# FUZZIFICATION OF THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM - A Fight against Nature

### Anikó Csébfalvi, György Csébfalvi, Sándor Danka

#### Abstract

In a recent article (Bhaskar et al., 2011) the authors proposed a heuristic method for the resource-constrained project scheduling problem (RCPSP) with fuzzy activity times. The apropos of this state-of-the-art work, we try identify and illuminate a popular misconception about fuzzification of RCPSP. The main statement of their approach, similarly to the other fuzzy approaches, is simple: the project completion time can be represented by a "good" fuzzy number. This statement is naturally true: in a practically axiomatic fuzzy thinking and model building environment, using only fuzzy operators and rules, we get a fuzzy output from the fuzzy inputs. But the real problem is deeper. The possibilistic (fuzzy) approach, traditionally, defines itself against the probabilistic approach, so in the "orthodox" fuzzy community everything is prohibited which is connected to somehow to the probability theory. For example, the Central Limit Theorem (CLT) is in the taboo list of this community. We have to emphasize, CLT is a humanized description of a miracle of nature. When we fight against CLT, we fight against nature. The situation in the "neologist" fuzzy community is not better, because they try to redefine somehow the probability theory within the fuzzy approach without using "forbidden" statistical terms. In this paper, we will show that the nature is working totally independently from our "magic" abstractions. According to the robustness of CLT, the distribution function of the completion time of real-size projects remains nearly normal, which is a manager friendly, natural and usable result. An abstraction and its "natural" operators are unable to modify the order of nature. When we want to add a practical scheduling method to the project managers we have to destroy the borders between the probabilistic and possibilistic approaches and have to define a "unified" approach to decrease the gap between scientific beliefs and reality. In this paper we present a unified (probabilistic/possibilistic) model for RCPSP with uncertain activity durations and a concept of a heuristic approach connected to the theoretical model. It will be shown, that the uncertainty management can be built into any heuristic algorithm developed to solve RCPSP with deterministic activity durations. The essence and viability of our unified model will be illustrated by a fuzzy example presented in the recent fuzzy RCPSP literature.

#### References

1. Alvarez-Valdés, R., Tamarit, J. M., 1993. The project scheduling polyhedron: Dimension, facets and lifting theorems, Journal of Operational Research, 96, 204- 220.
2. Bhaskar, T., Pal, M. N., Pal, A. K., 2011. A heuristic method for RCPSP with fuzzy activity times, European Journal of Operational Research, 208, 57- 66.
3. Csébfalvi, G., Csébfalvi, A., Szendroi, E., 2008. A harmony search metaheuristic for the resourceconstrained project scheduling problem and its multimode version, In Proceedings of the Eleventh International Workshop on Project Management and Scheduling, Istanbul, 56-59.

#### in Harvard Style

Csébfalvi A., Csébfalvi G. and Danka S. (2011). FUZZIFICATION OF THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM - A Fight against Nature . In Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011) ISBN 978-989-8425-83-6, pages 286-291. DOI: 10.5220/0003644402860291

#### in Bibtex Style

@conference{ecta11,
author={Anikó Csébfalvi and György Csébfalvi and Sándor Danka},
title={FUZZIFICATION OF THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM - A Fight against Nature},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011)},
year={2011},
pages={286-291},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003644402860291},
isbn={978-989-8425-83-6},
}

#### in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2011)
TI - FUZZIFICATION OF THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM - A Fight against Nature
SN - 978-989-8425-83-6
AU - Csébfalvi A.
AU - Csébfalvi G.
AU - Danka S.
PY - 2011
SP - 286
EP - 291
DO - 10.5220/0003644402860291