COMPROMISE ALLOCATION FOR TWO-STAGE SAMPLING WITH QUADRATIC TRAVEL COST USING DYNAMIC PROGRAMMING TECHNIQUE

Abstract

In the stratified sampling literature the main problem is to determine the sample sizes that should be selected from each stratum under (i) Equal Allocation, (ii) Proportional Allocation and (iii) Optimum Allocation. The best method is optimum allocation but in real situation the implementation of optimum allocation is not possible. In this case it is of interest to find near optimal allocation or compromise allocation. In case of multivariate sampling problem (where p different characteristics are under study) the optimal allocation method does not give the optimal solution for each variable and then researcher have to adapt in solution up to some extent by which the solution gives the optimal allocation in some sense. The compromise allocation is advisable in this situation. The present paper discusses a real situation problem where the two stage sampling are under study for more than one characteristics with quadratic travel cost of survey, the problem can be formulated as Multivariate Non Linear Programming Problem (MNLPP). The MNLPP is then solved by Dynamic Programming Technique with a numerical example. Received: October 26, 2021 c © 2022 Academic Publications Correspondence author 174 A. Ahmad, A.H. Ansari, Q. Rabbani AMS Subject Classification: 62D05