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Horizontally Elastic Edge-Finder Algorithm for Cumulative Resource Constraint Revisited

Author

Listed:
  • Sévérine Fetgo Betmbe

    (University of Dschang)

  • Clémentin Tayou Djamegni

    (University of Dschang
    University of Dschang)

Abstract

The success of constraint programming on scheduling problems comes from the low complexity and power of propagators. The data structure Profile recently introduced by Gingras and Quimper in Generalizing the edge-finder rule for the cumulative constraint. In: IJCAI, IJCAI/AAAI Press, pp 3103–3109, 2016, when applied to the edge-finder rule for the cumulative resource constraint (which we call horizontally elastic edge-finder) has improved the filtering power of this rule. In this paper, the algorithm proposed by Gingras and Quimper in Generalizing the edge-finder rule for the cumulative constraint. In: IJCAI, IJCAI/AAAI Press, pp 3103–3109, 2016 is revisited. It is proved that the data structure Profile can be further used for more adjustments. A new formulation of the horizontally elastic edge-finder rule is put forward. Similar to Gingras and Quimper in Generalizing the edge-finder rule for the cumulative constraint. In: IJCAI, IJCAI/AAAI Press, pp 3103–3109, 2016, an $$\mathcal {O}(kn^2)$$ O ( k n 2 ) algorithm (where n is the number of tasks sharing the resource and $$k\le n$$ k ≤ n , the number of distinct capacities required by tasks) based on new attributes of the Profile data structure is proposed for the new rule. Experimental results on instances of Resource-Constrained Project Scheduling Problems (RCPSPs) from the benchmark suites highlight that using this new algorithm reduces the number of backtracks for the majority of instances with a slight increase in running time.

Suggested Citation

  • Sévérine Fetgo Betmbe & Clémentin Tayou Djamegni, 2022. "Horizontally Elastic Edge-Finder Algorithm for Cumulative Resource Constraint Revisited," SN Operations Research Forum, Springer, vol. 3(4), pages 1-32, December.
    • Handle: RePEc:spr:snopef:v:3:y:2022:i:4:d:10.1007_s43069-022-00172-6
    DOI: 10.1007/s43069-022-00172-6
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    References listed on IDEAS

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    1. Carlier, J. & Neron, E., 2003. "On linear lower bounds for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 149(2), pages 314-324, September.
    2. Luc Mercier & Pascal Van Hentenryck, 2008. "Edge Finding for Cumulative Scheduling," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 143-153, February.
    3. Roger Kameugne & Laure Pauline Fotso, 2013. "A cumulative not-first/not-last filtering algorithm in O(n 2log(n))," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 95-115, February.
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