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Article(id=1239230401168863331, tenantId=1146029695717560320, journalId=1238823019242635269, issueId=1239230393547804821, articleNumber=null, orderNo=null, doi=10.12465/j.issn.0253-4339.2025.03.123, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1724601600000, receivedDateStr=2024-08-26, revisedDate=1729440000000, revisedDateStr=2024-10-21, acceptedDate=1730649600000, acceptedDateStr=2024-11-04, onlineDate=1773385151426, onlineDateStr=2026-03-13, pubDate=1750003200000, pubDateStr=2025-06-16, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773385151426, onlineIssueDateStr=2026-03-13, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773385151426, creator=13701087609, updateTime=1773385151426, updator=13701087609, issue=Issue{id=1239230393547804821, tenantId=1146029695717560320, journalId=1238823019242635269, year='2025', volume='46', issue='3', pageStart='1', pageEnd='166', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773385149609, creator=13701087609, updateTime=1773385254705, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1239230834402717933, tenantId=1146029695717560320, journalId=1238823019242635269, issueId=1239230393547804821, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1239230834402717934, tenantId=1146029695717560320, journalId=1238823019242635269, issueId=1239230393547804821, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=123, endPage=129, ext={EN=ArticleExt(id=1239230401407938670, articleId=1239230401168863331, tenantId=1146029695717560320, journalId=1238823019242635269, language=EN, title=Optimizing the Chilled Meat Supply Chain Based on Time and Temperature in Cold Chain Internet of Things, columnId=null, journalTitle=Journal of Refrigeration, columnName=null, runingTitle=null, highlight=null, articleAbstract=

With the development of cold chain Internet of Things (IoT) technology, real-time temperature monitoring and data sharing have become important means to improve the efficiency of chilled meat supply chain management. In this paper, a strategy for optimizing time and temperature coordination based on the cold chain IoT was proposed to improve the operational efficiency of the chilled meat supply chain. Based on predictive microbiology and system reliability theory, this study investigated the effects of time and temperature on the quality of chilled meat. A quality-change model for chilled meat and an energy consumption model for the chilled meat supply chain were developed. To illustrate this approach, a case study of a chilled chicken supply chain was conducted. The findings revealed that there is an optimal level of freshness in the chilled meat supply chain that maximizes the benefits of the supply chain. If the freshness level in one stage deviates from this optimal value, subsequent stages can adjust the time and temperature to achieve maximum supply chain efficiency.

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Zou Yifeng, male, Ph. D., associate professor, School of Management, Guangzhou University, 86-13924225470, E-mail: . Research fields: transportation management, cold chain logistics.
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随着冷链物联网技术的发展，实时温度监控和数据共享已成为提升冷鲜肉供应链管理效率的重要手段。通过提出一种基于冷链物联网的时间-温度协调优化策略来提升冷鲜肉供应链的运营效率。基于预测微生物学和系统可靠性理论，研究了时间和温度对冷鲜肉品质变化的影响，构建了冷鲜肉的品质变化模型和冷鲜肉供应链的能耗模型，并以冷鲜鸡供应链为案例进行分析。研究表明：冷鲜肉供应链中存在一个最佳的新鲜度水平，能够使供应链效益达到最大化；当某一环节的新鲜度偏离该最佳新鲜度水平，可通过后续环节调整时间和温度，实现供应链效益的最大化。

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邹毅峰，男，博士，副教授，广州大学管理学院，13924225470，E-mail：。研究方向：运输管理、冷链物流。
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Transactions of the Chinese Society of Agricultural Engineering, 2008, 24(4): 229-234.), articleTitle=Development of models to predict the growth of Pseudomonas isolated from chilling pork, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1239230415089758946, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, xref=1., ext=[AuthorCompanyExt(id=1239230415093953251, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, companyId=1239230415089758946, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Management, Guangzhou University, Guangzhou, 510006, China), AuthorCompanyExt(id=1239230415102341860, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, companyId=1239230415089758946, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1广州大学管理学院　广州　510006)]), AuthorCompany(id=1239230415198810858, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, xref=2., ext=[AuthorCompanyExt(id=1239230415203005163, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, companyId=1239230415198810858, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.School of Modern Logistics, Guangzhou Panyu Polytechnic, Guangzhou, 511483, China), AuthorCompanyExt(id=1239230415211393772, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, companyId=1239230415198810858, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2广州番禺职业技术学院现代物流学院　广州　511483)])], figs=[ArticleFig(id=1239230419816739754, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=EN, label=Fig.1, caption=Six flows in chilled meat supply chain, figureFileSmall=1uspPnvAI0oYFngiu6VZTg==, figureFileBig=AREYMYdhgA/13gZuvkmIgw==, tableContent=null), ArticleFig(id=1239230419921597360, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=CN, label=图1, caption=冷鲜肉供应链六流, figureFileSmall=1uspPnvAI0oYFngiu6VZTg==, figureFileBig=AREYMYdhgA/13gZuvkmIgw==, tableContent=null), ArticleFig(id=1239230420106146743, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=EN, label=Fig.2, caption=Optimal freshness in chilled meat supply chain, figureFileSmall=dvPZy9fCdhY2iJoTEDrTOA==, figureFileBig=TrbeFNFthQ5d/jeaQ7lL4w==, tableContent=null), ArticleFig(id=1239230420185838523, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=CN, label=图2, caption=冷鲜肉供应链最佳新鲜度水平, figureFileSmall=dvPZy9fCdhY2iJoTEDrTOA==, figureFileBig=TrbeFNFthQ5d/jeaQ7lL4w==, tableContent=null), ArticleFig(id=1239230420278113213, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=EN, label=Tab.1, caption=Growth characteristic parameters of pseudomonas in chilled chicken at different temperatures, figureFileSmall=null, figureFileBig=null, tableContent=
温度/℃模型lgN0pH值lgNmaxumax相关系数偏差度Bf准确度Af
0Logistic3.0073.150.02000.961 31.107 7797 1.122
Gompertz2.9873.140.003 50.907 91.317 331.232 01
10Logistic4.2076.250.07100.855 11.477 6464 1.477
Gompertz3.0576.030.071 00.997 60.981 991.092 49
20Logistic5.0078.260.18500.856 01.689 4679 1.689
Gompertz3.0278.250.162 30.998 11.056 041.157 93
), ArticleFig(id=1239230420366193604, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=CN, label=表1, caption=不同温度下冷鲜鸡假单胞菌生长特征参数值, figureFileSmall=null, figureFileBig=null, tableContent=
温度/℃模型lgN0pH值lgNmaxumax相关系数偏差度Bf准确度Af
0Logistic3.0073.150.02000.961 31.107 7797 1.122
Gompertz2.9873.140.003 50.907 91.317 331.232 01
10Logistic4.2076.250.07100.855 11.477 6464 1.477
Gompertz3.0576.030.071 00.997 60.981 991.092 49
20Logistic5.0078.260.18500.856 01.689 4679 1.689
Gompertz3.0278.250.162 30.998 11.056 041.157 93
), ArticleFig(id=1239230420437496776, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=EN, label=Tab.2, caption=Parameter values and optimal freshness levels, figureFileSmall=null, figureFileBig=null, tableContent=
参数值
市场需求a/kg10
新鲜度敏感系数β0.43
价格敏感系数η0.30
新鲜度成本系数v50
保鲜固定成本C0/（元/kg）15
销售价格p/（元/kg）35
新鲜度Ropt0.849
), ArticleFig(id=1239230420517188558, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=CN, label=表2, caption=参数值及最佳新鲜度水平, figureFileSmall=null, figureFileBig=null, tableContent=
参数值
市场需求a/kg10
新鲜度敏感系数β0.43
价格敏感系数η0.30
新鲜度成本系数v50
保鲜固定成本C0/（元/kg）15
销售价格p/（元/kg）35
新鲜度Ropt0.849
), ArticleFig(id=1239230420613657555, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=EN, label=Tab.3, caption=Harmonization factors for each segment of the chilled chicken supply chain, figureFileSmall=null, figureFileBig=null, tableContent=
 序号环节i温度Ti/℃修正温度/℃时间ti/h协调因子ξ/（℃2·h）新鲜度Ri
协同1冷藏加工5.013.733 581 508.872 1780.977
2冷库储存4.012.733 5182 918.556 4010.955
3冷链配送6.014.733 5102 170.760 2230.967
4冷藏销售5.914.733 5142 997.950 5120.954
合计     9 596.139 3130.853
非协同1冷藏加工4.012.733 581 297.136 1780.980
2冷库储存4.012.733 5182 918.556 4010.955
3冷链配送4.012.733 5101 621.420 2230.975
4冷藏销售4.012.733 5142 269.988 3120.965
合计     8 107.101 1130.876
), ArticleFig(id=1239230420697543639, tenantId=1146029695717560320, journalId=1238823019242635269, articleId=1239230401168863331, language=CN, label=表3, caption=冷鲜鸡供应链不同环节的协调因子, figureFileSmall=null, figureFileBig=null, tableContent=
 序号环节i温度Ti/℃修正温度/℃时间ti/h协调因子ξ/（℃2·h）新鲜度Ri
协同1冷藏加工5.013.733 581 508.872 1780.977
2冷库储存4.012.733 5182 918.556 4010.955
3冷链配送6.014.733 5102 170.760 2230.967
4冷藏销售5.914.733 5142 997.950 5120.954
合计     9 596.139 3130.853
非协同1冷藏加工4.012.733 581 297.136 1780.980
2冷库储存4.012.733 5182 918.556 4010.955
3冷链配送4.012.733 5101 621.420 2230.975
4冷藏销售4.012.733 5142 269.988 3120.965
合计     8 107.101 1130.876
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基于冷链物联网时间-温度的冷鲜肉供应链优化研究
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谢如鹤 1 , 孟祥超 1 , 邹毅峰 1 , 刘广海 1 , 廖晶 2 , 瑭杰 2
制冷学报 | 2025,46(3): 123-129
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制冷学报 | 2025, 46(3): 123-129
基于冷链物联网时间-温度的冷鲜肉供应链优化研究
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谢如鹤1, 孟祥超1, 邹毅峰1 , 刘广海1, 廖晶2, 瑭杰2
作者信息
  • 1广州大学管理学院　广州　510006
  • 2广州番禺职业技术学院现代物流学院　广州　511483

通讯作者:

邹毅峰，男，博士，副教授，广州大学管理学院，13924225470，E-mail：。研究方向：运输管理、冷链物流。
Optimizing the Chilled Meat Supply Chain Based on Time and Temperature in Cold Chain Internet of Things
Ruhe Xie1, Xiangchao Meng1, Yifeng Zou1 , Guanghai Liu1, Jing Liao2, Jie Tang2
Affiliations
  • 1.School of Management, Guangzhou University, Guangzhou, 510006, China
  • 2.School of Modern Logistics, Guangzhou Panyu Polytechnic, Guangzhou, 511483, China
出版时间: 2025-06-16 doi: 10.12465/j.issn.0253-4339.2025.03.123
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摘要
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随着冷链物联网技术的发展，实时温度监控和数据共享已成为提升冷鲜肉供应链管理效率的重要手段。通过提出一种基于冷链物联网的时间-温度协调优化策略来提升冷鲜肉供应链的运营效率。基于预测微生物学和系统可靠性理论，研究了时间和温度对冷鲜肉品质变化的影响，构建了冷鲜肉的品质变化模型和冷鲜肉供应链的能耗模型，并以冷鲜鸡供应链为案例进行分析。研究表明：冷鲜肉供应链中存在一个最佳的新鲜度水平，能够使供应链效益达到最大化；当某一环节的新鲜度偏离该最佳新鲜度水平，可通过后续环节调整时间和温度，实现供应链效益的最大化。

冷链物流  /  生鲜食品供应链  /  鲜度  /  时间-温度  /  易腐货物

With the development of cold chain Internet of Things (IoT) technology, real-time temperature monitoring and data sharing have become important means to improve the efficiency of chilled meat supply chain management. In this paper, a strategy for optimizing time and temperature coordination based on the cold chain IoT was proposed to improve the operational efficiency of the chilled meat supply chain. Based on predictive microbiology and system reliability theory, this study investigated the effects of time and temperature on the quality of chilled meat. A quality-change model for chilled meat and an energy consumption model for the chilled meat supply chain were developed. To illustrate this approach, a case study of a chilled chicken supply chain was conducted. The findings revealed that there is an optimal level of freshness in the chilled meat supply chain that maximizes the benefits of the supply chain. If the freshness level in one stage deviates from this optimal value, subsequent stages can adjust the time and temperature to achieve maximum supply chain efficiency.

cold chain  /  fresh food supply chain  /  freshness  /  time-temperature  /  perishable goods
谢如鹤, 孟祥超, 邹毅峰, 刘广海, 廖晶, 瑭杰. 基于冷链物联网时间-温度的冷鲜肉供应链优化研究. 制冷学报, 2025 , 46 (3) : 123 -129 . DOI: 10.12465/j.issn.0253-4339.2025.03.123
Ruhe Xie, Xiangchao Meng, Yifeng Zou, Guanghai Liu, Jing Liao, Jie Tang. Optimizing the Chilled Meat Supply Chain Based on Time and Temperature in Cold Chain Internet of Things[J]. Journal of Refrigeration, 2025 , 46 (3) : 123 -129 . DOI: 10.12465/j.issn.0253-4339.2025.03.123
正文
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时间和温度是影响生鲜食品品质和安全的关键因素[1-3]。近年来，冷鲜肉凭借高营养价值、良好的感官体验以及较高的安全性，受到消费者青睐。若冷鲜肉供应链管理不当，特别是在生产、运输等环节中时间和温度控制不规范时，不稳定或不适宜的温度会增加微生物的活性和繁殖速度，导致冷鲜肉腐败变质，造成损失与浪费，并增加食源性疾病的风险[4]。因此，保障冷鲜肉的品质和安全，提升供应链效率，不仅是我国冷链物流发展亟需解决的问题，也是拓展冷鲜肉市场和推动现代化农业发展的重要基础。
冷链物联网为解决冷鲜肉供应链管理中的挑战提供了新机遇，实时的温度采集、传输和处理为管理者提供了连续的时间-温度数据支持[5]。针对生鲜食品的时间-温度研究已经取得了较为丰富的研究成果，如冷链温度监控[6]、货架期评估[7]等。此外，冷链物联网在减少食品系统对环境的影响方面也表现良好[8-9]。尽管已有较多研究成果，但商业实施至今仍然非常有限，主要原因在于供应链合作问题[10]。冷鲜肉供应链是一个复杂的网络，涉及多个参与者，这些参与者一般不属于同一所有者，导致实施基于时间-温度的管理系统会带来一定的组织间挑战。
挑战之一是管理系统对供应链中各利益相关者的保鲜投入和回报不均。例如，生鲜食品腐败变质的责任通常归咎于观察到食品腐烂的零售店，即使导致质量下降的原因是供应链上游的温度控制不当。此外，实施基于时间-温度的管理系统相关的成本一般由供应链上游参与者承担。因此，如何制定合理的供应链协调机制，以解决因激励不一致等造成的“牛鞭效应”和“双重边际效应”，已成为生鲜农产品供应链管理研究中的重要课题。
近年来，生鲜农产品供应链优化的研究主要集中在影响供应链运作效率的因素、提高运营效率的途径以及新运作模式的构建[11]。研究表明，供应链各参与者之间的利益协调尤为关键，通过收益共享、数量折扣和回购契约等方式，可在供应链成员之间分散风险，实现收益关联，最终达到运营效率提升[12]。Cai Xiaoqiang等[13]分析了供应链中可能存在的2种类型的损耗，构建了一个考虑努力水平对流通损耗影响的供应链协调优化模型。董振宁等[14]针对“农超对接”模式下的生鲜农产品供应链，设计了“保鲜成本分担”契约，以改善供应链效益。这些研究主要集中在保鲜投入及其对供应链成员决策的影响。然而，从冷链物联网的时间-温度角度来提升冷鲜肉供应链效率的研究尚未得到充分的探索和实践。
本研究以冷鲜肉供应链为研究对象，以冷链物联网中的时间-温度信息为基础，构建品质变化和能耗模型，研究实现供应链效益最大化的最佳新鲜度水平和影响因素，为提高冷鲜肉供应链管理效率提供理论支持和实践探索。
1 模型描述
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1.1 问题描述
冷鲜肉供应链涵盖生产、运输和销售等多个环节，任何环节的时间和温度控制不当均会导致品质下降。根据3T理论（time，temperature，tolerance），时间和温度的控制虽然能够减缓冷鲜肉在流通过程中的品质下降，但无法完全阻止其下降趋势[15]。品质的变化与时间和温度之间存在累积效应，如图1所示，冷鲜肉的品质随供应链流通的时间和温度条件而逐渐下降，当供应链各环节协同不紧密或出现“断链”情况时，品质下降尤为显著。为保障冷鲜肉处于适宜的温度环境，制冷系统做功能耗将持续增加。同时，随着冷鲜肉在供应链中逐渐接近消费者，其市场价值也在不断上升。此外，冷鲜肉供应链中的“流”是相互联系和相互制约的，而时间-温度则是其中的关键因素，时间和温度的有效控制不仅影响冷鲜肉的品质变化，还直接关系到供应链的运营效益。
1.2 参数设置
冷鲜肉的市场需求受新鲜度（RN）和销售价格（p）的共同影响，与新鲜度成正相关，与销售价格成负相关，根据文献[11,16]的研究，冷鲜肉市场需求函数为：
式中：a为市场需求，kg；η（η>0）为价格敏感系数；β（β>0）为新鲜度敏感系数。
对于大多数易腐食品而言，约1/6的保质期用于生产和分销过程，以减少不必要的食品浪费并保持食品品质[17]。因此，零售商事先商定冷鲜肉送达零售店时的最低可接受新鲜度（RS）为0.8，否则将拒绝接收[18]，RS取值范围为[0.8，1]。
2 模型建立与求解
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2.1 模型建立
2.1.1 品质模型
越来越多的研究者通过预测微生物学模型来评估冷鲜肉的新鲜度和货架期[19-21]。具体而言，这些文献深入探究了腐败微生物在冷鲜肉中的生长特性，利用微生物指标来评估产品的货架期和新鲜度。由于预测微生物学模型呈非线性变化，本文结合系统可靠性理论，构建了冷鲜肉品质模型，实现对其动态品质监测。文献[22-23]表明，这些模型在品质分析中具有重要的应用价值。经过大量数据的拟合与验证，平方根模型被广泛认为是描述温度对微生物生长影响的最佳经验方程式[24-25]：
式中：T为温度，℃；t为时间，h；Nt为在温度为T和时间为t条件下的微生物浓度，cfu/g；N0为初始微生物浓度，cfu/g；b为取决于特定产品的参数；Tmin为微生物最低生长温度，℃；γ为迟滞时间，h；e为自然常数。
令φ=T-Tmin，γ=0
式（2）可表示为式（3）或式（4）：
根据式（3）和式（4）可知，冷鲜肉中的微生物浓度取决于温度和时间[26]。冷鲜肉在温度为T的条件下存放时间为t时，其新鲜度如下[25]：
式中：Rt为在温度为T的条件下，经过时间t后冷鲜肉新鲜度；ND为最小完全腐败微生物浓度，cfu/g。lg Nt/lgND为冷鲜肉的新鲜度损失程度，新鲜度和质量损失程度的和为1；即新鲜度为1时，腐败微生物浓度为1；新鲜度为0时，微生物浓度大于等于ND。
由于冷鲜肉在供应链开始时，腐败微生物已经过了生长迟滞期[24]，由式（3）~式（5）可知：
令d=0.434b2/lgND，R0=1-lgN0/lgND得到：
当冷鲜肉供应链由n个环节组成时，每个参与者完成供应链中的1个环节。Ni为供应链第i环节结束时冷鲜肉中的腐败微生物浓度；Ri为该环节结束时的新鲜度。每个环节的腐败微生物最低生长温度不变[27]，第i个环节冷鲜肉的温度与腐败微生物最低生长温度的差值为φi=Ti-Tmin，ti为第i环节的持续时间。若温度数据的记录间隔时间设定为Δt，第i环节有ti=miΔt，第i个环节内的第j个Δt间隔的温度为φij。
2.1.2 能耗模型
在冷鲜肉供应链的各环节中，制冷设备需要做功消耗能量以维持适宜的温度，从而减缓品质下降。根据文献[28]中冷藏运输模拟的实验数据，拟合得到冷链基础设施制冷的总能耗可近似表达为内外温差的二次函数。因此，供应链第i个环节的制冷能耗功率为：
式中：ωi为第i环节冷链基础设施能耗功率，kW；μi为第i环节冷链基础设施内外温差（Tio-Ti）；e1、e2为拟合参数。
式中：Tio、Ti、Tic分别为第i环节外界环境温度、冷链基础设施内部环境温度、外界环境温度与微生物最低生长温度的差值，℃。
将式（15）代入式（13）：
式中：为φi的平均值。
因此，对于具有n个环节的冷鲜肉供应链，总能耗Wn（kW·h）为：
令，则
式（21）用时间和温度表示：
2.1.3 保鲜成本及收益分配
冷鲜肉供应链的保鲜成本为制冷能耗，根据式（22），具有n个环节的冷鲜肉供应链的保鲜成本函数为：
式中：f为能耗单价，元/（kW·h）。
令，则：
式中：C0为冷鲜肉保鲜的固定成本，元/kg；v为新鲜度成本系数。
合理的收益分配机制是激励供应链成员在温度和时间方面进行有效协同的重要手段。本文的主要目的是构建理论模型，而不涉及对固定成本的补偿。根据式（19），第i个环节的保鲜成本为：
根据式（25）、式（26）得到供应链第i个环节的收益分配权重为：
2.2 模型求解
冷鲜肉供应链总收益为π（元）：
式中：Cm为冷鲜肉供应链中除保鲜成本外的其余成本，元，为简化模型推导将Cm归入式（23）的C0中。
为了求解最优零售价格和最佳新鲜度对供应链利润最大化，分别对利润函数π关于零售价格p和新鲜度Rn求一阶导数，并令其等于0。得到最佳新鲜度Ropt为：
为确保一阶导数为最优结果，需证明利润函数为凹函数。利润公式的海塞矩阵为：
当2vβη-β2+v2η2>0时，π的海塞矩阵是负定的，此时利润函数π是零售价格p和新鲜度Rn的凹函数。而新鲜度Ropt的取值区间为[0.8，1]，如图2所示。
情形1：消费者对冷鲜肉的新鲜度不敏感。消费者对冷鲜肉的新鲜度关注较少，而更多关注价格或其他因素。此时，供应链Ropt趋近于0.8，表明在相对较低的新鲜度水平下，供应链实现最大收益。
情形2：消费者对冷鲜肉的新鲜度敏感。当消费者对冷鲜肉的品质和安全性高度重视时，通常愿意为质量更高的冷鲜肉支付溢价。该情况下，Ropt趋近于1，表明只有达到较高的新鲜度水平时，供应链才能实现最大收益。
情形3：消费者对冷鲜肉的新鲜度具有一定关注。消费者虽然对新鲜度有所关注，但这并非唯一的决定性因素。在此情形下，供应链Ropt范围为0.8~1。表明供应链需根据市场需求变化灵活调整冷鲜肉的品质，以实现最大收益。
市场需求、价格敏感系数、冷鲜肉价格、新鲜度敏感系数、保鲜固定成本和新鲜度成本系数对冷鲜肉供应链效益最佳新鲜度水平Ropt的影响如下：1）随着市场需求的增加Ropt降低，表明在高需求情况下，消费者对新鲜度的要求可能会降低，因为市场上的选择增多，使得消费者更加关注其他因素，例如价格和便利性；2）随着冷鲜肉价格的增加，Ropt增加，较高的价格使消费者对冷鲜肉的新鲜度要求更高，要确保其质量与价格相匹配，从而增加其购买意愿；3）随着消费者对价格敏感度的增加，Ropt增加。消费者更倾向于接受更高的新鲜度，以获取更好的性价比，即使他们对价格仍然保持敏感；4）随着消费者对冷鲜肉品质关注度的提高，Ropt增加，当消费者越来越重视品质时，供应链须相应提高新鲜度，以满足市场的期望和需求，确保消费者的满意度；5）随着冷鲜肉保鲜固定成本和新鲜度成本系数的增加，Ropt降低，当保鲜成本上升时，供应链可能会倾向于降低新鲜度水平，以控制整体成本，从而维持竞争力，并避免利润的进一步压缩。
3 案例分析
收起
本文以冷鲜鸡供应链为例进行案例分析。基于文献[29-30]和实验数据表1，得出b=0.014 8。根据文献[25]，冷鲜鸡微生物浓度上限ND=1×106，因此得到d=1.572×105。结合文献[11]和文献[25]，以及市场调查结果，确定了某地冷鲜鸡相关参数，如表2所示。根据式（30）获得冷鲜鸡Ropt为0.849。根据式（12），在该Ropt下，冷鲜鸡供应链的时间-温度协调因子为9 600。根据文献[31]获得了冷鲜肉类腐败微生物的零生长温度，进而确定了供应链各环节的修正温度。
表3所示为某地冷鲜鸡供应链不同环节的协调因子。各环节的运作时间和温度分别为：冷藏加工8 h（5 ℃）、冷库储存18 h（2 ℃）、冷链配送10 h（7 ℃）和冷藏销售14 h（7.2 ℃）。该供应链协调因子之和约为9 600，接近冷鲜鸡供应链最佳新鲜度水平0.849，实现供应链效益最大化。然而，当整个供应链的温度设定在4 ℃时，冷链协调因子之和为8 107。尽管此时冷鲜鸡的新鲜度更高，但供应链效益并未达到最佳水平。
4 结论
收起
本文基于冷链物联网时间-温度信息，构建了冷鲜肉供应链的品质、能耗模型，并通过冷鲜鸡供应链的案例进行分析，得到如下结论：
1）冷鲜肉供应链中，存在一个最佳新鲜度水平，使供应链效益达到最大化。以某地冷鲜鸡为例，当新鲜度水平接近0.849时，供应链效益最大。
2）当供应链某个环节运作偏离了最佳新鲜度水平时，可以通过调整其他环节的时间和温度来保障供应链效益。
3）时间-温度调整具有有限性，随着温度和时间偏离度的增加，调整难度增加。
市场需求、价格以及消费者对新鲜度的关注程度等因素会直接影响供应链效益最佳的新鲜度水平。因此，决策者应根据市场情况灵活调整保鲜策略，例如，在市场需求旺盛时，可适当调整降低新鲜度水平；而对于高价值产品，应采取更为严格的保鲜措施。冷链物联网技术的广泛应用为供应链各参与者之间的信息共享与协同创造了新的机遇。通过构建完善的冷链物联网时间-温度管理系统，各利益相关者之间可以实现紧密协作，推动供应链更加敏捷、高效地运作。在保障质量和安全的同时，实现供应链经济效益的最大化。
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2025年第46卷第3期
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doi: 10.12465/j.issn.0253-4339.2025.03.123
  • 接收时间：2024-08-26
  • 首发时间：2026-03-13
  • 出版时间：2025-06-16
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  • 收稿日期：2024-08-26
  • 修回日期：2024-10-21
  • 录用日期：2024-11-04
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    1广州大学管理学院　广州　510006
    2广州番禺职业技术学院现代物流学院　广州　511483

通讯作者:

邹毅峰，男，博士，副教授，广州大学管理学院，13924225470，E-mail：。研究方向：运输管理、冷链物流。
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2种不同金属材料的力学参数
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Number of
genus		 种数
Number of
species		 占总种数比例
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total species (%)		 属
Genus		 种数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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