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<p>This paper examines improved estimation of shipment delivery times across four major regions of India—North, West, South, and East—using stratified sampling techniques to enhance estimation precision. Motivated by recent developments on optimal estimation under cost constraints in stratified sampling (Yadav et al. in Ann Data Sci 12:517–538, 2025), we propose a novel population mean estimator that incorporates shipment volume as an auxiliary variable alongside delivery time as the study variable. By effectively exploiting the correlation between shipment volume and delivery time, the proposed estimator achieves reduced estimation error and improved efficiency. The sampling properties of the estimator, including bias and mean squared error (MSE), are analytically derived to assess its theoretical performance. Comparative analysis with existing estimators demonstrates the superior efficiency of the proposed method in estimating expected delivery times. Extensive simulation experiments are conducted to evaluate robustness under heterogeneous regional delivery patterns. The results confirm consistent gains over traditional estimators, highlighting the practical relevance of the proposed approach for logistics optimization and informed supply chain decision-making.</p>

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On optimal estimation in supply chain management using stratified sampling

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Mukesh Kumar Verma,
  • Satyam R. Sharma,
  • Rahul Varshney,
  • Subhash Kumar Yadav

摘要

This paper examines improved estimation of shipment delivery times across four major regions of India—North, West, South, and East—using stratified sampling techniques to enhance estimation precision. Motivated by recent developments on optimal estimation under cost constraints in stratified sampling (Yadav et al. in Ann Data Sci 12:517–538, 2025), we propose a novel population mean estimator that incorporates shipment volume as an auxiliary variable alongside delivery time as the study variable. By effectively exploiting the correlation between shipment volume and delivery time, the proposed estimator achieves reduced estimation error and improved efficiency. The sampling properties of the estimator, including bias and mean squared error (MSE), are analytically derived to assess its theoretical performance. Comparative analysis with existing estimators demonstrates the superior efficiency of the proposed method in estimating expected delivery times. Extensive simulation experiments are conducted to evaluate robustness under heterogeneous regional delivery patterns. The results confirm consistent gains over traditional estimators, highlighting the practical relevance of the proposed approach for logistics optimization and informed supply chain decision-making.