On optimal estimation techniques for supply chain management with stratified sampling
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Abstract
In this study, improving the estimation of the population mean is critical in supply chain management for optimizing resource allocation, determining the optimum sample size, and enhancing operational efficiency. This study proposes an improved method for estimating the population mean within a stratified random sampling framework by incorporating an auxiliary variable to increase the precision of delivery time estimates and minimize costs incurred. Population data are generated under a bivariate normal distribution across four stratified regions, using shipment volume as an auxiliary variable correlated with delivery time. A first-order error approximation is employed to derive an efficient estimator, which reduces bias and improves accuracy. A simulation study with a proportionally allocated stratified sample is conducted to evaluate the performance of the proposed estimator. The results demonstrate reduced variation and increased estimation efficiency, and cost-effectiveness compared to traditional mean estimators. This approach provides robust statistical insights for logistics companies, enabling data-driven decision-making and enhanced supply chain performance.
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References
1. Aslam, M. S., Bilal, H., Band, S. S., and Ghasemi, P. Modeling of nonlinear supply chain management with lead-times based on Takagi-Sugeno fuzzy control model. Engineering applications of artificial intelligence, 133, 108-131 (2024). DOI: 10.1016/j.engappai.2024.108131
2. Cochran, W. G. (1977). Sampling techniques. John Wiley & Sons.
3. Cooper, M. C., Lambert, D. M., and Pagh, J. D. Supply chain management: more than a new name for logistics. The international journal of logistics management, 8(1), 1-14 (1997). https://doi.org/10.1108/09574099710805556
4. Cox, A. Power, value and supply chain management. Supply chain management: An international journal, 4(4), 167-175 (1999). https://doi.org/10.1108/13598549910284480
5. Daios, A., Kladovasilakis, N., Kelemis, A., and Kostavelis, I. AI applications in supply chain management: A survey. Applied Sciences, 15(5), 2775 (2025). https://doi.org/10.3390/app15052775
6. Davis, T. Effective supply chain management. Sloan management review, 34, 35-35 (1993). https://www.scirp.org/reference/referencespapers?referenceid=3505727
7. Deiva, A. G., and Kalpana, P. Supply chain risk identification: a real-time data-mining approach. Industrial management and data systems, 122(5), 1333-1354 (2022). https://doi.org/10.1108/IMDS-11-2021-0719
8. Deville, J. C., and Sarndal, C. E. Calibration estimators in survey sampling. Journal of the American statistical Association, 87(418), 376-382 (1992). https://www.tandfonline.com/doi/abs/10.1080/01621459.1992.10475217
9. Dey, B. K., Bhuniya, S., and Sarkar, B. Involvement of controllable lead time and variable demand for a smart manufacturing system under a supply chain management. Expert Systems with Applications, 184, 115464 (2021). https://doi.org/10.1016/j.eswa.2021.115464
10. Ellram, L. M. (1991). Supply chain management: the industrial organization perspective. International Journal of Physical Distribution & Logistics Management, 21(1), 13-22 (1991). https://doi.org/10.1108/09600039110137082
11. Hansen, M. H., Hurwitz, W. N., and Gurney, M. Problems and methods of the sample survey of business. Journal of the American Statistical Association, 41(234), 173-189 (1946). https://doi.org/10.1080/01621459.1946.10501862
12. Haval, A. M. and Afzal. Deploying cloud computing and data warehousing to optimize supply chain management and retail analytics. In Applications of Mathematics in Science and Technology, 810-816 (2025). https://www.taylorfrancis.com/chapters/edit/10.1201/9781003606659-156/deploying-cloud-computing-data-warehousing-optimize-supply-chain-management-retail-analytics-abhijeet-madhukar-haval-afzal
13. Kareem, S., Fehrer, J. A., Shalpegin, T. and Stringer, C. Navigating tensions of sustainable supply chains in times of multiple crises: A systematic literature review. Business Strategy and the Environment, 34(1), 316-337 (2025). https://doi.org/10.1002/bse.3990
14. Kim, J. M., Sungur, E. A. and Heo, T. Y. Calibration approach estimators in stratified sampling. Statistics & probability letters, 77(1), 99-103 (2007). https://ideas.repec.org/a/eee/stapro/v77y2007i1p99-103.html
15. Kumar, N., Kumar, K., Aeron, A., and Verre, F. Blockchain technology in supply chain management: Innovations, applications, and challenges. Telematics and Informatics Reports, 100204 (2025). https://doi.org/10.1016/j.teler.2025.100204
16. Maghsoodi, A. I., and Asadabadi, M. R. A stratified markovian multi-preference decision support system to assess supply chain blockchain platforms. IEEE Transactions on Engineering Management (2025). https://ieeexplore.ieee.org/document/10836802
17. Mangan, D. J., and Lalwani, C. Global logistics and supply chain management. John Wiley & Sons (2016). https://eprints.ncl.ac.uk/219945
18. Mentzer, J. T., DeWitt, W., Keebler, J. S., Min, S., Nix, N. W., Smith, C. D., and Zacharia, Z. G. Defining supply chain management. Journal of Business logistics, 22(2), 1-25 (2001). https://doi.org/10.1002/j.2158-1592.2001.tb00001.x
19. Muili, J. O., Singh, R. V. K., Onwuka, G. I., and Audu, A. New calibration of finite population mean of combined ratio estimators in stratified random sampling. Fudma Journal of Sciences, 6(4), 37-44 (2022). https://fjs.fudutsinma.edu.ng/index.php/fjs/article/view/920
20. Qing, S., and Valliant, R. Extending Cochran’s sample size rule to stratified simple random sampling with applications to audit sampling. Journal of Official Statistics, 41(1), 309-328 (2025). https://doi.org/10.1177/0282423X2412770544
21. Rouma, J. G. Theoretical framework of supply chain uncertainties. Journal of Enterprise and Business Intelligence, 15. (2022). https://anapub.co.ke/journals/jebi/jebi_pdf/2022/jebi_volume_2-issue_3/JEBI202202016.pdf
22. Sachan, A., and Datta, S. Review of supply chain management and logistics research. International Journal of Physical Distribution & Logistics Management, 35(9), 664-705 (2005). DOI: 10.1108/09600030510632032
23. Sanders, N. R. Supply chain management: A global perspective. John Wiley & Sons (2025).
24. Singh, S. Advanced sampling theory with applications: How Michael Selected Amy 2. Springer Science & Business Media. (2003). https://link.springer.com/book/10.1007/978-94-007-0789-4
25. Stevens, G. C. Successful supply chain management. Management Decision, 28(8) (1990). https://doi.org/10.1108/00251749010140790
26. Tarannum, T., and Hossain, M. Z. Impact of real-time MIS on supply chain management a case study approach. Pacific Journal of Business Innovation and Strategy, 1(1), 38-48 (2024). https://www.researchgate.net/publication/389001353_Impact_of_Real-Time_MIS_on_Supply_Chain_Management_A_Case_Study_Approach
27. Turner, F. Managing the supply chain. Proceedings of the Institution of Mechanical Engineers, Part B: Management and engineering manufacture, 201(4), 251-255 (1987). https://doi.org/10.1243/PIME_PROC_1987_201_077_02
28. Verma, M. K., Yadav, S. K., Varshney, R., and Vishwakarma, G. K. Improved estimation strategy of mean using linear cost function under stratified sampling. Quality & Quantity, 1-20 (2025). https://link.springer.com/article/10.1007/s11135-024-02021-6
29. Verma, M. K., Yadav, S. K., Varshney, R., and Vishwakarma, G. K. An optimal strategy for estimating the population mean in stratified random sampling under an auxiliary attribute. Life Cycle Reliability and Safety Engineering, 1-7 (2025). https://link.springer.com/article/10.1007/s41872-025-00337-2
30. Yadav S K and Kadilar C. Efficient family of exponential estimator for population mean. Hacettepe Journal of Mathematics and Statistics, 42(6), 671-677 (2013). https://www.researchgate.net/publication/257983423_Efficient_Family_of_Exponential_Estimators_for_the_Population_Mean
31. Yadav, S. K., Arya, D., Vishwakarma, G. K., and Verma, M. K. Generalized ratio-cum-exponential-log ratio type estimators of population mean under simple random sampling scheme. Lobachevskii Journal of Mathematics, 44(9), 3889-3901 (2023). https://link.springer.com/article/10.1134/S1995080223090445
32. Yadav, S. K., Kumar Verma, M., & Varshney, R. Optimal strategy for elevated estimation of population mean in stratified random sampling under linear cost function. Annals of Data Science, 12(2), 517-538 (2025). https://link.springer.com/article/10.1007/s40745-024-00520-9
33. Zaagan, A. A., Verma, M. K., Mahnashi, A. M., Yadav, S. K., Ahmadini, A. A. H., Meetei, M. Z., and Varshney, R. An effective and economic estimation of population mean in stratified random sampling using a linear cost function. Heliyon, 10(10). (2024). https://doi.org/10.1016/j.heliyon.2024.e31291