A multiple response stratified sampling design with travel cost

Abstract

In developing the theory of stratified sampling usually the cost function is taken as a linear function of sample sizes considering the measurement and the overhead costs only. In many practical situations the linear cost function does not approximate the actual cost incurred adequately. For example when the cost of traveling between the units selected in the sample within a stratum is significant, instead of linear cost function a cost function that is quadratic in will be a more close approximation to the actual cost. In this paper the problem of finding a compromise allocation for a multiple response stratified sample survey with a significant travel cost within strata is formulated as a multiobjective non linear programming problem. A solution procedure is proposed using the goal programming approach. A numerical example is also presented to illustrate the computational details.