# A New Metaheuristic for Float Management in Resource-constrained Project Scheduling - A Bi-criteria Approach

### Roni Levi, Sándor Danka

#### Abstract

In this paper, we present a new unified theoretical model and the conception of the corresponding heuristic algorithm to solve several "what if" like float management problems in resource-constrained project scheduling. The traditional time-oriented resource-constrained project scheduling model for makespan minimization gives an optimal starting time set therefore an activity movement, may be able to destroy the resource-feasibility. The float management, as a stating base, needs a so-called forbidden-set oriented model (a forbidden-set oriented heuristic), which gives an optimal resource conflict repairing relation set. After inserting the additional predecessor-successor relations, in a optimal schedule every movable activity can be moved without destroying the resource feasibility. In the other side, when we have a forbidden-set oriented schedule, then according to the total free float, we have some freedom to redistribute the float among activities to answer several "what if" like questions. For example, in the planning phase we can investigate the consequences of a delay or a longer duration which may be caused by a notorious element of the "critical" activity subset. The unified float management as a new tool was built into the forbidden-set oriented Sounds of Silence (SoS) metaheuristic frame (Csébfalvi et al., 2008a). From theoretical point of view, float management is invariant to the applied heuristic frame; therefore it can be built into any other heuristic which is developed to solve forbidden-set oriented resource-constrained project scheduling problem (RCPSP). The toolbox can be completed by any other new element (float measure), which can be described as a linear programming (LP) or a simple mixed integer linear programming (MILP) problem on the set of the forbidden-set oriented (freely movable without resource-conflicts) solutions as a problem-specific redistribution of the total free float of the project. The essence and viability of our unified approach is illustrated by a set of examples.

#### References

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#### Paper Citation

#### in Harvard Style

Levi R. and Danka S. (2012). **A New Metaheuristic for Float Management in Resource-constrained Project Scheduling - A Bi-criteria Approach** . In *Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)* ISBN 978-989-8565-33-4, pages 290-293. DOI: 10.5220/0004152702900293

#### in Bibtex Style

@conference{ecta12,

author={Roni Levi and Sándor Danka},

title={A New Metaheuristic for Float Management in Resource-constrained Project Scheduling - A Bi-criteria Approach},

booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)},

year={2012},

pages={290-293},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004152702900293},

isbn={978-989-8565-33-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)

TI - A New Metaheuristic for Float Management in Resource-constrained Project Scheduling - A Bi-criteria Approach

SN - 978-989-8565-33-4

AU - Levi R.

AU - Danka S.

PY - 2012

SP - 290

EP - 293

DO - 10.5220/0004152702900293