Compromise allocations of biobjective nonlinear programming problem under partial responses

In this article, a problem of bivariate stratified sample surveys in presence of partial responses has been considered. The population in each stratum is divided into three group’s i.e. complete non-respondents, respondents of questions of category I or partial respondents and complete respondents. It is assumed that the respondents of the questions of category II always reply the questions of category I but not necessarily the vice versa. The problem of finding optimum allocations is formulated as Bi-objective Nonlinear Programming Problem (BONLPP). Since the problem is bi-objective the optimum solution cannot be obtained because the optimum solution of one objective may or may not be optimum for the second objective, so we obtain compromise optimum solution using four different methods i.e. Value function, Fuzzy programming, Goal programming and Chebychev approximation. For the demonstration purpose an illustrative example has been solved and also an R simulation study has been carried out to show the efficiency of the methods. Comparison of the solutions obtained by four different methods is shown graphically in the figure.