Optimum Allocation in Stratified Sampling with Random Parameters

In this paper, we represent the allocation problem in stratified sampling as a convex programming problem with linear objective function and a single convex constraint in which the cost in the objective function and the sampling variances in the constraints are considered as random variables. By applying modified E-model, the stochastic objective function is converted into an equivalent deterministic objective function whereas the stochastic constraint is converted into a deterministic equivalent constraint by using chance constrained programming. A numerical example is presented to illustrate the computational procedure and the problem is solved by using the LINGO software.