A polyhedral approach for the generalized assignment problem.

The generalized assignment problem (GAP) consists of finding a maximal profit assignment of n jobs over m capacity constrained agents, whereby each job has to be processed by only one agent. This contribution approaches the GAP from the polyhedral point of view. A good upper bound is obtained by approximating the convex hull of the knapsack constraints in the GAP-polytope using theoretical work of Balas. Based on this result, we propose a procedure for finding close-to-optimal solutions, which gives us a lower bound. Computational results on a set of 60representative and highly capacitated problems indicate that these solutions lie within 0.06% of the optimum. After applying some preprocessing techniques and using the obtained bounds, we solve the generated instances to optimality by branch and bound within reasonable computing time.Assignment;

A model for the efficient use of energy resources

Research supported by the Energy Research and Development Administration through Contract 421072-S.Bibliography: leaf 37.by Silvia Pariente

Probabilistic combinatorial optimization: Moments, semidefinite programming, and asymptotic bounds

10.1137/S1052623403430610SIAM Journal on Optimization151185-20