. Parmi-celles-citées, on trouve le raisonnement Edge-Fiding étendu, le Time-Table-Edge-Finding et le Time-Table disjonctif. A l'inverse du raisonnement énergétique, ces règles sont très utilisées en pratique car leur complexité est relativement faible

. Dans-le-prochain-chapitre, nous présenterons l'adaptation de plusieurs de ces raisonnements dans le cadre du CECSP

C. Artigues, P. Brucker, S. Knust, O. Koné, P. Lopez et al., A note on ???event-based MILP models for resource-constrained project scheduling problems???, Computers & Operations Research, vol.40, issue.4, pp.1060-1063, 2013.
DOI : 10.1016/j.cor.2012.10.018

URL : https://hal.archives-ouvertes.fr/hal-00918016

[. Artigues, S. Demassey, and E. Néron, Resource-Constrained Project Scheduling : Models, Algorithms, Extensions and Applications, ISTE, 2007.
DOI : 10.1002/9780470611227

URL : https://hal.archives-ouvertes.fr/hal-00482946

C. Artigues and P. Lopez, Energetic reasoning for energy-constrained scheduling with a continuous resource, Journal of Scheduling, vol.48, issue.2, pp.225-241, 2015.
DOI : 10.1007/s10951-014-0404-y

URL : https://hal.archives-ouvertes.fr/hal-01108964

[. Artigues, P. Lopez, and A. Haït, The energy scheduling problem: Industrial case-study and constraint propagation techniques, International Journal of Production Economics, vol.143, issue.1, pp.13-23, 2013.
DOI : 10.1016/j.ijpe.2010.09.030

URL : https://hal.archives-ouvertes.fr/hal-00522387

[. Artigues, P. Lopez, and D. Rivreau, Integer programming and constraint propagation for scheduling under energy constraints, 27th European Conference on Operational Research, 2012.

C. Artigues, P. Michelon, and S. Reusser, Insertion techniques for static and dynamic resource-constrained project scheduling, European Journal of Operational Research, vol.149, issue.2, pp.249-267, 2003.
DOI : 10.1016/S0377-2217(02)00758-0

N. Beldiceanu and M. Carlsson, A New Multi-resource cumulatives Constraint with Negative Heights, Principles and Practice of Constraint Programming : 8th International Conference, CP 2002 Ithaca Proceedings, pp.63-79, 2002.
DOI : 10.1007/3-540-46135-3_5

P. Baptiste and S. Demassey, Tight LP bounds for resource constrained project scheduling, OR Spectrum, vol.26, issue.2, pp.251-262, 2004.
DOI : 10.1007/s00291-003-0155-1

URL : https://hal.archives-ouvertes.fr/inria-00124163

K. H. B?a?ewicz, E. Ecker, G. Pesch, J. Schmidt, and . W¸eglarzw¸eglarz, Scheduling Computer and Manufacturing Processes, 2001.
DOI : 10.1007/978-3-662-03217-6

[. Berthold, S. Heinz, and J. Schulz, An Approximative Criterion for the Potential of Energetic Reasoning, pp.229-239, 2011.
DOI : 10.1007/978-3-642-19754-3_23

J. Blazewicz, J. K. Lenstra, and A. H. Kan, Scheduling subject to resource constraints: classification and complexity, Discrete Applied Mathematics, vol.5, issue.1, pp.11-24, 1983.
DOI : 10.1016/0166-218X(83)90012-4

P. Baptiste, C. L. Pape, and W. Nuijten, Satisfiability tests and timebound adjustments for cumulative scheduling problems, Annals of Operations Research, vol.92, issue.0, pp.305-333, 1999.
DOI : 10.1023/A:1018995000688

P. Baptiste, C. L. Pape, and W. Nuijten, Constraint-based scheduling : applying constraint programming to scheduling problems. International series in operations research & management science, Kluwer Academic, vol.39, 2001.
DOI : 10.1007/978-1-4615-1479-4

URL : https://hal.archives-ouvertes.fr/inria-00123562

J. L. Bentley and T. A. Ottmann, Algorithms for Reporting and Counting Geometric Intersections, IEEE Transactions on Computers, vol.28, issue.9, pp.643-647, 1979.
DOI : 10.1109/TC.1979.1675432

URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA058768

[. Bonifas, A O(n 2 log n) propagation for the Energy Reasoning. In ROADEF - 17ème congrès annuel de la Société française de recherche opérationnelle et d'aide à la décision, 2016.

N. Beldiceanu and E. Poder, A Continuous Multi-resources cumulative Constraint with Positive-Negative Resource Consumption-Production, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems : 4th International Conference, pp.214-228, 2007.
DOI : 10.1007/978-3-540-72397-4_16

URL : https://hal.archives-ouvertes.fr/hal-00481560

N. Christofides, R. Alvarez-valdes, and J. M. Tamarit, Project scheduling with resource constraints: A branch and bound approach, European Journal of Operational Research, vol.29, issue.3, pp.262-273, 1987.
DOI : 10.1016/0377-2217(87)90240-2

N. Christofides, R. Alvarez-valdes, and J. M. Tamarit, Project scheduling with resource constraints: A branch and bound approach, European Journal of Operational Research, vol.29, issue.3, pp.262-273, 1987.
DOI : 10.1016/0377-2217(87)90240-2

J. Carlier and B. Latapie, Une méthode arborescente pour résoudre les problèmes cumulatifs. RAIRO -Operations Research -Recherche Opérationnelle, pp.311-340, 1991.
DOI : 10.1051/ro/1991250303111

E. Demeulemeester, B. De, and W. Herroelen, The discrete time/resource trade-off problem in project networks: a branch-and-bound approach, IIE Transactions, vol.27, issue.11, pp.1059-1069, 2000.
DOI : 10.1016/S0022-0000(75)80008-0

S. Demassey, Hybrid Constraint Programming-Integer Linear Programming approaches for the Resource-Constrained Project Scheduling Problem. Theses, 2003.
URL : https://hal.archives-ouvertes.fr/tel-00293564

A. Derrien, Cumulative scheduling in constraint programming : energetic characterization of reasoning and robust solutions, Theses, Ecole des Mines de Nantes, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01242789

[. Dorndorf, T. Phan-huy, and E. Pesch, A Survey of Interval Capacity Consistency Tests for Time- and Resource-Constrained Scheduling, Project Scheduling : Recent Models, Algorithms and Applications, pp.213-238, 1999.
DOI : 10.1007/978-1-4615-5533-9_10

A. Derrien and T. Petit, A New Characterization of Relevant Intervals for Energetic Reasoning, pp.289-297
DOI : 10.1007/978-3-319-10428-7_22

URL : https://hal.archives-ouvertes.fr/hal-01084436

E. Bert-de-reyck, W. Demeulemeester, and . Herroelen, Local search methods for the discrete time/resource trade-off problem in project networks, Naval Research Logistics, issue.6, pp.45553-578, 1998.

[. Fündeling and N. Trautmann, A priority-rule method for project scheduling with work-content constraints, European Journal of Operational Research, vol.203, issue.3, pp.568-574, 2010.
DOI : 10.1016/j.ejor.2009.09.019

[. Gay, R. Hartert, and P. Schaus, Simple and Scalable Time-Table Filtering for the Cumulative Constraint, Principles and Practice of Constraint Programming : 21st International Conference Proceedings, pp.149-157, 2015.
DOI : 10.1007/978-3-319-23219-5_11

URL : http://hdl.handle.net/2078.1/171186

S. Gay, R. Hartert, and P. Schaus, Time-Table Disjunctive Reasoning for the Cumulative Constraint, International Conference on AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, pp.157-172, 2015.
DOI : 10.1007/978-3-319-18008-3_11

R. Michael, D. S. Garey, and . Johnson, Computers and Intractability : A Guide to the Theory of NP-Completeness, 1979.

M. Robert, G. L. Haralick, and . Elliott, Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence, vol.14, issue.3, pp.263-313, 1980.

[. Erschler and P. Lopez, Scheduling under time and resource constraints, Proc. of Workshop on Manufacturing Scheduling, 11th IJCAI, 1989.

L. W. Johan and . Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Mathematica, vol.30, issue.1, pp.175-193, 1906.

O. Koné, C. Artigues, P. Lopez, and M. Mongeau, Event-based MILP models for resource-constrained project scheduling problems, Computers & Operations Research, vol.38, issue.1, pp.3-13, 2011.
DOI : 10.1016/j.cor.2009.12.011

[. Kis, A branch-and-cut algorithm for scheduling of projects with variable-intensity activities, Mathematical Programming, vol.136, issue.3, pp.515-539, 2005.
DOI : 10.1007/s10107-004-0551-6

R. Kolisch, Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation, European Journal of Operational Research, vol.90, issue.2, pp.320-333, 1996.
DOI : 10.1016/0377-2217(95)00357-6

O. Koné, Nouvelles approches pour la résolution du problème d'ordonnancement de projet à moyens limités. Theses, 2009.

R. Kolisch and A. Sprecher, PSPLIB - A project scheduling problem library, European Journal of Operational Research, vol.96, issue.1, pp.205-216, 1996.
DOI : 10.1016/S0377-2217(96)00170-1

A. Lahrichi and . Ordonnancements, La notion de "parties obligatoires" et son application aux problèmes cumulatifs. RAIRO -Recherche Opérationnelle, pp.241-262, 1982.
DOI : 10.1051/ro/1982160302411

URL : http://www.numdam.org/article/RO_1982__16_3_241_0.pdf

A. Letort, N. Beldiceanu, and M. Carlsson, A Scalable Sweep Algorithm for the cumulative Constraint, Principles and Practice of Constraint Programming : 18th International Conference, CP 2012 Proceedings, pp.439-454, 2012.
DOI : 10.1007/978-3-642-33558-7_33

URL : https://hal.archives-ouvertes.fr/hal-00754043

]. J. Lew08 and . Lewis, Algebra symposium : Optimizing fuel consumption, 2008.

C. , L. Van, M. N. Hung, and P. Michel, Non-convex aggregative technology and optimal economic growth, 2005.
URL : https://hal.archives-ouvertes.fr/halshs-00197556

A. Mingozzi, V. Maniezzo, S. Ricciardelli, and L. Bianco, An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation, Management Science, vol.44, issue.5, pp.714-729, 1998.
DOI : 10.1287/mnsc.44.5.714

L. Mercier and P. Van-hentenryck, Edge Finding for Cumulative Scheduling, INFORMS Journal on Computing, vol.20, issue.1, pp.143-153, 2008.
DOI : 10.1287/ijoc.1070.0226

M. Nattaf, C. Artigues, T. Kis, and P. Lopez, Inégalités valides pour les modèles à évènements des problèmes d'ordonnancement sous contraintes de ressource, ROADEF -17ème congrès annuel de la Société française de recherche opérationnelle et d'aide à la décision, 2016.

M. Nattaf, C. Artigues, T. Kis, and P. Lopez, Polyhedral results and valid inequalities for resource-constrained scheduling problem event-based models, 29th Conference of the European Chapter, 2016.

M. Nattaf, C. Artigues, and P. Lopez, Flow and energy based satisfiability tests for the continuous energy-constrained scheduling problem with concave piecewise linear functions, CP Doctoral Program 2015, pp.70-81, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01288033

M. Nattaf, C. Artigues, and P. Lopez, A hybrid exact method for a scheduling problem with a continuous resource and energy constraints, Constraints, vol.208, issue.1, pp.304-324, 2015.
DOI : 10.1007/s10601-015-9192-z

URL : https://hal.archives-ouvertes.fr/hal-01163561

M. Nattaf, C. Artigues, P. Lopez, and R. Medina, Lorena Pradenas, and Victor Parada. A batch sizing and scheduling problem on parallel machines with different speeds, maintenance operations, setup times and energy costs, International Conference on Industrial Engineering and Systems Management, 2015.

[. Nattaf, C. Artigues, and P. Lopez, Programmation linéaire mixte et programmation par contraintes pour un problème d'ordonnancement à contraintes énergétiques, Douzièmes Journées Francophones de Programmation par Contraintes (JFPC), 2016.

M. Nattaf, C. Artigues, P. Lopez, and D. Rivreau, Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions, OR Spectrum, vol.208, issue.3, pp.459-492, 2016.
DOI : 10.1007/s00291-015-0423-x

URL : https://hal.archives-ouvertes.fr/hal-01234466

A. Naber and R. Kolisch, MIP models for resource-constrained project scheduling with flexible resource profiles, European Journal of Operational Research, vol.239, issue.2, pp.335-348, 2014.
DOI : 10.1016/j.ejor.2014.05.036

URL : http://mediatum.ub.tum.de/doc/1229681/document.pdf

M. Nattaf, T. Kis, C. Artigues, and P. Lopez, Polyhedral results and valid inequalities for the Continuous Energy-Constrained Scheduling Problem, Research report, pp.laas -cnrs, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01391403

W. Nuijten, Time and resource constrained scheduling : A constraint satisfaction approach, 1994.

[. Olaguíbel and J. Goerlich, The project scheduling polyhedron: Dimension, facets and lifting theorems, European Journal of Operational Research, vol.67, issue.2, pp.204-220, 1993.
DOI : 10.1016/0377-2217(93)90062-R

P. Ouellet and C. Quimper, Time-Table Extended-Edge-Finding for the Cumulative Constraint, Principles and Practice of Constraint Programming : 19th International Conference, CP 2013 Proceedings, pp.562-577, 2013.
DOI : 10.1007/978-3-642-40627-0_42

[. Van-peteghem and M. Vanhoucke, A genetic algorithm for the preemptive and non-preemptive multi-mode resource-constrained project scheduling problem, European Journal of Operational Research, vol.201, issue.2, pp.409-418, 2010.
DOI : 10.1016/j.ejor.2009.03.034

A. , A. B. Pritsker, L. J. Waiters, and P. M. Wolfe, Multiproject scheduling with limited resources : A zero-one programming approach, Management Science, vol.16, issue.1, pp.93-108, 1969.
DOI : 10.1287/mnsc.16.1.93

R. Mohammad, F. Ranjbar, and . Kianfar, Solving the discrete time/resource tradeoff problem in project scheduling with genetic algorithms, Applied Mathematics and Computation, vol.191, issue.2, pp.451-456, 2007.

[. Ranjbar, B. De-reyck, and F. Kianfar, A hybrid scatter search for the discrete time/resource trade-off problem in project scheduling, European Journal of Operational Research, vol.193, issue.1, pp.35-48, 2009.
DOI : 10.1016/j.ejor.2007.10.042

A. Tesch, A Nearly Exact Propagation Algorithm for Energetic Reasoning in $$\mathcal O(n^2 \log n)$$, pp.493-519
DOI : 10.1007/978-3-319-44953-1_32

P. Vilím, Edge Finding Filtering Algorithm for Discrete Cumulative Resources in ${\mathcal O}(kn {\rm log} n)$, Principles and Practice of Constraint Programming : 15th International Conference Proceedings, pp.802-816, 2009.
DOI : 10.1287/ijoc.1070.0226

P. Vilím, Max Energy Filtering Algorithm for Discrete Cumulative Resources, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems : 6th International Conference Proceedings, pp.294-308, 2009.
DOI : 10.1007/978-3-642-01929-6_22

P. Vilím, Timetable edge finding filtering algorithm for discrete cumulative resources [Wal11] Grzegorz Waligóra. Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems : 8th International Conference. Proceedings, pp.230-245399, 2011.

J. Weglarz, Multiprocessor scheduling with memory allocation -a deterministic approach, IEEE Transactions on Computers, issue.8, pp.29703-709, 1980.
DOI : 10.1109/tc.1980.1675652

J. W¸eglarzw¸eglarz, Project Scheduling with Continuously-Divisible, Doubly Constrained Resources, Management Science, vol.27, issue.9, pp.1040-1053, 1981.
DOI : 10.1287/mnsc.27.9.1040

A. Laurence and . Wolsey, Integer programming, 1998.

P. Baptiste, C. L. Pape, and W. Nuijten, Constraint-based scheduling : applying constraint programming to scheduling problems. International series in operations research & management science, Kluwer Academic, vol.39, 2001.
DOI : 10.1007/978-1-4615-1479-4

URL : https://hal.archives-ouvertes.fr/inria-00123562

P. [. Erschler and . Lopez, Energy-based approach for task scheduling under time and resources constraints, 2nd International Workshop on Project Management and Scheduling, pp.115-121, 1990.

S. Gay, R. Hartert, and P. Schaus, Time-Table Disjunctive Reasoning for the Cumulative Constraint, International Conference on AI and OR Techniques in Constriant Programming for Combinatorial Optimization Problems, pp.157-172, 2015.
DOI : 10.1007/978-3-319-18008-3_11

M. Nattaf, C. Artigues, P. Lopez, and D. Rivreau, Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions, OR Spectrum, vol.208, issue.3, pp.459-492, 2016.
DOI : 10.1007/s00291-015-0423-x

URL : https://hal.archives-ouvertes.fr/hal-01234466

P. Vilím, Timetable edge finding filtering algorithm for discrete cumulative resources The energy scheduling problem : Industrial case-study and constraint propagation techniques, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems : 8th International Conference. Proceedings, pp.230-24513, 2011.

[. Beraldi, G. Ghiani, A. Grieco, and E. Guerriero, Rolling-horizon and fix-and-relax heuristics for the parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs, Computers & Operations Research, vol.35, issue.11, pp.3644-3656, 2008.
DOI : 10.1016/j.cor.2007.04.003

J. Chang, *. , and H. Chiu, A comprehensive review of lot streaming, International Journal of Production Research, vol.34, issue.8, pp.1515-1536, 2005.
DOI : 10.1016/S0305-0548(01)00032-6

[. Defersha and M. Chen, Mathematical model and parallel genetic algorithm for hybrid flexible flowshop lot streaming problem, The International Journal of Advanced Manufacturing Technology, vol.96, issue.2, pp.1-4249, 2012.
DOI : 10.1007/s00170-011-3798-0

S. Dauzere-peres and J. Lasserre, Lot Streaming in Job-Shop Scheduling, Operations Research, vol.45, issue.4, pp.584-595, 1997.
DOI : 10.1287/opre.45.4.584

A. Christodoulos, X. Floudas, and . Lin, Mixed integer linear programming in process scheduling : Modeling, algorithms, and applications, Annals of Operations Research, vol.139, issue.1, pp.131-162, 2005.

G. German, C. Desdouits, and C. L. Pape, Energy optimization in a manufacturing plant, 2015.

[. Hazir and S. Kedad-sidhoum, Batch sizing and just-in-time scheduling with common due date, Annals of Operations Research, vol.103, issue.11, pp.187-202, 2014.
DOI : 10.1007/s10479-012-1289-9

URL : https://hal.archives-ouvertes.fr/hal-01185283

J. Ross and B. James, Single and parallel machine capacitated lotsizing and scheduling : New iterative mip-based neighborhood search heuristics, Computers & Operations Research, vol.38, issue.12, pp.1816-1825, 2011.

[. Koné, C. Artigues, P. Lopez, and M. Mongeau, Comparison of mixed integer linear programming models for the resource-constrained project scheduling problem with consumption and production of resources, Flexible Services and Manufacturing Journal, vol.54, issue.8, pp.25-47, 2013.
DOI : 10.1007/s10696-012-9152-5

[. Mouzon, B. Mehmet, J. Yildirim, and . Twomey, Operational methods for minimization of energy consumption of manufacturing equipment, International Journal of Production Research, vol.85, issue.18-19, pp.18-194247, 2007.
DOI : 10.1109/92.335012

C. [. Nattaf, P. Artigues, and . Lopez, A hybrid exact method for a scheduling problem with a continuous resource and energy constraints. Constraints, DOI : 10, 1007.
URL : https://hal.archives-ouvertes.fr/hal-01163561

A. [. Queyranne and . Schulz, Polyhedral approaches to machine scheduling, 1994.

O. [. Riotteau, E. Scaloni, and . Néron, Ordonnancement sur des machines identiques avec splitting et temps de préparation dépendant de la sequence, MOSIM '01 : conference francophone de modélisation et simulation, 2001.

P. Serafini, Scheduling Jobs on Several Machines with the Job Splitting Property, Operations Research, vol.44, issue.4, pp.617-628, 1996.
DOI : 10.1287/opre.44.4.617

F. Tahar, C. Yalaoui, L. Chu, and . Amodeo, A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times, International Journal of Production Economics, vol.99, issue.1-2, pp.63-73, 2006.
DOI : 10.1016/j.ijpe.2004.12.007

J. F. and U. Jarpa, Modelo PAP que considera política de control de máxima demanda eléctrica en la producción de empresas manufactureras, 2014.

W. Xing and J. Zhang, Parallel machine scheduling with splitting jobs, Discrete Applied Mathematics, vol.103, issue.1-3, pp.259-269, 2000.
DOI : 10.1016/S0166-218X(00)00176-1

J. Xiao, C. Zhang, L. Zheng, N. Jatinder, and . Gupta, MIP-based fix-and-optimise algorithms for the parallel machine capacitated lot-sizing and scheduling problem, International Journal of Production Research, vol.196, issue.1, pp.5011-5028, 2013.
DOI : 10.1080/00207543.2013.790570

[. Yalaoui and C. Chu, An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times, IIE Transactions, vol.35, issue.2, pp.183-190, 2003.
DOI : 10.1080/07408170304382