Optimization of bicriterion quasi-concave functions subject to linear constraints

In this paper the authors provide algorithms for maximization and minimization of bicriterion quasi-concave function g(c1x,c2x) subject to linear constraints. The algorithm for maximisation is based on bisection approach. The algorithm for minimization is an implicit enumeration method. With some minor modifications, this algorithm also enumerates all efficient solutions of bicriterion linear programs. Maximization of system reliability of series-parallel and parallel-series systems (with two subsystems) through optimal assignment of components is treated as a special case.