Robustesse en programmation linéaire

Dans cette these nous nous interessons a la prise en compte d’incertitudes affectant les coefficients de programmes lineaires. Plus precisement, nous traitons les problemes admettant un second membre des contraintes incertain. Notre etude vise a repondre a la preoccupation de robustesse pour ces problemes et cela suivant leur contexte decisionnel. Nous considerons trois contextes de decision : le premier concerne la prise de decision en presence d’incertitudes, le deuxieme traite de l’evaluation des couts en fonction des aleas et cela dans une phase de planification et le troisieme comporte des problematiques multi-etapes, ou la decision robuste doit prendre en compte le caractere dynamique de ces problemes. Pour chacun de ses contextes nous presentons la formulation mathematique des problemes engendres, leur complexite et une approche de resolution. Nous nous interessons egalement a deux applications reelles : le probleme de localisation et de transport robuste comportant des demandes incertaines que nous traitons dans un contexte bi-etapes et, un probleme de gestion de stock admettant une demande incertaine aborde selon les trois contextes decisionnels precedents.

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