Turnpike properties of group testing for incomplete identification

A manufacturer needs to incompletely identify plenty of electronics chips with 100% quality from group testable chips. The computation workload of finding the optimal dynamic testing policy is terrible by the bottom-up approach. We prove that turnpike properties exist, i.e. when the problem scale is large enough, the optimal testing size is always the same as the test size of maximizing the number of expected perfect chips in one test, and it depends on only the defective rate of chips.