and B.W. Kernighan, An effective heuristic for the traveling salesman problem, Operations Research 21, No. 2 (1973)498–516.

    Google Scholar 

  9. J. Patterson and W.D. Huber, A horizon — varying, zero — one approach to project scheduling, Management Science 20, No. 6 (1974)990–998.

    Google Scholar 

  10. J. Patterson and G.W. Roth, Scheduling a project under multiple resource constraints: a zero — one programming approach, AIIE Transactions 8, No. 4 (1976)449–455.

    Google Scholar 

  11. B. Roy,Algèbre moderne et théorie des graphes, Vol. 2 (Dunod, Paris, 1970).

    Google Scholar 

  12. R. Słowiński, A node ordering heuristic for network scheduling under multiple resource constraints, Foundations of Control Engineering 3, No. 1 (1978)19–27.

    Google Scholar 

  13. R. Słowiński, Scheduling preemptible tasks on unrelated processors with additional resources to minimize schedule length, in: G. Bracchi and P.C. Lockemann, eds.,Lecture Notes in Computer Science 65 (Springer-Verlag, Berlin, 1978)536–547.

    Google Scholar 

  14. R. Słowiński, Two approaches to problems of resource allocation among project activities — a comparative study, Journal of the Operational Research Society 31, No. 8 (1980)711–723.

    Google Scholar 

  15. R. Słowiński, Algorithms for the allocation of resources of different categories in the complex of operations framework, (in Polish), Technical University of Poznań Press, ser. Rozprawy No. 114, Poznań, 1980.

  16. R. Słowiński, Multiobjective network scheduling with efficient use of renewable and non-renewable resources, European Journal of Operational Research 7, No. 3 (1981)265–273.

    Article  Google Scholar 

  17. R. Słowiński, L'ordonnancement des tâches préemptives sur les processeurs indépendants en présence de ressources supplémentaires, RAIRO — Informatique/Computer Science 15, No. 2 (1981)156–166.

    Google Scholar 

  18. R. Słowiński and J. Węglarz, Minimum — time network model with different performing modes of activities (in Polish). Przegląd Statystyczny 24, No. 4 (1977)409–416.

    Google Scholar 

  19. J. Stinson, A branch and bound algorithm for a general class of resource — constrained scheduling problems, AIIE Conference Proc., Las Vegas, 1975, pp. 337–342.

  20. B. Talbot, Project scheduling with resource — duration interactions: the nonpreemptive case, Management Science 28, No. 10 (1982)1137–1210.

    Google Scholar 

  21. B. Talbot and J. Patterson, An efficient integer programming algorithm with network cuts for solving resource — constrained scheduling problems, Management Science 24, No. 11 (1978)1163–1174.

    Google Scholar 

  22. D. de Werra, Preemptive scheduling, linear programming and network flows, SIAM J. Alg. Disc. Meth. 5, No. 1 (1984)11–20.

    Google Scholar 

  23. D. de Werra, A decomposition property of polyhedra, Mathematical Programming 30 (1984)261–266.

    Google Scholar 

  24. J. Węglarz, J. Błaźewicz, W. Cellary and R. Słowiński, Algorithm 520. An automatic revised simplex method for constrained resource network scheduling, ACM Trans. on Mathematical Software 3, No. 3 (1977)295–300.

    Article  Google Scholar 

  25. M. Yamamoto, An algorithm for general scheduling problem, Journal of the Operational Research Society of Japan 16, No. 2 (1973)65–77.

    Google Scholar 

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Chapter 3 Parallel machines — Linear programming and enumerative algorithms. Ann Oper Res 7, 99–132 (1986). https://doi.org/10.1007/BF02186435

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