Optimal replacement policy with stochastic maintenance and operation costs

An equipment replacement problem is considered in this paper. The state of a piece of equipment is described by the maintenance and operation cost which evolves continuously according to a Wiener process. The objective is to minimize the expected total discounted cost of maintenance and operation as well as of purchasing. Using the optimal stopping technique, a second order ordinary differential equation is derived with proper boundary conditions. Then, the optimal replacement policy is obtained and analyzed via the ordinary differential equation.