C. 8. Algorithmes-parall-`-elesparall-`-parall-`-eles, . Le-probl-`-emeprobl-`-probl-`-eme, and . De-d-´-ecoupe-`-aecoupe-`-ecoupe, A DEUX DIMENSIONS solution obtenue par PCGBS (les instances dont la solution optimale est connue, sont signalées par le symbole Pour chaque valeur de T , la table 8.7 rapporte, respectivement, les solutions obtenues et le temps de résolution de PCGBS 6 16, PCGBS, vol.10, issue.20, pp.16-16

. Dans-la-table-8, 8, la ligne 1 montre le nombre moyen de sauts (Av Nj), la ligne 2 rapporte le temps moyen de résolution (Av cpu) et la ligne 3 rapporte le nombre de fois (nb Best/Opt ) que PCGBS a amélioré la meilleure solution connue

P. Soit, 16 (T ) l'algorithmeparalì ele exécuté avec les paramètres ? (nombre de processeurs esclaves), T (la valeur associéè a la période de synchronisation)

]. A. Bibliographie and . Farley, The cutting stock problem in the industry, European Journal of Operational Research, vol.44, issue.1, pp.256-266, 1990.

A. A. Farley, Selection of stockplate characteristics and cutting style for two dimensional cutting stock situations, European Journal of Operational Research, vol.44, issue.2, pp.247-255, 1990.
DOI : 10.1016/0377-2217(90)90359-J

A. Lodi and M. Monaci, Integer linear programming models for 2-staged two-dimensional Knapsack problems, Mathematical Programming, vol.94, issue.2-3, pp.257-278, 2003.
DOI : 10.1007/s10107-002-0319-9

A. Rinnoykan, J. Dewit, and R. Wijmenga, Non?orthogonal two? dimensional cutting patterns, Management Sci, vol.33, 1987.

B. Mans, Performances of parallel branch and bound algorithms with best-first search, Discrete Applied Mathematics, vol.66, issue.1, pp.57-76, 1996.
DOI : 10.1016/0166-218X(94)00137-3

C. Carnieri, G. A. Mendoza, and L. G. Gavinho, Solution procedures for cutting lumber into furniture parts, European Journal of Operational Research, vol.73, issue.3, pp.295-501, 1994.
DOI : 10.1016/0377-2217(94)90244-5

D. Fayard and V. Zissimopoulos, An approximation algorithm for solving unconstrained two-dimensional knapsack problems, European Journal of Operational Research, vol.84, issue.3, pp.618-632, 1995.
DOI : 10.1016/0377-2217(93)E0221-I

E. Bischoff and M. Marriott, A comparative evaluation of heuristics for container loading, European Journal of Operational Research, vol.44, issue.2, pp.267-276, 1990.
DOI : 10.1016/0377-2217(90)90362-F

G. Belov, A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting, European Journal of Operational Research, vol.171, issue.1, pp.85-106, 2006.
DOI : 10.1016/j.ejor.2004.08.036

G. Kuntz and J. P. Uhry, Optimisation de Pertes deMatì ere en Industrie Textile, Thèse de doctorat, 1982.

H. Dickhoff and U. Finke, Cutting and Packing Problems in Production and Distribution : Typology and Bibliography, 1992.

H. Dyckhoff, A typology of cutting and packing problems, European Journal of Operational Research, vol.44, issue.2, pp.145-159, 1990.
DOI : 10.1016/0377-2217(90)90350-K

J. Blazewicz, M. Drozdowski, B. Soniewicki, and R. Walkowiak, Two?dimensional cutting problem, In International Inst.Appl.Sys.Analysis, 1991.

J. Daniels and P. Ghandforoush, An Improved Algorithm for the Non-Guillotine-Constrained Cutting-Stock Problem, Journal of the Operational Research Society, vol.41, issue.2, pp.141-150, 1990.
DOI : 10.1057/jors.1990.22

J. E. Beasley, An algorithm for the two-dimensional assortment problem, European Journal of Operational Research, vol.19, issue.2, pp.253-261, 1985.
DOI : 10.1016/0377-2217(85)90179-1

J. E. Beasley, Algorithms for Unconstrained Two-Dimensional Guillotine Cutting, Journal of the Operational Research Society, vol.36, issue.4, pp.297-306, 1985.
DOI : 10.1057/jors.1985.51

J. E. Beasley, An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure, Operations Research, vol.33, issue.1, pp.49-64, 1985.
DOI : 10.1287/opre.33.1.49

J. E. Beasley, An algorithm for set covering problem, European Journal of Operational Research, vol.31, issue.1, 1987.
DOI : 10.1016/0377-2217(87)90141-X

K. V. Viswanathan and A. Bagchi, Best-First Search Methods for Constrained Two-Dimensional Cutting Stock Problems, Operations Research, vol.41, issue.4, pp.768-776, 1993.
DOI : 10.1287/opre.41.4.768

L. V. Kantorovich, Mathematical methods of organizing and planing production, Management Sci, vol.6, pp.363-422, 1960.

M. Adamowicz and A. Albano, Two?stage solution of the cutting stock problem, Information Procc, North?Holland, vol.71, pp.1086-1091, 1972.

M. Adamowicz and A. , Albano : A solution of the rectangular cutting stock problem, IEEE Trans.Syst.Man and Sybern, vol.6, pp.302-310, 1976.

M. Biro and E. Boros, Network flows and non-guillotine cutting patterns, European Journal of Operational Research, vol.16, issue.2, pp.215-221, 1984.
DOI : 10.1016/0377-2217(84)90075-4

M. Cosnard and D. Trystram, Algorithmes et architectures paralleles, InterEditions, 1993.

M. Hifi, An improvement of viswanathan and bagchi's exact algorithm for constrained two-dimensional cutting stock, Computers & Operations Research, vol.24, issue.8, pp.727-736, 1997.
DOI : 10.1016/S0305-0548(96)00095-0

M. Hifi, Rapport d'habilitationàhabilitationà diriger les recherches, Thèse de doctorat, 1998.

M. Hifi, Exact algorithms for large?scale unconstrained two and three staged cutting problem, Computational Optimization and Applications, vol.18, issue.1, pp.63-88, 2001.
DOI : 10.1023/A:1008743711658

M. Hifi, Approximate algorithms for the container loading problem, International Transactions in Operational Research, vol.9, issue.6, pp.747-774, 2002.
DOI : 10.1111/1475-3995.00386

M. Hifi and R. Mhallah, An Exact Algorithm for Constrained Two-Dimensional Two-Staged Cutting Problems, Operations Research, vol.53, issue.1, pp.140-150, 2005.
DOI : 10.1287/opre.1040.0154
URL : https://hal.archives-ouvertes.fr/hal-00308680

M. Hifi and R. Mhallah, Strip generation algorithms for constrained two-dimensional two-staged cutting problems, European Journal of Operational Research, vol.172, issue.2, pp.515-527, 2006.
DOI : 10.1016/j.ejor.2004.10.020
URL : https://hal.archives-ouvertes.fr/hal-00284603

M. Hifi, R. Mhallah, and T. Saadi, Un algorithme par génération de couches pour le probì eme de découpè a deux niveaux, 7` eme congrès de la Société Française de Recherche Opérationnelle et d'Aidè a la Décision ?ROADEF?, 2006.

M. Hifi, R. Mhallah, and T. Saadi, Approximate and exact algorithms for??the??double-constrained two-dimensional guillotine cutting stock problem, Computational Optimization and Applications, vol.183, issue.2, 2007.
DOI : 10.1007/s10589-007-9081-5
URL : https://hal.archives-ouvertes.fr/hal-00284616

M. Hifi, R. Mhallah, and T. Saadi, Algorithms for the Constrained Two-Staged Two-Dimensional Cutting Problem, INFORMS Journal on Computing, vol.20, issue.2, pp.212-221, 2008.
DOI : 10.1287/ijoc.1070.0233
URL : https://hal.archives-ouvertes.fr/hal-00284595

M. Hifi and T. Saadi, Using strip generation procedures for solving constrained two?staged cutting problems, The Fifth ALIO/EURO conference on combinatorial optimization, ENST, 2005.

M. Hifi and T. Saadi, A Cooperative Algorithm for Constrained Two-staged 2D Cutting Problems, 2006 International Conference on Service Systems and Service Management, pp.928-933, 2006.
DOI : 10.1109/ICSSSM.2006.320756
URL : https://hal.archives-ouvertes.fr/hal-00284629

M. Hifi and T. Saadi, Using bounded knapsack problems for two?staged two?dimensional cutting stock problems, International Conference on Metaheuristics and Nature Inspired computing, 2006.

M. Hifi and T. Saadi, Un algorithme coopératif pour lesprobì emes de découpè a deux dimensionsàmensionsà deux niveaux, Conférence scientifique conjointe en Recherche Opérationnelle et Aidè a la Décision, 2007.

M. Hifi and T. Saadi, A cooperative algorithm for constrained two-staged two-dimensional cutting problems, International Journal of Operational Research, vol.9, issue.1, 2008.
DOI : 10.1504/IJOR.2010.034363
URL : https://hal.archives-ouvertes.fr/hal-00308705

M. Hifi and T. Saadi, A parallel algorithm for constrained two?staged 2d cutting problems, International workshop on Operation Research, 2008.

M. Hifi and T. Saadi, A parallel algorithm for constrainted two?staged two?dimensional cutting problems, Informs Journal On Computing, 2008.

M. Hifi and T. Saadi, A parallel cooperative algorithm for constrainted two?staged two?dimensional cutting problems, Operations Research, 2008.

M. Hifi and T. Saadi, Unprobì eme de placement en trois dimensions In 9` eme congrès de la Société Française de Recherche Opérationnelle et d'Aidè a la Décision, 2008.

M. Hifi and V. Zissimopoulos, Constrained two-dimensional cutting: an improvement of Christofides and Whitlock's exact algorithm, Journal of the Operational Research Society, vol.48, issue.3, pp.324-331, 1997.
DOI : 10.1057/palgrave.jors.2600364

M. J. Flynn, Some computer organisation and their effectiveness, IEEE Transaction on computer, vol.21, pp.948-960, 1979.
DOI : 10.1109/tc.1972.5009071

M. J. Quinn and N. Deo, An upper bound for the speedup of parallel branch and bound algorithms, The 3rd Conf.on Found.of Software Technology and Theorical Computer Science, 1985.

M. R. Garey and R. L. Graham, Bounds on multiprocessing scheduling with resource constraints. Siam, Jour.Comput, vol.4, issue.2, p.187, 1975.

N. Christofides and C. Whitlock, An Algorithm for Two-Dimensional Cutting Problems, Operations Research, vol.25, issue.1, pp.31-44, 1977.
DOI : 10.1287/opre.25.1.30

N. Christofides and E. Hadjiconstantinou, An exact algorithm for orthogonal 2-D cutting problems using guillotine cuts, European Journal of Operational Research, vol.83, issue.1, pp.21-38, 1995.
DOI : 10.1016/0377-2217(93)E0277-5

P. Decani, A note on the two?dimensional rectangular cutting?stock problem, European Journal of Operational Research, vol.29, pp.703-706, 1978.

P. E. Sweeney and R. W. , One-dimensional cutting stock decisions for rolls with multiple quality grades, European Journal of Operational Research, vol.44, issue.2, pp.224-231, 1990.
DOI : 10.1016/0377-2217(90)90357-H

P. Gilmore and R. Gomory, A Linear Programming Approach to the Cutting-Stock Problem, Operations Research, vol.9, issue.6, pp.849-859, 1961.
DOI : 10.1287/opre.9.6.849

P. Gilmore and R. Gomory, Multistage Cutting Stock Problems of Two and More Dimensions, Operations Research, vol.13, issue.1, pp.94-119, 1965.
DOI : 10.1287/opre.13.1.94

P. Gilmore and R. Gomory, The Theory and Computation of Knapsack Functions, Operations Research, vol.14, issue.6, pp.1045-1074, 1966.
DOI : 10.1287/opre.14.6.1045

P. S. Ow and T. E. Morton, Filtered beam search in scheduling???, International Journal of Production Research, vol.26, issue.1, pp.297-307, 1988.
DOI : 10.1080/00207548208947802

P. Sweeney and E. , Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography, Journal of the Operational Research Society, vol.43, issue.7, pp.691-706, 1992.
DOI : 10.1057/jors.1992.101

P. Y. Wang, Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems, Operations Research, vol.31, issue.3, pp.573-586, 1983.
DOI : 10.1287/opre.31.3.573

R. Alvarez?valdes, R. Mart-`-mart-`-i, A. Parajón, and J. M. Tamarit, Grasp and path relinking for the two?dimensional two?staged cutting stock problem, INFORMS Journal on Computing, vol.19, issue.2, pp.1-12, 2007.

R. Corrêra and A. Ferreira, A distributed implementation of asynchronous parallel branch and bound.In : Parallel Algorithms for Irregular Problems : State of the Art, 1995.

R. Ducan, R. G. Dyson, and A. S. Gregory, A survey of parallel computer architectures, The cutting stock problem in the flat glass industry

R. Morabito and M. Arenales, An AND/OR-graph approach to the container loading problem, International Transactions in Operational Research, vol.1, issue.1, pp.59-73, 1994.
DOI : 10.1016/0969-6016(94)90046-9

R. Morabito and V. Garcia, The cutting stock problem in a hardboard industry: A case study, Computers & Operations Research, vol.25, issue.6, pp.469-485, 1998.
DOI : 10.1016/S0305-0548(97)00087-7

R. W. Haessler, A Heuristic Programming Solution to a Nonlinear Cutting Stock Problem, Management Science, vol.17, issue.12
DOI : 10.1287/mnsc.17.12.B793

R. W. Haessler and P. E. Sweeney, Cutting stock problems and solution procedures, European Journal of Operational Research, vol.54, issue.2, pp.141-150, 1991.
DOI : 10.1016/0377-2217(91)90293-5

S. G. Hahn, On the Optimal Cutting of Defective Sheets, Operations Research, vol.16, issue.6, pp.1100-1114, 1968.
DOI : 10.1287/opre.16.6.1100

S. P. Fekete, A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems, Mathematical Methods of Operational Research, vol.60, issue.2, pp.311-329, 2004.
DOI : 10.1007/s001860400376

T. H. Lai and A. Sprague, Performance in parllel branch and bound algorithms, IEEE Trans.Comput, vol.34, pp.962-964, 1985.

T. H. Lai and S. Sahni, Anomalies in parallel branch-and-bound algorithms, Communications of the ACM, vol.27, issue.6, pp.594-602, 1984.
DOI : 10.1145/358080.358103

V. D. Cung, M. Hifi, and B. Cun, Constrained two-dimensional cutting stock problems a best-first branch-and-bound algorithm, International Transactions in Operational Research, vol.49, issue.3, 1997.
DOI : 10.1016/0360-8352(89)90013-2

V. Zissimopoulos, Heuristic methods for solving (un)constrained two?dimensional cutting stock problems, Math.Opns.Res, vol.49, pp.345-357, 1985.

L. Résultats-numériques-de and .. , et 3, en utilisant les stratégies de recherche en profondeur d'abord et meilleur d'abord sur les instances de taille moyenne, p.43

G. Résultats-numériques-de-lbs-m-?, et 4 ; utilisant les stratégies de recherche en meilleur d'abord pour unepremì ere découpe horizontale et unepremì ere découpe vertical, p.45

H. Résultats-numériques-de, P. , L. , and G. , ? est fixéfixéà 2 dans LBS et GBS avec une stratégie de recherche en meilleur d'abord, p.47

P. Résultats-numériques-de and ?. Gbs, 2}, utilisant les stratégies de recherche en profondeur d'abord et meilleur d'abord pour unepremì ere découpe horizontale et unepremì ere découpe verticale, p.59

P. Résultats-numériques-de, C. Gbs, and ?. , 2} utilisant les stratégies de recherche en profondeur d'abord et meilleur d'abord pour unepremì ere découpe horizontale et unepremì ere découpe verticale, p.60

. Etude-comparative-entre-cplex, GBA et CGBA sur les instances extralarges . Le symbole ? signifie que l'algorithme produit la meilleure solution, p.62

G. Qualité-des-bornes-inférieures-produites-par and I. , Le symbole h (resp. v) signifie que la borne inférieure est obtenue par des bandes horizontales (resp. verticales ) Le couple (h, v) signifie que la solution finale est obtenue en appliquant une construction horizontale complémentée par une construction verticale. La valeur a (resp. b) représente n i=1 a i (resp. n i=1 b i ), p.100