@MISC{Parmigiani94truncatedrecursive, author = {Giovanni Parmigiani}, title = {Truncated Recursive Algorithms For Scheduling}, year = {1994} }

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Abstract

this paper, I develop a general approach to the computation of optimal inspection schedules. Throughout the discussion, I will refer to it as truncated recursive method, since it is based on two elements: the first is truncating the evaluation of the risk function at a finite horizon, large enough to obtain an accurate result. The second is utilizing the recursive optimality condition of the infinite horizon case to express the optimal continuation policy as a function of the initial inspection ø 1 . In this way, the problem can be reduced to a one dimensional optimization, to be solved by numerical methods. One advantage of this approach is that it circumvents the exact dynamic programming solution of the finite horizon problem, involving the additional determination of the optimal number of inspections. The method can be applied to every situation in which the first order condition for the optimization recursively define the solution, so that the search for the optimum reduces to the search over the first inspection or, more generally, over a small set initial conditions. In Section 2, I introduce the notation and the basic ideas underlying the truncated recursive method, and discuss details of the convergence properties of the resulting algorithm. In Section 3, I consider an application to the basic model. Finally, in Section 4, I illustrate the accuracy of the result by means of numerical examples. 2 The Truncated Recursive Approach