Scheduling arc shut downs in a network to maximize flow over time with a bounded number of jobs per time period
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We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the period in which its maintenance is scheduled, making its capacity zero for that period. A set of arcs is designated to have maintenance during the planning period, which will require each to be shut down for exactly one time period. In general this problem is known to be NP-hard, and several special instance classes have been studied. Here we propose an additional constraint which limits the number of maintenance jobs per time period, and we study the impact of this on the complexity.
KeywordsNetwork models Complexity theory Maintenance scheduling Mixed integer programming
Mathematics Subject Classification90C10 90B10 68Q25
We would like to thank two anonymous referees for valuable comments that significantly improved the presentation of our results, in particular the proof of Proposition 2. This research was supported by the ARC Linkage Grants Nos. LP0990739 and LP1102000524 and HVCCC P/L.
- Boland N, Kalinowski T, Waterer H, Zheng L (2011) An optimisation approach to maintenance scheduling for capacity alignment in the Hunter Valley coal chain. In: Baafi EY, Kininmonth RJ, Porter I (eds) Proceedings of the 35th APCOM symposium: applications of computers and operations research in the minerals industry, The Australasian Institute of Mining and Metallurgy Publication Series, pp 887–897Google Scholar
- Boland N, McGowan B, Mendes A, Rigterink F (2013) Modelling the capacity of the Hunter Valley coal chain to support capacity alignment of maintenance activities. In: Piantadosi J, Anderssen RS, Boland J (eds) MODSIM2013, 20th international congress on modelling and simulation, Modelling and Simulation Society of Australia and New Zealand, pp 3302–3308Google Scholar
- Boland N, Savelsbergh MWP (2011) Optimizing the Hunter Valley coal chain. In: Gurnani H, Mehrotra A, Ray S (eds) Supply chain disruptions: theory and practice of managing risk. Springer-Verlag, London Ltd., LondonGoogle Scholar
- Gabow HN (1990) Data structures for weighted matching and nearest common ancestors with linking. In: Proceedings of the 1st ACM-SIAM symposium on discrete algorithms, SODA 1990, pp 434–443Google Scholar
- Kotnyek B (2003) An annotated overview of dynamic network flows. Technical Report 4936, INRIAGoogle Scholar
- Lidén T (2014) Survey of railway maintenance activities from a planning perspective and literature review concerning the use of mathematical algorithms for solving such planning and scheduling problems. Technical report, Linköpings universitetGoogle Scholar
- Nurre SG (2013) Integrated network design and scheduling problems: Optimization algorithms and applications. PhD thesis, Rensselaer Polytechnic Institute. online: http://search.proquest.com/docview/1466024106
- Orlin JB (2013) Max flows in \(O(nm)\) time, or better. In: Proceedings of the 45th ACM symposium on theory of computing (STOC 2013), ACM, pp 765–774Google Scholar