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Recent Advances in Scheduling Theory and Applications in Robotics and Communications

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Part of the Lecture Notes in Computer Science book series (LNCCN,volume 13144)

Abstract

Scheduling theory is a major field in operations research and discrete applied mathematics. This paper focuses on several recent developments in scheduling theory and a broad range of new applications – from multiagent scheduling to robots in communication networks. The survey presents a personal view on current trends, critical issues, strengths and limitations of this advantageous field.

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References

  1. Johnson, S.M.: Optimal two- and three-stage production schedules with setup times included. Naval Res. Logist. Q. 1, 61–68 (1954)

    CrossRef  Google Scholar 

  2. Bellman, R.: Mathematical aspects of scheduling theory. J. Soc. Ind. Appl. Math. 4, 168–205 (1956)

    MathSciNet  CrossRef  Google Scholar 

  3. Smith, W.E.: Various optimizers for single-stage production. Naval Res. Logist. Q. 3(1–2), 59–66 (1956)

    MathSciNet  CrossRef  Google Scholar 

  4. Tanaev, V.S., Gordon, V.S., Shafransky, Y.M.: Scheduling Theory. Single-Stage Systems. Kluwer, Dordrecht (1994)

    CrossRef  Google Scholar 

  5. Lee, C.Y., Lei, L., Pinedo, M.: Current trends in deterministic scheduling. Ann. Oper. Res. 70, 1–41 (1997). https://doi.org/10.1023/A:1018909801944

    MathSciNet  CrossRef  MATH  Google Scholar 

  6. Chen, B., Potts, C.N., Woeginger, G.J.: A review of machine scheduling: complexity, algorithms and approximability. In: Du, D.-Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, pp. 21–169. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  7. Pinedo, M.: Scheduling: Theory. Algorithms and Systems. Prentice Hall, Englewood Cliffs (2016)

    CrossRef  Google Scholar 

  8. Blazewicz, J., Ecker, K.H., Pesch, E., Schmidt, G., Weglarz, J.: Handbook on Scheduling. Springer, Berlin (2007). https://doi.org/10.1007/978-3-540-32220-7

    CrossRef  MATH  Google Scholar 

  9. Levner, E. (ed.): Multiprocessor Scheduling Theory and Applications. I-TECH Education and Publishing, Vienna (2007)

    Google Scholar 

  10. Lenstra, J.K., Shmoys, D.B. (eds.): Elements of Scheduling. Centrum Wiskunde & Informatica, Amsterdam (2020)

    Google Scholar 

  11. Baker, K., Smith, J.C.: A multiple criterion model for machine scheduling. J. Sched. 6, 7–16 (2003). https://doi.org/10.1023/A:1022231419049

    MathSciNet  CrossRef  MATH  Google Scholar 

  12. Agnetis, A., Mirchandani, P., Pacciarelli, D., Pacifici, A.: Scheduling problems with two competing agents. Oper. Res. 52, 229–242 (2004)

    MathSciNet  CrossRef  Google Scholar 

  13. Agnetis, A., Pacciarelli, D., Pacifici, A.: Combinatorial models for multi-agent scheduling problems. Ch. 2 in [9], pp. 21–47 (2007)

    Google Scholar 

  14. Agnetis, A., Billaut, J.-C., Gawiejnowicz, S., Pacciarelli, D., Soukhal, A.: Multiagent Scheduling. Models and Algorithms. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-41880-8

    CrossRef  MATH  Google Scholar 

  15. Cheng, C.T., Ng, J.J.Y.: Multi-agent scheduling on a single machine with max-form criteria. Eur. J. Oper. Res. 188, 603–609 (2008)

    MathSciNet  CrossRef  Google Scholar 

  16. Cohen, J., Dürr, C., Kim, T.N.: Non-clairvoyant scheduling games. Theory Comput. Syst. 49, 3–23 (2011). https://doi.org/10.1007/s00224-011-9316-9

    MathSciNet  CrossRef  MATH  Google Scholar 

  17. Vishnevsky, V., Semenova, O.: Polling systems and their application to telecommunication networks. Mathematics 9(2), 117 (2021). https://doi.org/10.3390/math9020117

    CrossRef  Google Scholar 

  18. Dudin, A.N., Klimenok, V.I., Vishnevsky, V.M.: The Theory of Queuing Systems with Correlated Flows. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-32072-0

    CrossRef  MATH  Google Scholar 

  19. Klimenok, V., Dudin, A., Vishnevsky, V.: Priority multi-server queueing system with heterogeneous customers. Mathematics 8(9), 1501 (2020). https://doi.org/10.3390/math8091501

    CrossRef  Google Scholar 

  20. Terekhov, D., Tran, T.T., Down, D.G., Beck, J.C.: Integrating Queueing theory and scheduling for dynamic scheduling problems. J. Artif. Intell. Res. 50(2014), 535–572 (2014)

    MathSciNet  CrossRef  Google Scholar 

  21. Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. The IBM Research Symposia Series, pp. 85–103. Springer, Boston (1972). https://doi.org/10.1007/978-1-4684-2001-2_9

    CrossRef  Google Scholar 

  22. Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem (PDF), Report 388. Graduate School of Industrial Administration, CMU (1976)

    Google Scholar 

  23. Serdyukov, A.I.: On some extremal walks in graphs. Upravlyaemye Sistemy 17, 76–79 (1978). (in Russian)

    MATH  Google Scholar 

  24. van Bevern, R., Slugina, V.A.: A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem (2020). arXiv:2004.02437v2 [cs.DS]

  25. Karpinski, M., Lampis, M., Schmied, R.: New inapproximability bounds for TSP. J. Comput. Syst. Sci. 81(8), 1665–1677 (2015)

    MathSciNet  CrossRef  Google Scholar 

  26. Karlin, A.R., Klein, N., Gharan, S.O.: A (slightly) improved approximation algorithm for metric TSP (2020). arXiv:2007.01409

  27. Held, M., Karp, R.M.: The traveling salesman problem and minimum spanning trees. Oper. Res. 18, 1138–1162 (1970). https://doi.org/10.1007/BF01584070

    MathSciNet  CrossRef  MATH  Google Scholar 

  28. Sahni, S.: Approximate algorithms for the 0/1 knapsack problem. J. ACM 22, 115–124 (1975)

    MathSciNet  CrossRef  Google Scholar 

  29. Babat, L.G.: Linear functions on the N-dimensional unit cube. Dokl. Akad. Nauk SSSR 222, 761–762 (1975). (in Russian)

    MathSciNet  MATH  Google Scholar 

  30. Gens, G.V., Levner, E.V.: Fast approximation algorithms for job sequencing with deadlines. Discrete Appl. Math. 3, 313–318 (1981)

    CrossRef  Google Scholar 

  31. Lawler, E.L.: A fully polynomial approximation scheme for the total tardiness problem. Oper. Res. Lett. 1, 207–208 (1982)

    CrossRef  Google Scholar 

  32. Kovalyov, M.Y., Potts, C.N., Van Wassenhove, L.N.: A fully polynomial approximation scheme for scheduling a single machine to minimize total weighted late work. Math. Oper. Res. 19, 86–93 (1994)

    MathSciNet  CrossRef  Google Scholar 

  33. Kovalyov, M.Y., Kubiak, W.: A fully polynomial time approximation scheme for minimizing Makespan of deteriorating jobs. J. Heuristics 3, 287–297 (1998). https://doi.org/10.1023/A:1009626427432

    CrossRef  MATH  Google Scholar 

  34. Woeginger, G.J.: When does a dynamic programming formulation guarantee the existence of an FPTAS? INFORMS J. Comput. 12, 57–75 (2000)

    MathSciNet  CrossRef  Google Scholar 

  35. van Hoesel, C.P.M., Wagelmans, A.P.M.: Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems. Math. Oper. Res. 26, 339–357 (2001)

    MathSciNet  CrossRef  Google Scholar 

  36. Liu, S.C., Wu, C.C.: A faster FPTAS for a supply chain scheduling problem to minimize holding costs with outsourcing. Asia-Pac. J. Oper. Res. 33, 05 (2016)

    MathSciNet  MATH  Google Scholar 

  37. Kacem, I., Levner, E.: An improved approximation scheme for scheduling a maintenance and proportional deteriorating jobs. J. Ind. Manage. Optim. 12(3), 811–817 (2016)

    MathSciNet  MATH  Google Scholar 

  38. Yin, Y.Q., Xu, J.Y., Cheng, T.C.E., Wu, C.C., Wang, D.-J.: Approximation schemes for single-machine scheduling with a fixed maintenance activity to minimize the total amount of late work. Naval Res. Logist. 63(2), 172–183 (2016)

    MathSciNet  CrossRef  Google Scholar 

  39. Zhao, C.L., Hsu, C.-J.: Fully polynomial-time approximation scheme for single machine scheduling with proportional-linear deteriorating jobs. Eng. Optim. 51(11), 1938–1943 (2019)

    MathSciNet  CrossRef  Google Scholar 

  40. Halman, N., Klabjan, D., Li, C.-L., Orlin, J., Simchi-Levi, D.: Fully polynomial time approximation schemes for stochastic dynamic programs. SIAM J. Discrete Math. 28(4), 1725–1796 (2014)

    MathSciNet  CrossRef  Google Scholar 

  41. Schuurman, P., Woeginger, G.J.: Approximation schemes, a tutorial. Unpublished book (2002). http://www.math.nsc.ru/LBRT/k5/DEP/P.Schuurman,%20G.Woeginger.pdf

  42. Vishnevsky, V.M., Mikhailov, E.A., Tumchenok, D.A., Shirvanyan, A.M.: Mathematical model of the operation of a tethered unmanned platform under wind loading. Math. Models Comput. Simul. 12(4), 492–502 (2020). https://doi.org/10.1134/S2070048220040201

    MathSciNet  CrossRef  Google Scholar 

  43. Vishnevsky, V., Meshcheryakov, R.: Experience of developing a multifunctional tethered high-altitude unmanned platform of long-term operation. In: Ronzhin, A., Rigoll, G., Meshcheryakov, R. (eds.) ICR 2019. LNCS (LNAI), vol. 11659, pp. 236–244. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26118-4_23

    CrossRef  Google Scholar 

  44. Dinh, T.D., Vishnevsky, V., Larionov, A., Vybornova, A., Kirichek, R.: Structures and deployments of a flying network using tethered multicopters for emergencies. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2020. LNCS, vol. 12563, pp. 28–38. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-66471-8_3

    CrossRef  Google Scholar 

  45. Nawaz, H., Ali, H.M., Laghari, A.A.: UAV communication networks issues: a review. Arch. Comput. Methods Eng. 28(3), 1349–1369 (2020). https://doi.org/10.1007/s11831-020-09418-0

    CrossRef  Google Scholar 

  46. Khan, M.A., Qureshi, I.M., Safi, A., Khan, I.U.: Flying ad-hoc networks (FANETs): a review of communication architectures, and routing protocols. In: 1st International Conference on Latest Trends in Electrical Engineering and Computing Technologies (2017). https://www.researchgate.net/publication/311707613

  47. Kats, V., Levner, E.: Minimizing the number of robots to meet a given cyclic schedule. Ann. Oper. Res. 69, 209–226 (1997). https://doi.org/10.1023/A:1018980928352

    MathSciNet  CrossRef  MATH  Google Scholar 

  48. Kats, V., Levner, E.: Minimizing the number of vehicles in periodic scheduling: the non-Eucledean case. Eur. J. Oper. Res. 107, 371–377 (1998)

    CrossRef  Google Scholar 

  49. Kendall, D.G.: Some problems in the theory of queues. J. Roy. Statist. Soc. Ser. B 13, 151–185 (1951)

    Google Scholar 

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Levner, E., Vishnevsky, V. (2021). Recent Advances in Scheduling Theory and Applications in Robotics and Communications. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_2

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  • DOI: https://doi.org/10.1007/978-3-030-92507-9_2

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