Optimizing system reliability with integer programming

This dissertation presents a polynomially-bounded computational method which uses a combination of exact, approximate and heuristic techniques to determine optimal allocation of redundancy in a mixed system with n subsystems in series where components are in parallel at each stage.; We first found the optimal solution which may not be integral. Next, we proved that the optimal integral solution can be found in time polynomially bounded by the size of the problem. We then designed a method which uses this nonintegral optimal solution to find an optimal integral solution by systematically reducing the dimension of the problem through linear transformations defined using unimodular matrices which map portions of the feasible set in the Euclidean n-space to a convex set in the positive cone of the Euclidean (n-2)-space. This process is successively repeated to reduce the problem to similar subproblems until a set of 2-dimensional subproblems is obtained.; Then we described how to find and used an optimal integral solution of any of these two-dimensional subproblems to get an optimal integral solution of the full problem.