{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T14:29:27Z","timestamp":1781533767087,"version":"3.54.5"},"reference-count":57,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T00:00:00Z","timestamp":1778457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010814","name":"Anhui Provincial Department of Education","doi-asserted-by":"publisher","award":["2024AH050611"],"award-info":[{"award-number":["2024AH050611"]}],"id":[{"id":"10.13039\/501100010814","id-type":"DOI","asserted-by":"publisher"}]},{"award":["2024AH050611"],"award-info":[{"award-number":["2024AH050611"]}],"id":[{"id":"https:\/\/ror.org\/012m7k033","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Key Project of Humanities and Social Sciences of Anhui Provincial Department of Education","award":["2024AH052542"],"award-info":[{"award-number":["2024AH052542"]}]},{"name":"Anhui Xinhua University Quality Engineering Project","award":["2020ylzyx06, 2023jgkcx07 and 2024jy016"],"award-info":[{"award-number":["2020ylzyx06, 2023jgkcx07 and 2024jy016"]}]},{"name":"Anhui Province Logistics Management Revitalization Project","award":["2013 zxs01"],"award-info":[{"award-number":["2013 zxs01"]}]},{"name":"Anhui Province Scientific Research Compilation Plan Project","award":["2023AH051794"],"award-info":[{"award-number":["2023AH051794"]}]},{"name":"Anhui Xinhua University Key Scientific Research Project","award":["2025rwzdi17"],"award-info":[{"award-number":["2025rwzdi17"]}]},{"name":"The Project of the College Students' Quality Education Research Center of Anhui Xinhua University","award":["IFQE202510"],"award-info":[{"award-number":["IFQE202510"]}]},{"award":["IFQE202510"],"award-info":[{"award-number":["IFQE202510"]}],"id":[{"id":"https:\/\/ror.org\/053d7x641","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The demand for the fabric warehouse presents obvious characteristics of hockey stick effect. This leads to problems such as peak congestion and labor shortages during its operation. In order to alleviate this phenomenon, we propose a combination strategy that uses a SARIMA\u2013Markov hybrid model for demand forecasting, and then applies Actor-Critic reinforcement learning for dynamic pricing. This model integrates SARIMA with Markov chains for residual correction, capturing linear trends and seasonal patterns while correcting residuals, yielding more accurate predictions for highly volatile demand in textile logistics. Experimental results indicate that our approach achieves better performance than SARIMA, Temporal Fusion Transformer (TFT), and Ensemble, especially in identifying and reproducing sharp demand peaks. By combining forecasting results with price elasticity, the proposed dynamic pricing scheme cuts peak-hour demand by 12.54%, which in turn eases pressure on labor scheduling and boosts the efficiency of workforce allocation. This work offers a data-driven approach to flattening demand fluctuations via intelligent pricing, improves operational efficiency without requiring extra hardware investment, and provides a practical response to a long-standing bottleneck in the textile logistics sector.<\/jats:p>","DOI":"10.3390\/a19050382","type":"journal-article","created":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T17:17:42Z","timestamp":1778519862000},"page":"382","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Data-Driven Dynamic Pricing for Mitigating the Hockey Stick Effect: A Hybrid Forecasting and Actor-Critic Reinforcement Learning Framework"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-9089-3994","authenticated-orcid":false,"given":"Shanshan","family":"Peng","sequence":"first","affiliation":[{"name":"School of Business, Anhui Xinhua University, Hefei 230088, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dandan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Business, Anhui Xinhua University, Hefei 230088, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fang","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ministry of General Education, Anhui Xinhua University, Hefei 230088, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1590\/1807-7692bar2014130044","article-title":"Hockey Stick Phenomenon: Supply Chain Management Challenge in Brazil","volume":"11","author":"Sanches","year":"2014","journal-title":"BAR\u2014Braz. Adm. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1108\/13598540510578306","article-title":"Five ways to simplify your supply chain","volume":"10","author":"Hoole","year":"2005","journal-title":"Supply Chain Manag. Int. J."},{"key":"ref_3","first-page":"112","article-title":"Analysis & countermeasures for \u201cHockey stick\u201d phenomenon between supply and demand","volume":"11","author":"Huaming","year":"2008","journal-title":"J. Manag. Sci. China"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1590\/S1807-76922009000300007","article-title":"The stockouts study: An examination of the extent and the causes in the S\u00e3o Paulo supermarket sector","volume":"6","author":"Vasconcellos","year":"2009","journal-title":"Braz. Adm. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.ijpe.2012.06.006","article-title":"An empirical investigation on causes and effects of the bullwhip-effect: Evidence from the personal care sector","volume":"143","author":"Zotteri","year":"2013","journal-title":"Int. J. Prod. Econ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4601","DOI":"10.1080\/00207543.2016.1269969","article-title":"The inverse hockey stick effect: An empirical investigation of the fiscal calendar\u2019s impact on firm inventories","volume":"55","author":"Hoberg","year":"2017","journal-title":"Int. J. Prod. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1002\/j.2158-1592.2007.tb00059.x","article-title":"The impact of demand uncertainty and configuration capacity on customer service performance in a configure-to-order environment","volume":"28","author":"Nyaga","year":"2007","journal-title":"J. Bus. Logist."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1002\/nav.20417","article-title":"Threshold incentives over multiple periods and the sales hockey stick phenomenon","volume":"57","author":"Sohoni","year":"2010","journal-title":"Nav. Res. Logist."},{"key":"ref_9","first-page":"3","article-title":"The Impact of the Hockey-Stick Phenomenon on the Retail Industry in India: Pre and During COVID-19","volume":"2","author":"Ahmed","year":"2022","journal-title":"J. World Econ. Transform. Transit."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Nasseri, M., Falatouri, T., Brandtner, P., and Darbanian, F. (2023). Applying machine learning in retail demand prediction\u2014A comparison of tree-based ensembles and long short-term memory-based deep learning. Appl. Sci., 13.","DOI":"10.3390\/app131911112"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"128259","DOI":"10.1016\/j.eswa.2025.128259","article-title":"Reinforcement learning-based simulation optimization for an integrated manufacturing-warehouse system: A two-stage approach","volume":"290","author":"Hosseini","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.cirp.2023.04.019","article-title":"Dynamic pricing of product and delivery time in multi-variant production using an actor critic reinforcement learning","volume":"72","author":"Stamer","year":"2023","journal-title":"CIRP Ann."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.dss.2013.01.026","article-title":"A multivariate intelligent decision-making model for retail sales forecasting","volume":"55","author":"Guo","year":"2013","journal-title":"Decis. Support Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.procs.2019.01.100","article-title":"Demand forecasting in pharmaceutical supply chains: A case study","volume":"149","author":"Merkuryeva","year":"2019","journal-title":"Procedia Comput. Sci."},{"key":"ref_15","first-page":"107","article-title":"Industry 4.0 and demand forecasting of the energy supply chain: A literature review","volume":"154","author":"Nia","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kontopoulou, V.I., Panagopoulos, A.D., Kakkos, I., and Matsopoulos, G.K. (2023). A review of ARIMA vs. machine learning approaches for time series forecasting in data driven networks. Future Internet, 15.","DOI":"10.3390\/fi15080255"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1111\/opec.12287","article-title":"Predicting indian electricity exchange-traded market prices: Sarima and mlp approach","volume":"47","author":"Gupta","year":"2023","journal-title":"OPEC Energy Rev."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Xu, Z., Zhang, H., and Huang, Z. (2022). A continuous markov-chain model for the simulation of COVID-19 epidemic dynamics. Biology, 11.","DOI":"10.3390\/biology11020190"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"109985","DOI":"10.1016\/j.ecolind.2023.109985","article-title":"Spatial and temporal characteristics and evolutionary prediction of urban health development efficiency in China: Based on super-efficiency SBM model and spatial Markov chain model","volume":"147","author":"Wang","year":"2023","journal-title":"Ecol. Indic."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1080\/14680629.2024.2376271","article-title":"Airfield pavement performance prediction using clustered Markov chain models","volume":"26","author":"Clemmensen","year":"2025","journal-title":"Road Mater. Pavement Des."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Bilotta, G., Meduri, G.M., Genovese, E., Bibb\u00f2, L., and Barrile, V. (2025). Safeguarding the Aspromonte Forests: Random Forests and Markov Chains as Forecasting Models for Predicting Land Transformations. Forests, 16.","DOI":"10.3390\/f16020290"},{"key":"ref_22","first-page":"7682","article-title":"Solar air heaters performance prediction using multi-layer perceptron neural network\u2013a systematic review","volume":"47","author":"Ghritlahre","year":"2025","journal-title":"Energy Sources Part A Recovery Util. Environ. Eff."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"113452","DOI":"10.1016\/j.dss.2020.113452","article-title":"A multivariate approach for multi-step demand forecasting in assembly industries: Empirical evidence from an automotive supply chain","volume":"142","author":"Cortez","year":"2021","journal-title":"Decis. Support Syst."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Pasupuleti, V., Thuraka, B., Kodete, C.S., and Malisetty, S. (2025). Enhancing supply chain agility and sustainability through machine learning: Optimization techniques for logistics and inventory management. Logistics, 8.","DOI":"10.3390\/logistics8030073"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"115102","DOI":"10.1016\/j.eswa.2021.115102","article-title":"A machine learning approach for forecasting hierarchical time series","volume":"182","author":"Mancuso","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"012031","DOI":"10.1088\/1757-899X\/926\/1\/012031","article-title":"A study on the deep learning based prediction of production demand by using LSTM under the state of data sparsity","volume":"926","author":"Jung","year":"2020","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Li, T., Wang, S., Liu, B., Hu, F., Chen, Y., and Han, Y. (2025). Bayesian Optimization of LSTM-Driven Cold Chain Warehouse Demand Forecasting Application and Optimization. Processes, 13.","DOI":"10.3390\/pr13103085"},{"key":"ref_28","first-page":"39741","article-title":"Inventory-forecasting: Mind the gap","volume":"2992","author":"Goltsos","year":"2022","journal-title":"Eur. J. Oper. Res."},{"key":"ref_29","unstructured":"Mohan, B.A., Harshavardhan, B., Karan, S., Mohammed, J.S., and Pranav, M.G. (2021). Demand forecasting and Route Optimization in Supply chain industry using Data Analytics. 2021 Asian Conference on Innovationin Technology (ASIANCON), IEEE."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Lei, M., Li, S., and Yu, S. (2019). Demand forecasting approaches based on associated relationships for multiple products. Entropy, 21.","DOI":"10.3390\/e21100974"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1016\/j.ijforecast.2021.03.012","article-title":"Temporal Fusion Transformers for interpretable multi-horizon time series forecasting","volume":"37","author":"Lim","year":"2021","journal-title":"Int. J. Forecast."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.ijforecast.2020.06.008","article-title":"Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions","volume":"37","author":"Hewamalage","year":"2020","journal-title":"Int. J. Forecast."},{"key":"ref_33","first-page":"3037","article-title":"Comparison of statistical and machine learning methods for daily SKU demand forecasting","volume":"22","author":"Spiliotis","year":"2022","journal-title":"Oper. Res."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Oliveira, J.M., and Ramos, P. (2024). Evaluating the Effectiveness of Time Series Transformers for Demand Forecasting in Retail. Mathematics, 12.","DOI":"10.3390\/math12172728"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1016\/j.procir.2022.05.119","article-title":"Review and analysis of artificial intelligence methods for demand forecasting in supply chain management","volume":"107","author":"Mediavilla","year":"2022","journal-title":"Procedia CIRP"},{"key":"ref_36","first-page":"54","article-title":"Bayesian Structural Time Series Model and SARIMA Model for Rainfall Forecasting in Nigeria","volume":"7","author":"Ogundeji","year":"2025","journal-title":"J. Stat. Model. Anal. (JOSMA)"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"357","DOI":"10.2307\/1912559","article-title":"A new approach to the economic analysis of nonstationary time series and the business cycle","volume":"57","author":"Hamilton","year":"1989","journal-title":"Econometrica"},{"key":"ref_38","first-page":"574","article-title":"What causes the forecasting failure of markov-switching models? A monte carlo study","volume":"9","author":"Bessec","year":"2005","journal-title":"Econometrics"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Pattnaik, S., Liew, N., Kures, A.O., Pinsky, E., and Park, K. (2024). Catalyzing supply chain evolution: A comprehensive examination of artificial intelligence integration in supply chain management. Eng. Proc., 68.","DOI":"10.3390\/engproc2024068057"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1038\/s41598-024-84821-2","article-title":"Bio particle swarm optimization and reinforcement learning algorithm for path planning of automated guided vehicles in dynamic industrial environments","volume":"15","author":"Lin","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2292","DOI":"10.1109\/TNSE.2025.3546961","article-title":"Rumor suppression in a three-layer network: A reinforcement learning algorithm","volume":"12","author":"Zhong","year":"2025","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"112005","DOI":"10.1016\/j.ymssp.2024.112005","article-title":"Visual feedback vibration control of flexible hinged plate system based on reinforcement learning algorithm","volume":"224","author":"Qiu","year":"2025","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1109\/TNN.1998.712192","article-title":"Reinforcement learning: An introduction","volume":"9","author":"Sutton","year":"1998","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"128570","DOI":"10.1016\/j.eswa.2025.128570","article-title":"Dynamic pricing and inventory control of perishable products by a deep reinforcement learning algorithm","volume":"291","author":"Kavoosi","year":"2026","journal-title":"Expert Syst. Appl."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"122948","DOI":"10.1016\/j.eswa.2023.122948","article-title":"Data-driven dynamic pricing and inventory management of an omni-channel retailer in an uncertain demand environment","volume":"244","author":"Liu","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Liang, Y., Hu, Y., Luo, D., Zhu, Q., Chen, Q., and Wang, C. (2024). Distributed dynamic pricing strategy based on deep reinforcement learning approach in a presale mechanism. Sustainability, 15.","DOI":"10.3390\/su151310480"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1016\/j.cirpj.2022.07.009","article-title":"An integrated energy management system using double deep Q-learning and energy storage equipment to reduce energy cost in manufacturing under real-time pricing condition: A case study of scale-model factory","volume":"38","author":"Yi","year":"2022","journal-title":"CIRP J. Manuf. Sci. Technol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"111864","DOI":"10.1016\/j.asoc.2024.111864","article-title":"Deep reinforcement learning algorithms for dynamic pricing and inventory management of perishable products","volume":"163","author":"Yavuz","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"108353","DOI":"10.1016\/j.patcog.2021.108353","article-title":"Learning to select cuts for efficient mixed-integer programming","volume":"123","author":"Huang","year":"2022","journal-title":"Pattern Recognit."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"109411","DOI":"10.1016\/j.compchemeng.2025.109411","article-title":"Comparison of actor\u2013critic reinforcement learning methods for adaptive cut selection for integer programming with applications to sensor network design","volume":"204","author":"Arjun","year":"2026","journal-title":"Comput. Chem. Eng."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1109\/TSMCC.2012.2218595","article-title":"A survey of actor-critic reinforcement learning: Standard and natural policy gradients","volume":"42","author":"Grondman","year":"2012","journal-title":"IEEE Trans. Syst. Man Cybern. Part C"},{"key":"ref_52","first-page":"102397","article-title":"Fleet planning under demand and fuel price uncertainty using actor-critic reinforcement learning","volume":"109","author":"Geursen","year":"2021","journal-title":"J. SSRN Electron. J."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"112601","DOI":"10.1016\/j.enbuild.2022.112601","article-title":"A multi-task learning model for building electrical load prediction","volume":"278","author":"Liu","year":"2023","journal-title":"Energy Build."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"71752","DOI":"10.1109\/ACCESS.2020.2987820","article-title":"Actor\u2013critic deep reinforcement learning for solving job shop scheduling problems","volume":"8","author":"Liu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1080\/00207543.2018.1488086","article-title":"The impact of digital technology and Industry 4.0 on the ripple effect and supply chain risk analytics","volume":"57","author":"Ivanov","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/S0169-2070(01)00110-8","article-title":"A state space framework for automatic forecasting using exponential smoothing methods","volume":"18","author":"Hyndman","year":"2002","journal-title":"Int. J. Forecast."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1016\/j.ijforecast.2021.11.013","article-title":"M5 accuracy competition: Results; findings, and conclusions","volume":"38","author":"Makridakis","year":"2022","journal-title":"Int. J. Forecast."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/5\/382\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T04:53:53Z","timestamp":1779339233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/5\/382"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,11]]},"references-count":57,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["a19050382"],"URL":"https:\/\/doi.org\/10.3390\/a19050382","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,11]]}}}