Modelisation and resolution of a problem of resource pooling in a hospital context

Modelisation and resolution of a problem of resource pooling in a hospital context

Arnaud Laurent Laurent Deroussi Nathalie Grangeon Sylvie Norre 

LIMOS CNRS UMR 6158, Université Blaise Pascal Campus Universitaire des Cézeaux, 2 rue de la chebarde, TSA 60125, CS 60026,63173 Aubière Cedex, France

Corresponding Author Email: 
arnaud.laurent@isima.fr
Page: 
677-702
|
DOI: 
https://doi.org/10.3166/JESA.49.677-702
Received: 
25 June 2015
| |
Accepted: 
25 November 2015
| | Citation
Abstract: 

This article proposes a modelisation and a resolution of a problem of resource pooling in a hospital context. This problem is an extension of the Resource Constrained Project Scheduling Problem: the Multi-Site RCPSP with resource pooling in a multisite environment. This extension considers new constraints for the RCPSP like transportation times and choice of the site where tasks are executed. A linear program of this problem is given. Three resolution methods are described: local search, simulated annealing and Iterated Local Search with two different acceptance criteria: simulated annealing type acceptance criterion and better acceptance criterion. We compare the results obtained with each method. ILS with simulated annealing type acceptance criterion gives the best results.

Keywords: 

RCPSP, multi-Site, scheduling, transportation time, resource pooling, metaheuristic.

1. Introduction
2. Problématique
3. Les problèmes similaires de la littérature
4. Modélisation mathématique du RCPSP multi-site
5. Proposition de méthodes approchées
6. Expérimentations
7. Conclusion
  References

Bilge U., Ulusoy G. (1995). A time window approach to simultaneous scheduling of machines and material handling system in an fms. Operations Research, vol. 43, n" 6, p. 10581070

Blazewicz J., Lenstra J., Kan A. (1983). Scheduling subject to resource constraints:

classification and complexity. Discrete Applied Mathematics, vol. 5,n1,p.1124

Carlier J. (1984). Problèmes diordonnancement à contraintes de ressources : algorithmes et complexité. Thèse de doctorat, Université Paris VI, Paris.

Chassiakos A., Sakellaropoulos S. (2005). Time-cost optimization of construction projects with generalized activity constraints. Journal of Construction Engineering and Management, vol. 131,n10,p.11151124

Correia I., Lourenço L. L., Gama F. Saldanha-da. (2012). Project scheduling with flexible resources: formulation and inequalities. OR spectrum, vol. 34,n3,p.635663

Michael R. Garey and David S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of Np-Completeness. W. H. Freeman \& Co., New York, NY, USA.

Gourgand M., Grangeon N., Klement N. (2014). Activities planning and resource assignment on multi-place hospital system: Exact and approach methods adapted from the bin packing problem. In 7 th international conference on health informatics, p. 117124 Angers, France.

Hwang J., Chow Y., Anger F., Lee C. (1989). Scheduling precedence graphs in systems with interprocessor communication times. SLAM Joumal on Computing, vol. 18,n2,p.244257

Johnson S. M. (1954). Optimal two-and three-stage production schedules with setup times included. Naval research logistics quarterly, vol. 1, n " , p. 61-68.

Kan A. R. (2012). Machine scheduling problems: classification, complexity and (2012). Machine schedling computations. Springer Science \& Business Media.

Kirkpatrick S. (1984). Optimization by simulated annealing: Quantitative studies. Joumal of statisticalphysics, vol 34, ne 5-6, p. 975-986.

Kise H. (1991). On an automated two-machine flowshop scheduling problem with infinite buffer. J. Oper. Res. Soc. Japan, vol. 34, p. 354-361. 

Klein R (2000). Project scheduling with time-varying resource constraints. Intermational Joumal of Production Research, vol. 38,n16,p.39373952 

Klein R. Scholl A. (1999). Computing lower bounds by destnuctive improvement: An application to resource-constrained project scheduling. European Joumal of Operational Research, vol 112,n2,p.322346

Klein R. Scholl A (2000). Progress: Optimally solving the generalized resource-constrained project scheduling problem Mathematical Methods of Operations Research, vol. 52,n3 p. 467488.

Kolisch R. (1998). Integrated scheduling, assembly area- and part-assignment for large scale, make-to-order assemblies. International Joumal of Production Economics, vol. 64 p. 127-141.

Langston M. A. (1987). Interstage transportation planning in the deterministic flow-shop environment. Operations Research, vol. 35, n"4, p. 556-564. 

Lee C.-Y., Chen Z-L. (2001). Machine scheduling with transportation considerations. Joumal of Scheduling, vol. 4, n 1, p. 324 

Lombardi M. Milano M. (2009). A precedence constraint posting approach for the rcpsp with time lags and variable durations. In I Gent (Ed), Principles and practice of constratint programmmg - cp 2009, vol 5732, p. 569583. Springer Berlin Heidellberg 

Lourenço H. R, Martin O. C., Stutzle T. (2003). Handbook of metaheruristics. In F. Glover, G. Kochenberger (Eds), p. 321-353. Kluwers Academic Publishers. 

Maggu P., Das G. (1980). On 2x n sequencing problem with transportation times of jobs. Pure and Applied Mathematika Sciences, vol. 12, n" 1, p. 219-227. 

Maggu P. L., Das G., Kumar R. (1981). On equivalent-job for job-block in 2x n sequencing problem with transportation-times. Joumal of the Operations Research Soctety of Japan, vol. 24,n2,p.136146

Maggu P. L., Smghal M. L., Mohammad N., Yadav S. K. (1982, sep). On n-job, 2-machine flow-shop scheduling problem with arbitrary time lags and transportation times of jobs. Joumal of the Operations Research Society of Japan, vol 25,n3,p.219227 

Metropolis N., Rosenbluth A. W., Rosenbluth M. N., Teller A. H, Teller E. (1953). Equation of state calculations by fast computing machines. The joumal of chemical physics, vol 21, n^ 6, p. 1087-1092.

Mitten L. (1959). Sequencing n jobs on two machines with arbitrary time lags. Management science, vol. 5, n 13, p. 293298

Norre S. (1993). Problèmes de placement de táches: méthodes stochastique et evaluation des performances. These de doctorat, Université Blaise Pascal, Clermont-Ferrand.

Ogũz O... Bala H. (1994). A comparative study of computational procedures for the re- source constrained project scheduling problem European Joumal of Operational Research, vol 72,n2,p406416