In a multivariate stratified sampling design, the individual optimum allocation of one character may not remain optimum to other characteristics. For the solution of such problems, a usable allocation must be required to get precise estimates of the unknown population parameters, which may be near optimum to all characteristics in some sense. The compromise criterion is required to obtain such usable allocation in sampling literature. In this paper, the sample allocation problem is considered as a stochastic nonlinear programming problem and thereafter formulated into a multiobjective programming problem to provide the usable allocation. The formulated problem is solved by using different models of stochastic optimization. Afterwards, the proposed allocation is worked out and compared with some other allocations, which are well defined in sampling, to give a comparative study. Also, the numerical study defines the practical utility of the proposed technique.

在多变量分层抽样设计中，一个字符的个体最佳分配可能不会对其他特征保持最佳状态。为了解决此类问题，必须要求可用分配来获得未知总体参数的精确估计，在某种意义上，该估计值可能对所有特征都接近最佳。为了在抽样文献中获得这种可用分配，需要折衷标准。在本文中，样本分配问题被认为是一个随机的非线性规划问题，然后被公式化为一个多目标规划问题，以提供可用的分配。通过使用不同的随机优化模型可以解决提出的问题。之后，拟议的分配将与抽样中定义明确的其他分配进行比较，进行比较研究。此外，数值研究定义了所提出的技术的实用性。