A Metaheuristic Approach to the Resource Constrained Project Scheduling with Variable Activity Durations and Convex Cost Functions

  • Koji Nonobe
  • Toshihide Ibaraki
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 92)


We introduce a generalized model of the resource constrained project scheduling problem (RCPSP). It features that (i) the duration of an activity is not constant, but can vary in a specified range, and (ii) the objective is to minimize a convex function of time-lag costs, where a time-lag cost is charged according to the difference between the start/completion times of activities. These features achieve the flexibility of the model. It is known that, in the RCPSP, resource constraints can be replaced by some precedence constraints appropriately defined between the activities that require a common scarce resource. If we remove resource constraints by precedence constraints, our problem can be formulated as the dual problem of a minimum cost flow problem, and thus can be solved efficiently. Exploiting this property, we design a heuristic algorithm based on local search. We conducted computational experiments with benchmark instances to minimize the weighted earliness-tardiness costs, as well as instances in which activity-crashing or relaxation of temporal constraints are allowed. These results indicate the usefulness of our generalized RCPSP model and the proposed algorithm.


Resource constrained project scheduling convex objective functions variable activity durations metaheuristics 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Koji Nonobe
    • 1
  • Toshihide Ibaraki
    • 2
  1. 1.Department of Art and Technology, Faculty of EngineeringHosei UniversityKoganei, TokyoJapan
  2. 2.Department of Informatics, School of Science and TechnologyKwansei Gakuin UniversitySanda, HyogoJapan

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