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Aiming at the military supply chain coordination with contracts under normal order demand, this paper first explains the concept and main characteristics of the military supply chain, defines the concept of supply chain coordination, analyzes the supply chain coordination mechanism, and puts forward the hypotheses of modeling. Based on the bi-level programming theory, the minimum total cost of military enterprises and maximum profit of manufacturers are further taken as the objectives of the upper and lower levels, and such factors as cost of means of production, ordering cost of parts, inventory cost, cost of late delivery and penalty cost are taken into account in this paper. On this basis, a bi-level programming model for military supply chain coordination with contracts is built. The model is then solved by hierarchical particle swarm optimization (HPSO), and specific operation steps are given. Finally, the model is verified in terms of rationality and feasibility through case analysis.<\/jats:p>","DOI":"10.1177\/14727978251317313","type":"journal-article","created":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T05:49:29Z","timestamp":1738216169000},"page":"2964-2975","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Bi-level programming model for military supply chain coordination with contracts based on particle swarm optimization algorithm"],"prefix":"10.66113","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-5005-204X","authenticated-orcid":false,"given":"Yachen","family":"Shen","sequence":"first","affiliation":[{"name":"School of Equipment Management and Unmanned Aerial Vehicle Engineering, Air Force Engineering University, Xi\u2019an, China"},{"name":"School of Accounting and Finance, Xi\u2019an Eurasia University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huachun","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Equipment Management and Unmanned Aerial Vehicle Engineering, Air Force Engineering University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7125-234X","authenticated-orcid":false,"given":"Jing","family":"Li","sequence":"additional","affiliation":[{"name":"School of Accounting and Finance, Xi\u2019an Eurasia University, Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"55691","published-online":{"date-parts":[[2025,1,30]]},"reference":[{"key":"e_1_3_3_2_2","volume-title":"Research on cooperative supply chain and coping mechanism of emergency events","author":"Li H","year":"2017","unstructured":"Li H, Li C. 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