Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-02T22:31:29.517Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow Polyhedra and Resource Constrained Project Scheduling Problems

Published online by Cambridge University Press:  21 December 2012

Alain Quilliot  and
Hélène Toussaint
Alain Quilliot
Affiliation:
LIMOS, UMR CNRS 6158, Bat. ISIMA, Université Blaise Pascal, Campus des Cézeaux, BP 125, 63173 Aubiere, France. [email protected]
Get access

Abstract

This paper aims at describing the way Flow machinery may be used in order to deal with Resource Constrained Project Scheduling Problems (RCPSP). In order to do it, it first introduces the Timed Flow Polyhedron related to a RCPSP instance. Next it states several structural results related to connectivity and to cut management. It keeps on with a description of the way this framework gives rise to a generic Insertion operator, which enables programmers to design greedy and local search algorithms. It ends with numerical experiments.

Keywords

Scheduling with resource constraintsnetwork flow theory
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 4 , October 2012 , pp. 373 - 409
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

Abbasi, B., Shadrokh, S. and Arkat, J., Bi-objective resource-constrained project scheduling with robustness and makespan criteria. Appl. Math. Comput. 180 (2006) 146–152. Google Scholar
Ahuja, R.K., Magnanti, T.L., Orlin, J.B. and Reddy, M.R., Applications of network optimization, in Network Models (Chapter 1). Handbooks Oper. Res. Manage. Sci. 7 (1995) 1–83. Google Scholar
R.V. Ahuja, T.L. Magnanti and J.B. Orlin. Network flows : theory, algorithms and applications. Prentice hall, Englewood Cliffs, N.J (1993).
Alcaraz, J. and Maroto, C., A robust genetic algorithm for resource allocation in project scheduling. Ann. Oper. Res. 102 (2001) 83–109. Google Scholar
J. Alcaraz, C. Maroto and R. Ruiz, Improving the performance of genetic algorithms for the RCPSP problem, in Proc. 9th Int. workshop on project management and scheduling (2004) 40–43.
Artigues, C. and Roubellat, F., A polynomial activity insertion algorithm in a multiresource schedule with cumulative constraints and multiple nodes. EJOR 127 (2000) 297–316. Google Scholar
Artigues, C., Michelon, P. and Reusser, S., Insertion techniques for static and dynamic resource constrained project scheduling. EJOR 149 (2003) 249–267. Google Scholar
Artigues, C. and Briand, C., The resource-constrained activity insertion problem with minimum and maximum time lags. J. Schedul. 12 (2009) 447–460. Google Scholar
K.R. Baker, Introduction to sequencing and scheduling. Wiley, N.Y (1974).
P. Baptiste, Resource constraints for preemptive and non preemptive scheduling, MSC Thesis, University PARIS VI (1995).
Baptiste, P. and Demassey, S., Tight LP-bounds for resource constrained project scheduling. OR Spectrum 26 (2004) 251–262. Google Scholar
P. Baptiste, P. Laborie, C. Lepape and W. Nuijten, Constraint-based scheduling and planning, in Handbook of Constraint Programming 22, edited by F. Rossi, P. Van Beek. Elsevier (2006) 759–798.
T. Baar, P. Brucker and S. Knust, Tabu-search algorithms and lower bounds for the resource-constrained project scheduling problem, in Meta-heuristics : Advances and trends in local search paradigms for optimization, edited by S. Voss, S. Martello, I. Osman and C. Roucairol. Kluwer Academic Publishers (1998) 1–8.
C. Berge, Graphes et Hypergraphes. Dunod Ed (1975).
J. Blazewiecz, K.H. Ecker, G. Schmlidt and J. Weglarcz, Scheduling in computer and manufacturing systems. 2th edn, Springer-Verlag, Berlin (1993).
Bouleimen, K. and Lecocq, H., A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode version. EJOR 149 (2003) 268–281. Google Scholar
C. Briand, A new any-order schedule generation scheme for resource-constrained project scheduling. RAIRO - Oper. Res. (2009) 297–308.
Brucker, P. and Knust, S., A linear programming and constraint propagation based lower bound for the RCPSP. EJOR 127 (2000) 355–362. Google Scholar
Brucker, P., Knust, S., Schoo, A. and Thiele, O., A branch and bound algorithm for the resource constrained project scheduling problem. EJOR 107 (1998) 272–288. Google Scholar
Brucker, P., Drexl, A., Mohring, R., Neumann, K. and Pesch, E., Resource-constrained project scheduling : notation, classification, models and methods. EJOR 112 (1999) 3–41. Google Scholar
J. Carlier and P. Chrétienne. Problèmes d’ordonnancements : modélisation, complexité et algorithmes. Masson Ed, Paris (1988).
Carlier, J. and Neron, E., Computing redundant resources for the resource constrained project scheduling problem. EJOR 176 (2007) 1452–1463. Google Scholar
Carlier, J. and Neron, E., On linear lower bounds for the resource constrained project scheduling problem. EJOR 149 (2003) 314–324. Google Scholar
H. Chtourou and M. Haouari, A two-stage-priority rule based algorithm for robust resource-constrained project scheduling. Comput. Indust. Engin. 12 (2008).
N. Chistophides and C.A. Whitlock, Network synthesis with connectivity constraint : a survey. Oper. Res. (1981) 705–723.
J. Coelho and L. Tavares, Comparative analysis of metaheuricstics for the resource constrained project scheduling problem. Technical report, Department of Civil Engineering, Instituto Superior Tecnico, Portugal (2003).
Dahl, G. and Stoer, M., A polyhedral approach to multicommodity survivable network design. Numerische Math. 68 (1994) 149–167. Google Scholar
J. Damay, Techniques de resolution basées sur la programmation linéaire pour l’ordonnancement de projet. PH.D. Thesis, Université de CLERMONT-FERRAND (2005).
J. Damay, A. Quilliot and E. Sanlaville, Linear programming based algorithms for preemptive and non preemptive RCPSP. EJOR 182 1012–1022. (2007).
Demassey, S., Artigue, C. and Michelon, P., Constraint–propagation-based cutting planes : an application to the resource-constrained-project-scheduling problem. INFORMS J. Comput. 17 (2005) 1. Google Scholar
Demeulemeester, E. and Herroelen, W., New benchmark results for the multiple RCPSP. Manage. Sci. 43 (1997) 1485–1492. Google Scholar
De Reyck, B. and Herroelen, W., A branch and bound procedure for the resource-constrained project scheduling problem with generalized precedence relations. EJOR 111 (1998) 152–174. Google Scholar
Djellab, K., Scheduling preemptive jobs with precedence constraints on parallel machines. EJOR 117 (1999) 355-367. Google Scholar
Dolev, D. and Warmuth, M.K., Scheduling DAGs of bounded heights. J. Algor. 5 (1984) 48–59. Google Scholar
Debels, D., De Reyck, B., Leus, R., Vanhoucke, M., A hybrid scatter search/electromagnetism meta-heuristic for project scheduling. EJOR 169 (2006) 638–653. Google Scholar
Dushnik, B. and Miller, W., Partially ordered sets. Amer. J. Math. 63 (1941) 600–610. Google Scholar
Fortemps, P. and Hapke, M., On the disjunctive graph for project scheduling. Foundat. Comput. Decis. Sci. 22 (1997) 195–209. Google Scholar
Fulkerson, D.R. and Gross, J.R., Incidence matrices and interval graphs. Pac. J. Maths 15 (1965) 835–855. Google Scholar
Grahamson, R.L., Lawler, E.L., Lenstra, J.K. and Rinnoy-Khan, A.H.G., Optimization and approximation in deterministic scheduling : a survey. Annal. Disc. Math. 5 (1979) 287–326. Google Scholar
Hartmann, S. and Briskorn, D., A survey of variants and extensions of the resource-constrained project scheduling problem. Europ. J. Operat. Res. 207 (2010) 1–14. Google Scholar
W. Herroelen, E. Demeulemeester and B. de Reyck, A classification scheme for project scheduling, in Project Scheduling : recent models, algorithms and applications. Kluwer Acad Publishers (1999) 1–26.
Herroelen, W., Project Scheduling-Theory and Practice. Prod. Oper. Manag. 14 (2006) 413–432. Google Scholar
Haouari, M., Gharbi, A., A improved max-flow based lower bound for minimizing maximum lateness on identical parallele machines. Operat. Res. Lett. 31 (2003) 49–52 . Google Scholar
Josefowska, J., Mika, M., Rozycki, R., Waligora, G., Weglarcz, J., An almost optimal heuristic for preemptive Cmax scheduling of dependant task on parallel identical machines. Annal. OR 129 (2004) 205–216. Google Scholar
Kolisch, R. and Drexl, A., Adaptive search for solving hard project scheduling problems. Naval Res. Logist. 43 (1996) 23–40. Google Scholar
Kolisch, R. and Hartmann, S., Experimental investigation of heuristics for the resource constrained scheduling problem : an update. EJOR 174 (2006) 23–37. Google Scholar
A. Kimms, Mathematical programming and financial objectives for scheduling projects. Oper. Res. Manag. Sci. Kluwer Academic Publisher (2001).
Kolisch, R., Sprecher, A. and Drexel, A., Characterization and generation of a general class of resource constrained project scheduling problems. Manag. Sci. 41 (1995) 1693–1703. Google Scholar
Kolisch, R., Serial and parallel resource-constrained project scheduling methods revisited : Theory and computation. Eur. J. Oper. Res. 90 (1996) 320–333. Google Scholar
Kolisch, R., R. Padman. An integrated survey of deterministic project scheduling. Omega 48 (1999) 249–272. Google Scholar
R. Kolisch and S. Hartmann, Heuristic algorithms for solving the resource-constrained project scheduling problem : classification and computational analysis, in edited by J. Weglarcz. Project Scheduling : recent models, algorithms and applications, Kluwer Acad Press (1999).
Y. Kochetov and A. Stolyar, Evolutionnary local search with variable neighbourhood for the resource constrained scheduling problem, in Proc. 3 th int. Conf. Computer Sciences and Information Technologies, Russia (2003).
E.L. Lawler, K.J. Lenstra, A.H.G. Rinnoy-Kan and D.B. Schmoys, Sequencing and scheduling : algorithms and complexity, in Handbook of Operation Research and Management Sciences, Vol 4 : Logistics of Production and Inventory, edited by S. C. GRAVES, A.H.G. Rinnoy-kan, P.H. Zipkin. North-Holland (1993) 445–522.
R. Leus and W. Herroelen, Stability and resource allocation in project planning. IIE transactions. 36 (2004) 1–16.
Leon, V.J. and Ramamoorthy, B., Strength and adaptability of problem-space based neighborhoods for resource-constrained scheduling. OR Spektrum 17 (1995) 173–182. Google Scholar
Mingozzi, A., Maniezzo, V., Ricciardelli, S. and Bianco, L., An exact algorithm for project scheduling with resource constraints based on a new mathematical formulation. Manage. Sci. 44 (1998) 714–729. Google Scholar
Minoux, M., Network synthesis and optimum network design problems : models, solution methods and application. Networks 19 (1989) 313–360. Google Scholar
P.B. Mirchandani and R.L. Francis, Discrete location theory. John Wiley and sons (1990).
Mohring, R.H. and Rademacher, F.J., Scheduling problems with resource duration interactions. Methods Oper. Res. 48 (1984) 423–452. Google Scholar
Moukrim, A. and Quilliot, A., Optimal preemptive scheduling on a fixed number of identical parallel machines. Oper. Res. Lett. 33 (2005) 143–151. Google Scholar
Moukrim, A. and Quilliot, A., A relation between multiprocessor scheduling and linear programming. Order 14 (1997) 269–278. Google Scholar
Muntz, R.R. and Coffman, E.G., Preemptive scheduling of real time tasks on multiprocessor systems. J. ACM 17 (1970) 324–338. Google Scholar
K. Neumann, C. Schwindt and J. Zimmermann, Project scheduling with time windows and scarce resources. Springer, Berlin (2003).
K. Nonobe and T. Ibaraki, Formulation and tabu search algorithm for the resource constrained project scheduling problem. In C.C. Ribeiro and P. Hansen, editors, Essays and surveys in metaheuristics. Kluwer Academic Publishers, Dordrecht (2002) 557–588.
Palpant, M., Artigues, C. and Michelon, P., LSSPER : solving the resource-constrained project scheduling problem with large neighbourhood search. Ann. Oper. Res. 131 (2004) 237–257. Google Scholar
Papadimitriou, C.H. and Yannanakis, M., Scheduling interval ordered tasks. SIAM J. Comput. 8 (1979) 405–409. Google Scholar
P.M. Pardalos and D.Z. Du, Network design : connectivity and facility location. DIMACS Series 40, N.Y, American Math Society (1998).
Patterson, J.H., A comparizon of exact approaches for solving the multiple constrained resource project scheduling problem. Manag. Sci. 30 (1984) 854–867. Google Scholar
Sauer, N. and Stone, M.G., Rational preemptive scheduling. Order 4 (1987) 195–206. Google Scholar
Sauer, N. and Stone, M.G., Preemptive scheduling of interval orders is polynomial. Order 5 (1989) 345–348. Google Scholar
Schirmer, A., Case-based reasoning and improved adaptive search for project scheduling. Naval Res. Logist. 47 (2000) 201–222. Google Scholar
Liu, S.S. and Wang, C.J., Resource-constrained construction project scheduling model for profit maximization considering cash flow. Automat. Constr. 17 (2008) 966–974. Google Scholar
Tormos, P. and Lova, A., Project scheduling with time varying resource constraints. Int. J. Prod. Res. 38 (2000) 3937–3952. Google Scholar
Tormos, P. and Lova, A., A competitive heuristic solution technique for resource-constrained project scheduling. Ann. Oper. Res. 102 (2001) 65–81. Google Scholar
Tormos, P. and Lova, A., An efficient multi-pass heuristic for project scheduling with constrained resources. Int. J. Prod. Res. 41 (2003) 1071–1086. Google Scholar
P. Tormos and A. Lova, Integrating heuristics for resource constrained project scheduling : One step forward. Technical report, Department of Statistics and Operations Research, University of Valencia (2003).
V. Valls, F. Ballestin and S. Quintanilla, A hybrid genetic algorithm for the RCPSP. Technical report, Department of Statistics and Operations Research, University of Valencia (2003).
Valls, V., Ballestin, B. and Quintanilla, S., Justification and RCPSP : a technique that pays. EJOR 165 (2005) 375–386. Google Scholar
P. Van Hentenryk, Constraint Programming. North Holland (1997).