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UBC Theses and Dissertations

Solution for a class of combinatorial problems with emphasis on project sequencing in water resources planning Tsou, C. Anthony


An algorithm is presented to obtain the optimal permutation for a class of combinatorial optimization problems. Included in the class of problems dealt with are the following: project construction sequencing, the minimum tardiness job scheduling, and several sequential search and testing problems. The algorithm is based on a simple necessary condition for an optimal permutation incorporated into a Branch-and-Bound solution method. In many cases, optimal permutations can be obtained, with very little computational effort, by using only the necessary condition of optimality. For more complex problems, this condition is utilized in both branching and bounding operations, resulting in a powerful mechanism to eliminate subsets of solutions from optimal permutation consideration. Optimization techniques for use in water resources planning, where a series of developments will be required to meet a growing demand, should not only be efficient in finding the optimal solution but also offer means to perform sensitivity analysis. An approach is proposed in this thesis which will not only identify the project that is most likely to be the first element in the optimal construction sequence, but also allow estimates to be made of the amount by which the cost of any other project would have to be changed before it' could occupy the first position in the optimal sequence. A combination of the methods for finding the optimal sequence and the sensitivity analysis represents a "planning tool" which should provide an opportunity for an effective planning strategy which can be used in many different situations.

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