## A Benders Decomposition Method for the Network Design Problem in a Combined Distribution and Assignment Environment |

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_ F exp ASSIGNMENT ENVIRONMENT ASSIGNMENT MODELS Benders decomposition approach BENDERS DECOMPOSITION METHOD Benders master problem bound upper bound Bq,y budget constraints candidate links CDA problem choosen combined distribution cost constraint cost function design variables destination q discrete network design distribution and assignment dualization scheme entropy constraint entropy Under cost explicit capacity constraints fixed feasible following we outline formulated given in Tomlin including the constraints instance a tangential integer interactivity Iter Jdrnsten Lagrange multipliers corresponding link cost links give lower bound upper maximize entropy modified distribution problem nested generalized Benders network design problem number of journeys Optimal solution original network polyhedron Primal Dual resulting master problem solution method solution yl lower solved by relaxation solves the CDA system optimal tangential approximation method total cost total travel cost traffic assignment problem trip distribution upper bound 12006h vgq fpq yi _D0 yl lower bound Zfpq