Abstract
The anchored rescheduling problem, recently introduced in the literature, is to find a schedule under precedence constraints with a maximum number of prescribed starting times. Namely, prescribed starting times may correspond to a former schedule that must be modified while maintaining a maximum number of starting times unchanged. In the present work two extensions are investigated. First we introduce a new tolerance feature, so that starting times can be considered as unchanged when modified less than a tolerance threshold. The sensitivity of the anchored rescheduling problem to tolerance is studied. Second we consider generalized precedence constraints, which include, e.g., deadline constraints. Altogether this leads to a more realistic rescheduling problem. The main result is to show that the problem is polynomial. We discuss how to benefit from the polynomiality result in a machine scheduling environment.
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References
Bendotti, P., Chrétienne, P., Fouilhoux, P., Quilliot, A.: Anchored reactive and proactive solutions to the CPM-scheduling problem. Eur. J. Oper. Res. 261, 67–74 (2017)
Pinedo, M.: Scheduling: Theory, Algorithms, and Systems. Prentice Hall, Upper Saddle River (2002)
Herroelen, W., Leus, R.: Robust and reactive project scheduling: a review and classification of procedures, p. 42. Katholieke Universiteit Leuven, Open Access publications from Katholieke Universiteit Leuven, April 2004
Smith, S.F.: Reactive Scheduling Systems. In: Brown, D.E., Scherer, W.T. (eds.) Intelligent Scheduling Systems. Operations Research/Computer Science Interfaces Series, vol. 3, pp. 155–192. Springer, Boston (1995). https://doi.org/10.1007/978-1-4615-2263-8_7
Sakkout, H., Wallace, M.: Probe backtrack search for minimal perturbation in dynamic scheduling. Constraints 5, 359–388 (2000)
Calhoun, K., Deckro, R., Moore, J., Chrissis, J., Hove, J.: Planning and re-planning in project and production scheduling. Omega 30, 155–170 (2002)
Artigues, C., Roubellat, F.: A polynomial activity insertion algorithm in a multi-resource schedule with cumulative constraints and multiple modes. Eur. J. Oper. Res. 127(2), 297–316 (2000)
Herroelen, W., Leus, R.: Project scheduling under uncertainty: survey and research potentials. Eur. J. Oper. Res. 165, 289–306 (2002)
Herroelen, W., Leus, R.: The construction of stable project baseline schedules. Eur. J. Oper. Res. 156(3), 550–565 (2004)
Bendotti, P., Chrétienne, P., Fouilhoux, P., Pass-Lanneau, A.: The anchor-robust project scheduling problem, May 2019. https://hal.archives-ouvertes.fr/hal-02144834. Working paper or preprint
Liebchen, C., Lübbecke, M., Möhring, R., Stiller, S.: The concept of recoverable robustness, linear programming recovery, and railway applications. Robust Online Large-Scale Optim. 5868, 1–27 (2009)
D’Angelo, G., Di Stefano, G., Navarra, A., Pinotti, C.: Recoverable robust timetables: an algorithmic approach on trees. IEEE Trans. Comput. 60, 433–446 (2011)
Schieber, B., Shachnai, H., Tamir, G., Tamir, T.: A theory and algorithms for combinatorial reoptimization. Algorithmica 80(2), 576–607 (2018)
Şeref, O., Ahuja, R.K., Orlin, J.B.: Incremental network optimization: theory and algorithms. Oper. Res. 57(3), 586–594 (2009)
Dilworth, R.P.: A decomposition theorem for partially ordered sets. Ann. Math. 51(1), 161–166 (1950)
Schrijver, A.: Combinatorial Optimization - Polyhedra and Efficiency. Springer, Heidelberg (2003)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., New York (1979)
Chrétienne, P.: Reactive and proactive single-machine scheduling to maintain a maximum number of starting times. Ann. Oper. Res. 1–14 (2018). https://hal.sorbonne-universite.fr/hal-02078478
Bruni, M., Di Puglia Pugliese, L., Beraldi, P., Guerriero, F.: An adjustable robust optimization model for the resource-constrained project scheduling problem with uncertain activity durations. Omega 71, 66–84 (2016)
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Bendotti, P., Chrétienne, P., Fouilhoux, P., Pass-Lanneau, A. (2020). Anchored Rescheduling Problems Under Generalized Precedence Constraints. In: Baïou, M., Gendron, B., Günlük, O., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2020. Lecture Notes in Computer Science(), vol 12176. Springer, Cham. https://doi.org/10.1007/978-3-030-53262-8_13
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