Tight Low-Complexity Approximation for the QmCmax Problem via Mathematical Programming Modeling

Published Online:https://doi.org/10.1287/ijoc.2025.1129

References

  • Berndt S, Brinkop H, Jansen K, Mnich M, Stamm T (2023) New support size bounds for integer programming, applied to makespan minimization on uniformly related machines. Iwata S, Kakimura N, eds. 34th Internat. Sympos. Algorithms Comput. (ISAAC 2023), Leibniz International Proceedings in Informatics (LIPIcs), vol. 283 (Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl, Germany), 13:1–13:18.Google Scholar
  • Burkard R, He Y (1998) A note on multifit scheduling for uniform machines. Computing 61(3):277–283.CrossrefGoogle Scholar
  • De Bontridder K, Halldórsson B, Halldórsson M, Hurkens C, Lenstra J, Ravi R, Stougie L (2021) Local improvement algorithms for a path packing problem: A performance analysis based on linear programming. Oper. Res. Lett. 49(1):62–68.CrossrefGoogle Scholar
  • Della Croce di Dojola F (2016) MP or not MP: That is the question. J. Scheduling 19(1):33–42.CrossrefGoogle Scholar
  • Della Croce di Dojola F, Scatamacchia R (2020) The longest processing time rule for identical parallel machines revisited. J. Scheduling 23(2):163–176.CrossrefGoogle Scholar
  • Dobson G (1984) Scheduling independent tasks on uniform processors. SIAM J. Comput. 13(4):705–716.CrossrefGoogle Scholar
  • Fishkin A, Jansen K, Mastrolilli M (2008) Grouping techniques for scheduling problems: Simpler and faster. Algorithmica 51(2):183–199.CrossrefGoogle Scholar
  • Friesen D (1987) Tighter bounds for LPT scheduling on uniform processors. SIAM J. Comput. 16(3):554–560.CrossrefGoogle Scholar
  • Friesen D, Langston M (1983) Bounds for multifit scheduling on uniform processors. SIAM J. Comput. 12(1):60–70.CrossrefGoogle Scholar
  • Gonzalez T, Ibarra O, Sahni S (1977) Bounds for LPT schedules on uniform processors. SIAM J. Comput. 6(1):155–166.CrossrefGoogle Scholar
  • Graham R (1969) Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17(2):416–429.CrossrefGoogle Scholar
  • Graham R, Lawler E, Lenstra J, Rinnooy Kan A (1979) Optimization and approximation in deterministic sequencing and scheduling: A survey. Hammer P, Johnson E, Korte B, eds. Discrete Optimization II, Annals of Discrete Mathematics, vol. 5 (North-Holland, Amsterdam), 287–326.CrossrefGoogle Scholar
  • Horowitz E, Sahni S (1976) Exact and approximate algorithms for scheduling nonidentical processors. J. Assoc. Comput. Machinery 23(2):317–327.CrossrefGoogle Scholar
  • Jansen K, Porkolab L (2001) Improved approximation schemes for scheduling unrelated parallel machines. Math. Oper. Res. 26(2):324–338.LinkGoogle Scholar
  • Kononov A, Kononova P, Gordeev A (2020) Branch-and-bound approach for optima localization in scheduling multiprocessor jobs. Internat. Trans. Oper. Res. 27(1):381–393.CrossrefGoogle Scholar
  • Koulamas C, Kyparisis G (2009) A modified LPT algorithm for the two uniform parallel machine makespan minimization problem. Eur. J. Oper. Res. 196(1):61–68.CrossrefGoogle Scholar
  • Kovács A (2010) New approximation bounds for LPT scheduling. Algorithmica 57(2):413–433.CrossrefGoogle Scholar
  • Mireault P, Orlin J, Vohra R (1997) A parametric worst case analysis of the LPT heuristic for two uniform machines. Oper. Res. 45(1):116–125.LinkGoogle Scholar
  • Mitsunobu T, Suda R, Suppakitpaisarn V (2024) Worst-case analysis of LPT scheduling on a small number of non-identical processors. Inform. Processing Lett. 183:106424.CrossrefGoogle Scholar
  • Savant Aira L, Scatamacchia R, Della Croce di Dojola F (2025) Tight low-complexity approximation for the Qm‖Cmax problem via mathematical programming modeling. https://doi.org/10.1287/ijoc.2025.1129.cd, https://github.com/INFORMSJoC/2025.1129.Google Scholar
  • Sevastianov S, Tchernykh I (1998) Computer-aided way to prove theorems in scheduling. Bilardi G, Italiano GF, Pietracaprina A, Pucci G, eds. Algorithms—ESA ’98: 6th Annual Eur. Sympos., Proceedings, Lecture Notes in Computer Science, vol. 1461 (Springer, Berlin, Heidelberg), 502–513.Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.