. De-taille, Ces instances ont été générées avec des coûts aléatoires compris dans l'intervalle [a, b] avec une distribution uniforme U [a, b] : ? Coût unitaire de production : U [0, 5

N. Absi and S. Kedad-sidhoum, The multi-item capacitated lot-sizing problem with safety stocks and demand shortage costs, Computers & Operations Research, vol.36, issue.11, pp.2926-2936, 2009.
DOI : 10.1016/j.cor.2009.01.007

URL : https://hal.archives-ouvertes.fr/emse-00429420

K. Akartunali and A. J. Miller, A heuristic approach for big bucket multi-level production planning problems, European Journal of Operational Research, vol.193, issue.2, pp.396-411, 2009.
DOI : 10.1016/j.ejor.2007.11.033

URL : https://hal.archives-ouvertes.fr/hal-00387052

A. Alfieri, S. D. Orazio, and P. Brandimarte, LP-based heuristics for the capacitated lot-sizing problem: The interaction of model formulation and solution algorithm, International Journal of Production Research, vol.40, issue.2, pp.441-458, 2002.
DOI : 10.1287/mnsc.35.3.353

F. P. Alvelos, J. M. Carvalho, and C. M. Pimentel, Algoritmo de partição e geração de colunas para dimensionamento de lotes de produção, Investigação Operacional, vol.26, pp.139-146, 2006.

M. Arenales and V. A. , Armentano et R. Morabito : Pesquisa Operacional -Modelagem e Algoritmos. Campus, 2006.

V. A. Armentano and F. M. Toledo, A Lagrangean-based Heuristic for the Capacitated Lot-sizing Problem in Parallel Machines, pp.1070-1083, 2006.

E. Balas, A restricted Lagrangean approach to the traveling salesman problem, Mathematical Programming, vol.1, issue.1, pp.19-46, 1007.
DOI : 10.1007/BF01584228

J. F. Bard and N. Nananukul, The integrated production???inventory???distribution???routing problem, Journal of Scheduling, vol.177, issue.2, pp.257-280, 2009.
DOI : 10.1007/s10951-008-0081-9

C. Barnhart, E. L. Johnson, G. L. Nemhauser, M. W. Savelsbergh, and P. H. Vance, Branch-and-Price: Column Generation for Solving Huge Integer Programs, Operations Research, vol.46, issue.3, pp.316-329, 1998.
DOI : 10.1287/opre.46.3.316

R. Barták, Constraint programming: In pursuit of the holy grail, Proceedings of Week of Doctoral Students (WDS99), pp.555-564, 1999.

G. Belvaux and L. A. , Wolsey : Lot-Sizing Problems: Modelling Issues and a Specialized Branch-and-Cut System bc-prod. Internal report, Center for Operations Research and Econometrics, 1998.

G. Belvaux and L. A. , Wolsey : LOTSIZELIB: A Library of Models and Matrices for Lot-Sizing Problems. Internal report, Center for Operations Research and Econometrics, 1999.

G. R. Bitran and H. H. , Computational Complexity of the Capacitated Lot Size Problem, Management Science, vol.28, issue.10, pp.1174-1186, 1982.
DOI : 10.1287/mnsc.28.10.1174

M. Boudia, M. A. Louly, and C. , Prins : Global optimization of production and distribution, Proceedings of the International Conference on Industrial Engineering and Systems Management, 2005.

M. Boudia, M. A. Louly, and C. , Prins : Grasp for the combined optimization of production and distribution, MIC2005: The Sixth Metaheuristics International Conference, 2005.

M. Boudia, M. A. Louly, and C. , A reactive GRASP and path relinking for a combined production???distribution problem, Computers & Operations Research, vol.34, issue.11, pp.3402-3419, 2007.
DOI : 10.1016/j.cor.2006.02.005

M. Boudia, M. A. Louly, and C. , Prins : Fast heuristics for a combined production planning and vehicle routing problem. Production Planning & Control: The Management of Operations, 2008.

M. Boudia and C. , A memetic algorithm with dynamic population management for an integrated production???distribution problem, European Journal of Operational Research, vol.195, issue.3, pp.703-715, 2009.
DOI : 10.1016/j.ejor.2007.07.034

N. Brahimi, S. Dauzere-pérès, N. M. Najid, and A. Nordli, Single item lot sizing problems, European Journal of Operational Research, vol.168, issue.1, pp.1-16, 2006.
DOI : 10.1016/j.ejor.2004.01.054

URL : https://hal.archives-ouvertes.fr/hal-00468355

O. Bräysy, M. Gendreau, G. Hasle, A. Løkketangen, and J. Y. Potvin, Metaheuristics for the vehicle routing problem and its extensions: a categorized bibliography, éditeurs : The Vehicle Routing Problem -Latest Advances and New Challenges, 2008.

G. Carpaneto and P. Toth, Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem, Management Science, vol.26, issue.7, pp.736-743, 1980.
DOI : 10.1287/mnsc.26.7.736

P. Chandra and M. L. Fisher, Coordination of production and distribution planning, European Journal of Operational Research, vol.72, issue.3, pp.503-517, 1994.
DOI : 10.1016/0377-2217(94)90419-7

G. Clarke and J. W. Wright, Scheduling of Vehicles from a Central Depot to a Number of Delivery Points, Operations Research, vol.12, issue.4, pp.568-581, 1964.
DOI : 10.1287/opre.12.4.568

M. Comelli, M. Gourgand, and D. Lemoine, A review of tactical planning models, Journal of Systems Science and Systems Engineering, vol.44, issue.1, pp.204-229, 1007.
DOI : 10.1007/s11518-008-5076-8

URL : https://hal.archives-ouvertes.fr/hal-00860324

M. Constantino, T. Grant, and P. Hahn, Lower Bounds in Lot-Sizing Models: A Polyhedral Study, Mathematics of Operations Research, vol.23, issue.1, pp.101-118, 1998.
DOI : 10.1287/moor.23.1.101

J. Cordeau, G. Desaulniers, J. Desrosiers, M. M. Solomon, and F. Soumis, The VRP with time windows, chapitre 7, SIAM monographs on discrete mathematics and applications, pp.157-194, 2001.

G. Dantzig, R. Fulkerson, and S. Johnson, Solution of a Large-Scale Traveling-Salesman Problem, Journal of the Operations Research Society of America, vol.2, issue.4, pp.393-410, 1954.
DOI : 10.1287/opre.2.4.393

G. B. Dantzig and J. H. , The Truck Dispatching Problem, Management Science, vol.6, issue.1, pp.80-91, 1959.
DOI : 10.1287/mnsc.6.1.80

S. A. De-araujo and M. N. , Arenales : Problema de dimensionamento de lotes monoestagio com restrição de capacidade: Modelagem, método de resolução e resultados computacionais, Pesquisa Operacional, vol.20, 2000.

L. P. De-assis, Algoritmos para o problema de roteamento de veículos com coleta e entrega simultâneas, 2007.

Z. Degraeve and R. , Jans : Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches, European Journal of Operational Research, vol.177, issue.3, pp.1855-1875, 2007.

J. Desrosiers and M. E. Lübbecke, Selected topics in column generation, Operations Research, vol.53, pp.1007-1023, 2002.

C. Dillenberger, L. F. Escudero, A. Wollensak, and W. Zhang, On practical resource allocation for production planning and scheduling with period overlapping setups, European Journal of Operational Research, vol.75, issue.2, pp.275-286, 1994.
DOI : 10.1016/0377-2217(94)90074-4

G. Dobson, The Economic Lot-Scheduling Problem: Achieving Feasibility Using Time-Varying Lot Sizes, Operations Research, vol.35, issue.5, pp.764-771, 1987.
DOI : 10.1287/opre.35.5.764

A. Drexl, Lot sizing and scheduling ??? Survey and extensions, European Journal of Operational Research, vol.99, issue.2, pp.221-235, 1997.
DOI : 10.1016/S0377-2217(97)00030-1

D. Erlenkotter, Ford Whitman Harris and the Economic Order Quantity Model, Operations Research, vol.38, issue.6, pp.937-946, 1990.
DOI : 10.1287/opre.38.6.937

L. G. Espejo and R. D. , Galvão : O uso das relaxações lagrangeana e surrogate em problemas de programação inteira, Pesquisa Operacional, vol.22, pp.387-402, 2002.

S. Çetinkaya, C. Lee, and A. P. , Wagelmans : A dynamic lot-sizing model with demand time windows. Tinbergen Institute Discussion Papers 99-095, 1999.

S. M. Fatemi-ghomi, B. Karimi, and J. M. Wilson, The capacitated lot sizing problem: a review of models and algorithms, OMEGA -The International Journal of Management Science, vol.31, pp.365-378, 2003.

A. Federgruen and M. Tzur, A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time, Management Science, vol.37, issue.8, pp.909-925, 1991.
DOI : 10.1287/mnsc.37.8.909

D. Feillet, A tutorial on column generation and branch-and-price for vehicle routing problems, 4OR, vol.34, issue.1, pp.407-424, 2010.
DOI : 10.1007/s10288-010-0130-z

URL : https://hal.archives-ouvertes.fr/emse-00505959

T. A. Feo and M. G. , Greedy Randomized Adaptive Search Procedures, Journal of Global Optimization, vol.68, issue.2, pp.109-133, 1995.
DOI : 10.1007/BF01096763

M. Florian, J. K. Lenstra, and R. Kan, Deterministic Production Planning: Algorithms and Complexity, Management Science, vol.26, issue.7, 1980.
DOI : 10.1287/mnsc.26.7.669

B. Gavish and S. C. Graves, The travelling salesman problem and related problems. Working paper, 1978.

C. D. Gelatt, S. Kirkpatrick, and M. P. Vecchi, Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.4598671-680, 1983.

M. Gendreau, Pesant : A constraint programming framework for local search methods, J. Heuristics, vol.5, issue.3, pp.255-279, 1999.

F. Glover, G. Jones, D. Karney, D. Klingman, and J. Mote, An Integrated Production, Distribution, and Inventory Planning System, Interfaces, vol.9, issue.5, pp.21-35, 1979.
DOI : 10.1287/inte.9.5.21

F. Glover and G. A. , Kochenberger : Handbook of Metaheuristics, 2003.

F. Glover and M. Laguna, Fundamentals of Scatter Search and Path Relinking, Control and Cybernetics, vol.29, issue.3, pp.653-684, 2000.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, p.1, 1989.

M. Gondran, Minoux : Graphes et algorithmes, Collection EDF R&D. Tec & Doc, 2009.

K. Haase, Lotsizing and scheduling for production planning, Lecture Notes in Economics and Mathematical Systems, vol.408, 1994.
DOI : 10.1007/978-3-642-45735-7

J. Hahm and C. A. Yano, The economic lot and delivery scheduling problem: The single item case, International Journal of Production Economics, vol.28, issue.2, pp.235-252, 1992.
DOI : 10.1016/0925-5273(92)90036-7

W. Heuvel and A. P. , Wagelmans : Four equivalent lot-sizing models Econometric institute report, 2007.

H. Hwang and W. Jaruphongsa, Dynamic lot-sizing model with demand time windows and speculative cost structure, Operations Research Letters, vol.34, issue.3, pp.251-256, 2006.
DOI : 10.1016/j.orl.2005.05.014

J. Jaffar and J. Lassez, Constraint logic programming, Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '87, pp.111-119, 1987.
DOI : 10.1145/41625.41635

R. Karp, R. Miller, and J. Thatcher, Reducibility among combinatorial problems, Complexity of Computer Computations, pp.85-103, 1972.

B. M. Khumawala, J. Thizy, and L. N. Van-wassenhove, Comparison of exact and approximate methods of solving the uncapacitated plant location problem, Journal of Operations Management, vol.6, issue.1, pp.23-34, 1985.

C. Kilger, Stadtler : Supply Chain Management and Advanced Planning: Concepts, Models, Software and Case Studies, 2008.

G. Laporte, The traveling salesman problem: An overview of exact and approximate algorithms, European Journal of Operational Research, vol.59, issue.2, pp.231-247, 1992.
DOI : 10.1016/0377-2217(92)90138-Y

F. B. Lawrence and E. P. Robinson, Coordinated capacitated lot-sizing problem with dynamic demand: A lagrangian heuristic, Decision Sciences, vol.35, issue.1, pp.25-53, 2004.

L. Lei, S. Liu, S. Park, and A. Ruszczynski, On the integrated production, inventory, and distribution routing problem, IIE Transactions, vol.47, issue.11, pp.955-970, 2006.
DOI : 10.1287/mnsc.27.3.336

R. Levi, A. Lodi, and M. Sviridenko, Approximation algorithms for the multi-item capacitated lot-sizing problem via flow-cover inequalities, Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization, IPCO'07, pp.454-468, 2007.

J. Maes, J. O. Mcclain, and L. N. Van-wassenhove, Multilevel capacitated lotsizing complexity and LP-based heuristics, European Journal of Operational Research, vol.53, issue.2, pp.131-148, 1991.
DOI : 10.1016/0377-2217(91)90130-N

A. S. Manne, Programming of Economic Lot Sizes, Management Science, vol.4, issue.2, pp.115-135, 1958.
DOI : 10.1287/mnsc.4.2.115

S. E. Merzouk, Probleme de Dimensionnement de Lots et de Livraisons - Application au cas d'une Chaine Logistique, 2007.

B. Meyer, Hybrids of Constructive Metaheuristics and Constraint Programming: A Case Study with ACO, Hybrid Metaheuristics, pp.151-183, 2008.
DOI : 10.1007/978-3-540-78295-7_6

C. E. Miller, A. W. Tucker, and R. A. , Integer Programming Formulation of Traveling Salesman Problems, Journal of the ACM, vol.7, issue.4, pp.326-329, 1960.
DOI : 10.1145/321043.321046

D. L. Miller and J. F. Pekny, Results from a parallel branch and bound algorithm for the asymmetric traveling salesman problem, Operations Research Letters, vol.8, issue.3, pp.129-135, 1989.
DOI : 10.1016/0167-6377(89)90038-2

M. C. Nascimento, Uma Heurística GRASP para o Problema de Dimensionamento de Lotes com Múltiplas Plantas, 2007.

M. C. Nascimento, M. G. Resende, and F. M. Toledo, GRASP heuristic with path-relinking for the multi-plant capacitated lot sizing problem, European Journal of Operational Research, vol.200, issue.3, pp.747-754, 2009.
DOI : 10.1016/j.ejor.2009.01.047

G. Pesant and L. Rousseau, Programmation par contraintes, chapitre 10, Presses Internationales Polytechnique, pp.223-246, 2005.

D. Pisinger and S. Ropke, A unified heuristic for a large class of vehicle routing problems with backhauls, European Journal of Operational Research, pp.750-775, 2004.

D. Pisinger and S. Ropke, A general heuristic for vehicle routing problems, Computers & Operations Research, vol.34, issue.8, pp.2403-2435, 2007.
DOI : 10.1016/j.cor.2005.09.012

Y. Pochet and L. A. , Wolsey : Production Planning By Mixed Integer Programming, 2006.

C. N. Potts and L. N. Van-wassenhove, Integrating Scheduling with Batching and Lot-Sizing: A Review of Algorithms and Complexity, Journal of the Operational Research Society, vol.43, issue.5, pp.395-406, 1992.
DOI : 10.1057/jors.1992.66

T. Prabhakar, A Production Scheduling Problem with Sequencing Considerations, Management Science, vol.21, issue.1, pp.34-42, 1974.
DOI : 10.1287/mnsc.21.1.34

J. Rogers, A Computational Approach to the Economic Lot Scheduling Problem, Management Science, vol.4, issue.3, 1958.
DOI : 10.1287/mnsc.4.3.264

M. Sambasivan and S. Yahya, A Lagrangean-based heuristic for multi-plant, multi-item, multi-period capacitated lot-sizing problems with inter-plant transfers, Computers & Operations Research, vol.32, issue.3, pp.537-555, 2005.
DOI : 10.1016/j.cor.2003.08.002

K. Smith, Investigation of the Uncapacitated Lot-Sizing Problem with Probabilistic Constraints. Working paper, program in applied mathematics, 2008.

H. Stadtler, Multilevel lot sizing with setup times and multiple constrained resources: Internally rolling schedules with lot-sizing windows. Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 20204, Institute for Business Studies, 2003.

C. Suerie, Lecture Notes in Economics and Mathematical Systems Time Continuity in Discrete Time Models: New Approaches for Production Planning in Process Industries, 2005.

F. M. Toledo and A. L. , Lot-sizing problem with several production centers, Pesquisa Operacional, vol.25, issue.3, pp.479-492, 2005.
DOI : 10.1590/S0101-74382005000300010

D. Toth and P. Vigo, The Vehicle Routing Problem, SIAM, 2002.
DOI : 10.1137/1.9780898718515

URL : https://hal.archives-ouvertes.fr/hal-01223571

H. Toussaint, Algorithmique rapide pour les problèmes de tournées et d'ordonnancement, Thèse de doctorat, 2010.

C. P. Van-hoesel and A. P. , Wagelmans : Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems, Research Memoranda, vol.014, 1997.

A. Wagelmans, S. Van-hoesel, and A. Kolen, Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case, Operations Research, vol.40, issue.1-supplement-1, pp.145-156, 2006.
DOI : 10.1287/opre.40.1.S145

H. M. Wagner and T. M. , Whitin : Dynamic Version of the Economic Lot Size Model, pp.89-96, 1958.

P. Zipkin, Computing Optimal Lot Sizes in the Economic Lot Scheduling Problem, Operations Research, vol.39, issue.1, pp.56-63, 1991.
DOI : 10.1287/opre.39.1.56