A Branch and Bound Approach to Optimal Allocation in Stratified Sampling

Abstract

For practical applications of any allocations, integer values of the sample sizes are required. This could be done by simply rounding off the non-integer sample sizes to the nearest integral values. When the sample sizes are large enough or the measurement cost in various strata are not too high, the rounded off sample allocation may work well. However for small samples in some situations the rounding off allocations may become infeasible and non-optimal. This means that rounded off values may violate some of the constraints of the problem or there may exist other sets of integer sample allocations with a lesser value of the objective function. In such situations we have to use some integer programming technique to obtain an optimum integer solution.

Keywords:  Stratified sampling, Non-linear Integer Programming, Allocation Problem,  Langrangian Multiplier, Branch & Bound Technique