Optimizing a General Optimal Replacement Model by Fractional Programming Techniques

In this paper we adapt the well-known parametric approach from fractional programming to solve a class of fractional programs with a noncompact feasible region. Such fractional problems belong to an important class of single component preventive maintenance models. Moreover, for a special but important subclass we show that the subproblems occurring in this parametric approach are easy solvable. To solve the problem directly we also propose for a related subclass a specialized version of the bisection method. Finally, we present some computational results for these two methods applied to an inspection model and a minimal repair model having both a unimodal failure rate.