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Optimization guided lower and upper bounds for the resource investment problem

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  • Drexl, Andreas
  • Kimms, Alf

Abstract

The resource investment problem deals with the issue of providing resources to a project such that a given deadline can be met. The objective is to make the resources available in the cheapest possible way. For each resource, expenses depend on the maximum amount required during the course of the project. In this paper we develop two lower bounds for this NP-hard problem using Lagrangean relaxation and column generation techniques, respectively. Both procedures are capable of yielding feasible solutions as well. Hence, we also have two optimization guided heuristics. A computational study consisting of a set of 3210 instances compares both approaches and allows insight into the performance. E.g., for the instances from Möhring's test set it turns out that in 56% of the cases the heuristic solution derived on the basis of Lagrangean relaxation is optimal. Using column generation, the gap between the lower bound and the optimum objective function value is below 5% in 50% of the cases, it is below 10% in 71% of the cases, and it is below 20% in all cases.

Suggested Citation

  • Drexl, Andreas & Kimms, Alf, 1998. "Optimization guided lower and upper bounds for the resource investment problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 481, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    • Handle: RePEc:zbw:cauman:481
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    References listed on IDEAS

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    1. Erik Demeulemeester, 1995. "Minimizing Resource Availability Costs in Time-Limited Project Networks," Management Science, INFORMS, vol. 41(10), pages 1590-1598, October.
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    3. Rainer Kolisch & Arno Sprecher & Andreas Drexl, 1995. "Characterization and Generation of a General Class of Resource-Constrained Project Scheduling Problems," Management Science, INFORMS, vol. 41(10), pages 1693-1703, October.
    4. Ron Shamir, 1987. "The Efficiency of the Simplex Method: A Survey," Management Science, INFORMS, vol. 33(3), pages 301-334, March.
    5. Drexl, Andreas & Kimms, Alf, 1998. "Minimizing total weighted completion times subject to precedence constraints by dynamic programming," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 475, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
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