Optimal allocation of inspection effort over a finite planning horizon

We address the problem of managing the intensity, sequence and timing of inspection effort in an N-stage production system with M inspection activities possible at each stage. The objective is to minimize the sum of the inspection costs and the penalties caused by undetected defects. By means of the maximum principle we prove several properties of the optimal solution, which allow us to reduce the continuous-time inspection effort allocation problem to a combinatorial one. We suggest an efficient algorithm that solves the problem in O(NM2+N-2) time.