Numerical Method for an Optimal Repair Replacement Model in Mathematical Economics

The optimal replacement model can be represented as a nonlinear Volterra integral equa-tion with unknown functions in both the integrand and the upper limit of integration as thefollowing form: In this paper, we are interested in numerical analysis of the state-dependent delay integralequation (1) using an iterative decomposition algorithm to nd the optimal sequence of thelifetime of machine.As , we restrict the model to the more real case in which the technological progress andcapital deterioration are exponential function with respect to t.Our strategy for determining the optimal time for replacing the machine with new one con-sists of two steps: In the rst step, we construct a proper initial function x(t) = m(t) onthe interval [x(t1); t1] by using the ADM method. In the second step, we apply the recursiveformula to nd x(t) on the interval [t0; x(t0)]. The asymptotic behavior of the solution bythe proposed method is also investigated.

Keywords:

Optimal Replacement , Delay Integral Equation , Numerical Treat ment , Mathematical Economics