PUB
  • Home
  • Sources
  • Search
  • About

Calibrated Quantile Transformers for Cost-Aware Inventory Control in Simulated Multi-Echelon Supply Networks

Quinn Williams
Academic Journal of Management Science and Engineering, (2026), Vol.1, No.7, pp.145-156
Published: November 1, 2026
DOI: 10.62051/ajmse.v1n7.14
PDF: Download Full Text PDF
Abstract

Accurate demand quantiles do not automatically yield low-cost network inventory decisions. We evaluate a series-aware quantile Transformer linked to a rolling residual correction that shrinks item-specific errors toward pooled calibration residuals. The corrected 0.90 demand quantile drives retailer order-up-to decisions under shared distribution-center supply, with explicit replenishment lead times. To distinguish the value of calibration from forecasting architecture, a LightGBM quantile model and fixed-buffer controls are subjected to the same simulation. 10 independently generated synthetic networks each contain 48 product-store demand series over 176 weeks, and all policies use the same chronological 31-week holdout. Across the networks, the calibrated Transformer lowers average simulated cost by 13.1% relative to static stock and 3.6% relative to its uncalibrated quantiles. The network-paired mean incremental cost reduction is 3.54% with a 95% bootstrap interval [2.33%, 4.78%]. The study isolates decision postprocessing in a controlled simulation rather than making a real-retailer deployment claim.

Keywords: Probabilistic Time Series, Quantile Transformer, Safety Stock, Multi-echelon Inventory, Rolling Calibration, Supply Chain Simulation
APA Citation: Quinn Williams (2026). Calibrated Quantile Transformers for Cost-Aware Inventory Control in Simulated Multi-Echelon Supply Networks. Academic Journal of Management Science and Engineering, 1(7), 145-156. https://doi.org/10.62051/ajmse.v1n7.14

References

  1. Lee, H. L., Padmanabhan, V., & Whang, S. (1997). Information distortion in a supply chain: The bullwhip effect. Management Science, 43(4), 546–558. https://doi.org/10.1287/mnsc.43.4.546.
  2. Clark, A. J., & Scarf, H. (1960). Optimal policies for a multi-echelon inventory problem. Management Science, 6(4), 475–490. https://doi.org/10.1287/mnsc.6.4.475.
  3. Bertsimas, D., & Kallus, N. (2020). From predictive to prescriptive analytics. Management Science, 66(3), 1025–1044. https://doi.org/10.1287/mnsc.2018.3253.
  4. Vaswani, A., et al. (2017). Attention is all you need. Advances in Neural Information Processing Systems, 30. https://research.google/pubs/attention-is-all-you-need/.
  5. Lim, B., & Zohren, S. (2021). Time-series forecasting with deep learning: A survey. Philosophical Transactions of the Royal Society A, 379(2194), 20200209. https://doi.org/10.1098/rsta.2020.0209.
  6. Lim, B., Arık, S. Ö., Loeff, N., & Pfister, T. (2021). Temporal fusion transformers for interpretable multi-horizon time series forecasting. International Journal of Forecasting, 37(4), 1748–1764. https://doi.org/10.1016/j.ijforecast.2021.03.012.
  7. Salinas, D., Flunkert, V., Gasthaus, J., & Januschowski, T. (2020). DeepAR: Probabilistic forecasting with autoregressive recurrent networks. International Journal of Forecasting, 36(3), 1181–1191. https://doi.org/10.1016/j.ijforecast.2019.07.001.
  8. Zhou, H., et al. (2021). Informer: Beyond efficient transformer for long sequence time-series forecasting. Proceedings of the AAAI Conference on Artificial Intelligence, 35(12), 11106–11115. https://doi.org/10.1609/aaai.v35i12.17325.
  9. Wu, H., Xu, J., Wang, J., & Long, M. (2021). Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting. Advances in Neural Information Processing Systems, 34. https://proceedings.neurips.cc/paper_files/paper/2021/hash/bcc0d400288793e8bdcd7c19a8ac0c2b-Abstract.html.
  10. Zeng, A., Chen, M., Zhang, L., & Xu, Q. (2023). Are transformers effective for time series forecasting? Proceedings of the AAAI Conference on Artificial Intelligence, 37(9), 11121–11128. https://doi.org/10.1609/aaai.v37i9.26317.
  11. Nie, Y., Nguyen, N. H., Sinthong, P., & Kalagnanam, J. (2023). A time series is worth 64 words: Long-term forecasting with transformers. International Conference on Learning Representations. https://dblp.org/rec/conf/iclr/NieNSK23.html.
  12. Zhang, X., Sun, T., Han, X., Yang, Y., & Li, P. (2025). Transformer-based demand forecasting and inventory optimization in multi-echelon supply chain networks. Journal of Banking and Financial Dynamics, 9(12), 1–9. https://doi.org/10.55220/2576-6821.v9.796.
  13. Koenker, R., & Bassett, G., Jr. (1978). Regression quantiles. Econometrica, 46(1), 33–50. https://doi.org/10.2307/1913643.
  14. Ban, G.-Y., & Rudin, C. (2019). The big data newsvendor: Practical insights from machine learning. Operations Research, 67(1), 90–108. https://doi.org/10.1287/opre.2018.1757.
  15. Croston, J. D. (1972). Forecasting and stock control for intermittent demands. Operational Research Quarterly, 23(3), 289–303. https://doi.org/10.1057/jors.1972.50.
  16. Romano, Y., Patterson, E., & Candès, E. J. (2019). Conformalized quantile regression. Advances in Neural Information Processing Systems, 32. https://proceedings.neurips.cc/paper/2019/hash/5103c3584b063c431bd1268e9b5e76fb-Abstract.html.
  17. Elmachtoub, A. N., & Grigas, P. (2022). Smart “predict, then optimize”. Management Science, 68(1), 9–26. https://doi.org/10.1287/mnsc.2020.3922.
  18. Oroojlooyjadid, A., Snyder, L. V., & Takáč, M. (2020). Applying deep learning to the newsvendor problem. IISE Transactions, 52(4), 444–463. https://doi.org/10.1080/24725854.2019.1632502.
  19. Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2022). M5 accuracy competition: Results, findings, and conclusions. International Journal of Forecasting, 38(4), 1346–1364. https://doi.org/10.1016/j.ijforecast.2021.11.013.
  20. Makridakis, S., et al. (2022). The M5 uncertainty competition: Results, findings and conclusions. International Journal of Forecasting, 38(4), 1365–1385. https://doi.org/10.1016/j.ijforecast.2021.10.009.
  21. Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688. https://doi.org/10.1016/j.ijforecast.2006.03.001.
  22. Chen, F., Drezner, Z., Ryan, J. K., & Simchi-Levi, D. (2000). Quantifying the bullwhip effect in a simple supply chain: The impact of forecasting, lead times, and information. Management Science, 46(3), 436–443. https://doi.org/10.1287/mnsc.46.3.436.12069.
  23. Weng, T., Liu, W., & Xiao, J. (2020). Supply chain sales forecasting based on lightGBM and LSTM combination model. Industrial Management & Data Systems, 120(2), 265–279. https://doi.org/10.1108/IMDS-03-2019-0170.
  24. Kilimci, Z. H., et al. (2019). An improved demand forecasting model using deep learning approach and proposed decision integration strategy for supply chain. Complexity, 2019, 9067367. https://doi.org/10.1155/2019/9067367.
  25. Zhou, T., Ma, Z., Wen, Q., Wang, X., Sun, L., & Jin, R. (2022). FEDformer: Frequency enhanced decomposed transformer for long-term series forecasting. Proceedings of the 39th International Conference on Machine Learning, PMLR, 162, 27268–27286. https://proceedings.mlr.press/v162/zhou22g.html.
  26. Punia, S., Singh, S. P., & Madaan, J. K. (2020). From predictive to prescriptive analytics: A data-driven multi-item newsvendor model. Decision Support Systems, 136, 113340. https://doi.org/10.1016/j.dss.2020.113340.
© 2026 PUB · Seek truth with rigour