| The Distribution Systems Planning (DSP) situation typically involves a number of plants producing several commodities that are shipped, either directly or via distribution centers (warehouses), to specified customer zones such that demands at each zone are satisfied. New plants and new warehouses are to be integrated into the existing plant-warehouse complex in such a way that, given certain plant and warehouse capacity constraints and certain demand requirements, the total cost of the overall system is minimal.;Among special purpose algorithms, Benders' Decomposition has become quite popular for the solution of DSP MLIP problems. However, techniques based on Benders' Decomposition may converge very slowly, requiring a large number of iterations. Existing procedures solve one linear program and one integer program at each iteration, and have problems efficiently solving the integer programs. The development of a new procedure that overcomes this difficulty constitutes the central part of this thesis. The DSP problem is formulated as a mixed linear integer program which is partitioned into linear and integer programs, following Benders partitioning guidelines. The suggested procedure, then, solves a complete linear program only one time. In all subsequent iterations only sensitivity analysis involving changes in the objective function is performed. The biggest computational savings come when solving the integer program. This program consists of only one inequality. Solutions to this inequality are passed through a series of filters that reduce the set of potential solutions. The main claim is that the size of this reduced set is such that explicit enumeration of alternative integer solutions becomes a practical possibility. A computer package based on this enumeration scheme was successfully applied to a DSP problem for a consumers' products corporation operating in the USA.;DSP situations involve the simultaneous solution of plant location and flow optimization problems, hence their difficulty. Typical DSP formulations take the form of mixed linear integer programming (MLIP) problems that can be tackled by general purpose or by special purpose algorithms. General purpose algorithms have not been found to be very efficient for the solution of large scale DSP problems. |
