Generalized Estimator on Operations Research Guided Sampling (ORGS)

*Pranjal Kaser, Research Scholar, SoS in Statistics, Pt. RSU Raipur, C.G.
kaserpranjal@gmail.com

Abstract:Survey sampling seeks to achieve statistical precision with limited resources. Classical approaches such as Neyman allocation minimize estimator variance under a fixed total sample size but often ignore heterogeneous costs, logistical constraints, and field feasibility. This paper introduces the Operations Research Guided Sampling (ORGS) framework, which integrates  optimization techniques from Operations Research (OR) into traditional sampling theory to derive cost-efficient and operationally feasible sample allocations. By formulating sample allocation as a constrained optimization problem minimizing estimator variance subject to budget and feasibility limits- ORGS generalizes Neyman’s allocation and yields the closed-form optimal solution 𝑛ℎ ∗ = 𝐶,𝑊ℎ𝑆ℎ/√𝑐ℎ 𝐻 𝑗=1∑ 𝑊𝑗𝑆𝑗√𝑐𝑗 where (𝑐ℎ) denotes per-unit cost, (𝑊ℎ) stratum weight, and (𝑆ℎ) within � � stratum standard deviation. The resulting minimum variance 𝑉𝑚𝑖𝑛 = (∑ 𝑊ℎ𝑆ℎ√𝑐ℎℎ=1 )2𝐶 directly influences statistical efficiency.demonstrates how cost heterogeneityKeywords: stratified sampling, optimal allocation, operations research, cost constraint, variance minimization, integeroptimization.