Abstract

This paper studies the problem of optimal allocation for multivariate stratified survey as a bi-objective programming problem with the objective to minimize the costs (i.e. measurement and travel) incurred in the survey subject to precision constraint for each characteristic. The unitary cost of measurement and travel are considered as normally distributed random variables. Population variances are assumed to be unknown and replaced by sample variances which are also normally distributed random variables. The precision for each characteristic is specified as multi-choice. To remove the randomness from objective functions, Expected Value Standard Deviation (EVSD) criterion is applied after converting the biobjective problem into a single objective problem. Chance constraint programming technique is then used for deterministic equivalent of constraints. Thus, the problem of optimal allocation is treated as Stochastic Bi-objective Programming Problem (SBOPP) with multi-choice in right hand side. A numerical illustration is also given for the demonstration of proposed approach solved by Lingo Software.

Author: Shamsher Khan and M. M. Khalid

Received on: November, 2014

Accepted on: January, 2015