{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T11:33:29Z","timestamp":1778585609927,"version":"3.51.4"},"reference-count":33,"publisher":"Emerald","issue":"11","license":[{"start":{"date-parts":[[2022,6,28]],"date-time":"2022-06-28T00:00:00Z","timestamp":1656374400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["K"],"published-print":{"date-parts":[[2023,11,9]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to maximize the average profit of the supply chain by calculating the order quantity, the number of shipments during the production time of the vendor, the number of shipments during the supply cycle of the vendor and the time when the retailer\u2019s inventory level reaches to zero.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>A production and inventory model for degrading commodities with stochastic demand and two-level partial trade credit in a supply chain is presented. The model\u2019s applicability and the processes' feasibility for solving are verified by GAMS software with BARON.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>The impact of the model\u2019s parameters on the vendor and retailer\u2019s average profit was found through sensitivity analysis. The effect of the model\u2019s parameters on the supply chain\u2019s average profit was also found. Moreover, the reasons for this effect were given.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Practical implications<\/jats:title><jats:p>First, decision-makers may use this model to increase the supply chain's average profit. Second, the proposed model takes a general form. Third, the policymakers can also adjust the model\u2019s parameters according to their preferences to get the desired results.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>First, this paper develops an inventory and production model for perishable goods. Second, it is believed that the demand is random because the demand is affected by many factors, which make the study more realistic. Third, this paper studies production and inventory problems from the supply chain perspective. Finally, the interest for partial trade credit is calculated. The interest caused by stochastic shortages is also considered and calculated.<\/jats:p><\/jats:sec>","DOI":"10.1108\/k-02-2022-0188","type":"journal-article","created":{"date-parts":[[2022,6,27]],"date-time":"2022-06-27T10:17:29Z","timestamp":1656325049000},"page":"4846-4875","source":"Crossref","is-referenced-by-count":9,"title":["A production and inventory model for deteriorating items with two-level partial trade credit and stochastic demand in a supply chain"],"prefix":"10.1108","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7843-0244","authenticated-orcid":false,"given":"Zhuo","family":"Dai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0939-2907","authenticated-orcid":false,"given":"Yiju","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2022,6,28]]},"reference":[{"issue":"3","key":"key2023110803372418800_ref001","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1007\/s12351-018-0391-4","article-title":"Analyzing an inventory model with two-level trade credit period including the effect of customers' credit on the demand function using q-fuzzy number","volume":"20","year":"2020","journal-title":"Operational Research"},{"issue":"9","key":"key2023110803372418800_ref002","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1016\/j.camwa.2010.12.054","article-title":"Some improved algorithms to locate the optimal solutions for exponentially deteriorating items under trade credit financing in a supply chain system","volume":"61","year":"2011","journal-title":"Computers and Mathematics With Applications"},{"issue":"6","key":"key2023110803372418800_ref003","doi-asserted-by":"crossref","first-page":"2011","DOI":"10.1016\/j.camwa.2012.03.102","article-title":"The integrated inventory model with the transportation cost and two-level trade credit in supply chain management","volume":"64","year":"2012","journal-title":"Computers and Mathematics With Applications"},{"issue":"1","key":"key2023110803372418800_ref004","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1016\/j.aej.2020.10.054","article-title":"A production inventory model with partial trade credit policy and reliability","volume":"60","year":"2021","journal-title":"Alexandria Engineering Journal"},{"issue":"12","key":"key2023110803372418800_ref005","doi-asserted-by":"crossref","first-page":"7563","DOI":"10.1002\/int.22599","article-title":"Carbon emission sensitive deteriorating inventory model with trade credit under volumetric fuzzy system","volume":"36","year":"2021","journal-title":"International Journal of Intelligent Systems"},{"key":"key2023110803372418800_ref006","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.cam.2016.03.027","article-title":"On the comparison of inventory replenishment policies with time-varying stochastic demand for the paper industry","volume":"309","year":"2017","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"key2023110803372418800_ref007","first-page":"1645","article-title":"A non-instantaneous inventory model of agricultural products considering deteriorating impacts and pricing policies","volume":"49","year":"2020","journal-title":"Kybernetes"},{"key":"key2023110803372418800_ref008","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1108\/K-04-2017-0122","article-title":"Dynamics analysis of a production-inventory control system with two pipelines feedback","volume":"46","year":"2017","journal-title":"Kybernetes"},{"issue":"1","key":"key2023110803372418800_ref009","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1080\/00207543.2018.1480839","article-title":"Multi-item inventory model with variable backorder and price discount under trade credit policy in stochastic demand","volume":"57","year":"2019","journal-title":"International Journal of Production Research"},{"issue":"1","key":"key2023110803372418800_ref010","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.tre.2009.06.003","article-title":"An integrated production-inventory system in a multi-stage multi-firm supply chain","volume":"46","year":"2010","journal-title":"Transportation Research Part E-Logistics and Transportation Review"},{"issue":"2","key":"key2023110803372418800_ref011","first-page":"1661","article-title":"Optimal ordering policy for a two-warehouse inventory model use of two-level trade credit","volume":"13","year":"2016","journal-title":"Journal of Industrial and Management Optimization"},{"issue":"2","key":"key2023110803372418800_ref012","first-page":"468","article-title":"Technical note\u2014managing inventory for firms with trade credit and deficit penalty","volume":"67","year":"2019","journal-title":"Operations Research"},{"issue":"11","key":"key2023110803372418800_ref013","doi-asserted-by":"crossref","first-page":"7271","DOI":"10.1007\/s00500-021-05635-2","article-title":"Joint pricing and inventory management for growing items in a supply chain under trade credit","volume":"25","year":"2021","journal-title":"Soft Computing"},{"issue":"1","key":"key2023110803372418800_ref014","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1051\/ro\/2020067","article-title":"Advance sustainable inventory management through advertisement and trade-credit policy","volume":"55","year":"2021","journal-title":"RAIRO-operations Research"},{"key":"key2023110803372418800_ref015","first-page":"1645","article-title":"Non-instantaneous deteriorating inventory model under the joined effect of trade-credit, preservation technology and advertisement policy","volume":"49","year":"2020","journal-title":"Kybernetes"},{"issue":"5","key":"key2023110803372418800_ref016","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1108\/K-01-2020-0052","article-title":"A sustainable inventory system with the advanced payment policy and trade-credit strategy for a two-warehouse inventory system","volume":"50","year":"2021","journal-title":"Kybernetes"},{"issue":"11","key":"key2023110803372418800_ref017","doi-asserted-by":"crossref","first-page":"3273","DOI":"10.1016\/j.apm.2010.02.019","article-title":"An inventory model for deteriorating items under stock-dependent demand and two-level trade credit","volume":"34","year":"2010","journal-title":"Applied Mathematical Modelling"},{"issue":"6","key":"key2023110803372418800_ref018","doi-asserted-by":"crossref","first-page":"11441","DOI":"10.3233\/JIFS-202622","article-title":"System dynamics model of production-inventory-routing system in the green supply chain","volume":"40","year":"2021","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"2","key":"key2023110803372418800_ref019","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.amc.2012.06.038","article-title":"Three-layer supply chain \u2013 a production-inventory model for reworkable items","volume":"219","year":"2012","journal-title":"Applied Mathematics and Computation"},{"issue":"9","key":"key2023110803372418800_ref020","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1080\/00207721.2012.757383","article-title":"Three stage trade credit policy in a three-layer supply chain\u2013a production-inventory model","volume":"45","year":"2014","journal-title":"International Journal of Systems Science"},{"issue":"3","key":"key2023110803372418800_ref021","first-page":"1289","article-title":"Note on: supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit risk customers","volume":"15","year":"2017","journal-title":"Journal of Industrial and Management Optimization"},{"key":"key2023110803372418800_ref022","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/j.dss.2010.11.012","article-title":"A production-inventory model of imperfect quality products in a three-layer supply chain","volume":"50","year":"2011","journal-title":"Decision Support Systems Archive"},{"issue":"5","key":"key2023110803372418800_ref023","doi-asserted-by":"crossref","first-page":"3138","DOI":"10.1016\/j.apm.2012.07.026","article-title":"A production-inventory model with probabilistic deterioration in two-echelon supply chain management","volume":"37","year":"2013","journal-title":"Applied Mathematical Modelling"},{"issue":"23","key":"key2023110803372418800_ref024","article-title":"Two level trade credit policy approach in inventory model with expiration rate and stock dependent demand under nonzero inventory and partial backlogged shortages","volume":"13","year":"2021","journal-title":"Sustainability"},{"issue":"11","key":"key2023110803372418800_ref025","doi-asserted-by":"crossref","first-page":"3967","DOI":"10.1002\/mma.5626","article-title":"Some modified mathematical analytic derivations of the annual total relevant cost of the inventory model with two levels of trade credit in the supply chain system","volume":"42","year":"2019","journal-title":"Mathematical Methods in The Applied Sciences"},{"issue":"1","key":"key2023110803372418800_ref026","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s10479-019-03369-x","article-title":"Inventory ordering policies for mixed sale of products under inspection policy, multiple prepayment, partial trade credit, payments linked to order quantity and full backordering","volume":"287","year":"2020","journal-title":"Annals of Operations Research"},{"issue":"10","key":"key2023110803372418800_ref027","first-page":"4","article-title":"Two-level trade credit with default risk in the supply chain under stochastic demand","volume":"88","year":"2019","journal-title":"Omega"},{"issue":"Special issues","key":"key2023110803372418800_ref028","first-page":"1","article-title":"Inventory and production dynamics in a discrete-time vendor-managed inventory supply chain system","volume":"2018","year":"2018","journal-title":"Discrete Dynamics in Nature and Society"},{"issue":"1","key":"key2023110803372418800_ref029","first-page":"459","article-title":"Optimal inventory policies for deteriorating items with trapezoidal-type demand patterns and maximum lifetimes under upstream and downstream trade credits","volume":"264","year":"2018","journal-title":"Annals of Operations Research"},{"key":"key2023110803372418800_ref030","doi-asserted-by":"crossref","first-page":"2707","DOI":"10.1109\/LRA.2019.2916471","article-title":"A joint ordering, pricing, and freshness-keeping policy for perishable inventory systems with random demand over infinite horizon","volume":"4","year":"2019","journal-title":"IEEE Robotics and Automation Letters"},{"key":"key2023110803372418800_ref031","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.ijpe.2014.03.019","article-title":"Supply chain coordination with trade credit and quantity discount incorporating default risk","volume":"153","year":"2014","journal-title":"International Journal of Production Economics"},{"issue":"4","key":"key2023110803372418800_ref032","first-page":"1","article-title":"Analysis and optimisation of perishable inventory with stocks-sensitive stochastic demand and two-stage pricing:A discrete event simulation study","volume":"15","year":"2020","journal-title":"Journal of Simulation"},{"issue":"8","key":"key2023110803372418800_ref033","doi-asserted-by":"crossref","first-page":"3809","DOI":"10.1016\/j.amc.2012.10.009","article-title":"The model and algorithm for determining optimal ordering\/trade-credit policy of supply chains","volume":"219","year":"2012","journal-title":"Applied Mathematics and Computation"}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/K-02-2022-0188\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/K-02-2022-0188\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T21:46:59Z","timestamp":1753393619000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/k\/article\/52\/11\/4846-4875\/458943"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,28]]},"references-count":33,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,6,28]]},"published-print":{"date-parts":[[2023,11,9]]}},"alternative-id":["10.1108\/K-02-2022-0188"],"URL":"https:\/\/doi.org\/10.1108\/k-02-2022-0188","relation":{},"ISSN":["0368-492X"],"issn-type":[{"value":"0368-492X","type":"print"}],"subject":[],"published":{"date-parts":[[2022,6,28]]}}}