An Improved Branch and Bound Algorithm for Minimum Concave Cost Network Flow Problems

This paper formulates the minimum concave cost network flow (MCCNF) problem as a mixed integer program and solves this program using a new branch and bound algorithm. The algorithm combines Driebeek's "up and down" penalties with a new technique referred to as the simple bound improvement (SBI) procedure. An efficient numerical method for the SBI procedure is described and computational results are presented which show that the SBI procedure reduces both the in-core storage and the CPU time required to solve the MCCNF problem. In fact, for large problems (with over 200 binary decision variables) the SBI procedure reduced the in-core storage by more than one-third and the CPU time by more than 40 percent

Decomposition algorithms for global solution of deterministic and stochastic pooling problems in natural gas value chains

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Includes bibliographical references (leaves 153-158).In this thesis, a Benders decomposition algorithm is designed and implemented to solve both deterministic and stochastic pooling problems to global optimality. Convergence of the algorithm to a global optimum is proved and then it is implemented both in GAMS and C++ to get the best performance. A series of example problems are solved, both with the proposed Benders decomposition algorithm and commercially available global optimization software to determine the validity and the performance of the proposed algorithm. Moreover, a two stage stochastic pooling problem is formulated to model the optimal capacity expansion problem in pooling networks and the proposed algorithm is applied to this problem to obtain global optimum. A number of example stochastic pooling problems are solved, both with the proposed Benders decomposition algorithm and commercially available global optimization software to determine the validity and the performance of the proposed algorithm applied to stochastic problems.by Emre Armagan.S.M