Optimum allocation by dynamic programming for sampling on successive occasions with partial replacement of units

The sequential nature of sampling on successive occasions with partial replacement of units (SPR) was exploited to cast the optimal SPR design problem as a multistage decision model which could be optimized through dynamic programming (DP). The objective of the design was to determine the number of remeasured and new sampling units at the successive occasions such that the cost of sampling was minimized and subject to the side conditions that the specified variance levels of the variables of interest were met. Using data published elsewhere, the DP approach was shown to give solutions almost identical to those obtained by other optimization techniques such as the graphical procedure. The advantage of the DP approach, however, was that it could handle optimization problems in which the sampling extended over several occasions.