Authors:
Shuaibu Idris Adam,Quazzafi Rabbani,DOI NO:
https://doi.org/10.26782/jmcms.2026.07.00006Keywords:
: multivariate stratified sampling,optimum allocation,nonlinear constraints,Survey optimization,Lagrange multipliers,(SDG 12 responsible consumption and production).,Abstract
This study proposes a framework of a Multi-Constrained Nonlinear Programming Problem (MCNLPP) for optimum sample allocation in multivariate stratified sampling with simultaneous nonlinear time constraint and cost constraint. The proposed model uses the Karush–Kuhn–Tucker conditions and the Lagrange multiplier technique to minimize the weighted sum of variances with operational resource constraints. Logarithmic, piecewise, and quadratic time functions are included as well as the nonlinear cost functions, and the resulting models are used to implement optimum stratum allocations under different operational scenarios using LINGO. The proposed framework, compared with representative deterministic allocation methods under the same resource conditions, demonstrates a balanced approach to survey precision, cost of operations, and time to collect the data. Finally, sensitivity analyses show that allocations are robust to changes in resource constraints. Overall, the framework generalizes the current compromise allocation methods by explicitly including nonlinear operational time and cost in a single deterministic optimization model.Refference:
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