{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:41:25Z","timestamp":1760240485482,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T00:00:00Z","timestamp":1562198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Henan Province Soft Science Research Plan Project","award":["182400410054"],"award-info":[{"award-number":["182400410054"]}]},{"name":"Henan provincial government decision research tendering project","award":["2018B019"],"award-info":[{"award-number":["2018B019"]}]},{"name":"Henan provincial social science planning decision consultation project","award":["2018JC05"],"award-info":[{"award-number":["2018JC05"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we study a dual-channel closed-loop supply chain in which a manufacturer considers the market waste products recovery and remanufacture, and a retailer considers provide services to customers. We build a Stackelberg game model and a centralized game model in a static and dynamic state, respectively, and analyze the two dynamic models by mathematical analysis and explore the stability and entropy of the two models using bifurcation, the basin of attraction, chaotic attractors, and so on. The influences of service level and profit distribution rate on the system\u2019s profit are discussed. The theoretical results show that higher price adjustment speed will lead to the system lose stability with a larger entropy value. In the Stackelberg game model, the stability of the system increases as the service value and the recovery rate increases; in the centralized model, the stability of the system decreases with the increase of the service value and increases with the recovery rate increases. When the Stackelberg game model is in a stable state, the manufacturer\u2019s profit increases first and then decreases, and the retailer\u2019s profit first decreases and then increases as the service value of the retailer increases. The research will serve as good guidance for both the manufacturer and retailer in dual-channel closed-loop supply chains to improve decision making.<\/jats:p>","DOI":"10.3390\/e21070659","type":"journal-article","created":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T11:13:18Z","timestamp":1562238798000},"page":"659","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["The Complexity Entropy Analysis of a Supply Chain System Considering Recovery Rate and Channel Service"],"prefix":"10.3390","volume":"21","author":[{"given":"Qiuxiang","family":"Li","sequence":"first","affiliation":[{"name":"Institute of Modern Logistics, Henan University, Kaifeng 475004, China"},{"name":"Institute of Management Science and Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengnan","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Business, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Business, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi-min","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Management &amp; Economics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,4]]},"reference":[{"key":"ref_1","first-page":"81","article-title":"Proposal of a concept for improving the sustainable management of supply chains in the textile industry","volume":"26","author":"Dominik","year":"2018","journal-title":"Fibres Text. 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