{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T20:56:43Z","timestamp":1773176203805,"version":"3.50.1"},"reference-count":35,"publisher":"Emerald","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,28]]},"abstract":"<jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>Spurred by the high turnover in the pharmaceutical industry, locating pharmacies inside urban areas along with the high product perishability in this industry, the pharmaceutical supply chain management has recently gained increasing attention. Accordingly, this paper unveils an inventory-routing problem for designing a pharmaceutical supply chain with perishable products and time-dependent travel time in an uncertain environment.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Design\/methodology\/approach<\/jats:title>\n                    <jats:p>In this study, mathematical programming is employed to formulate a multi-graph network affected by the traffic volume in order to adapt to real-world situations. Likewise, by transforming the travel speed function to the travel time function using a step-by-step algorithm, the first-in-first-out property is warranted. Moreover, the Box\u2013Jenkins forecasting method is employed to diminish the demand uncertainty.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Findings<\/jats:title>\n                    <jats:p>An appealing result is that the delivery horizon constraint in the under-study multi-graph network may eventuate in selecting a longer path. Our analysis also indicates that the customers located in the busy places in the city are not predominantly visited in the initial and last delivery horizon, which are the rush times. Moreover, it is concluded that integrating disruption management, routing planning and inventory management in the studied network leads to a reduction of costs in the long term.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Originality\/value<\/jats:title>\n                    <jats:p>Applying the time-dependent travel time with a heterogeneous fleet of vehicles on the multi-graph network, considering perishability in the products for reducing inventory costs, considering multiple trips of transfer fleet, considering disruption impacts on supply chain components and utilizing the Box\u2013Jenkins method to reduce uncertainty are the contributions of the present study.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1108\/k-12-2023-2547","type":"journal-article","created":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T11:35:23Z","timestamp":1718192123000},"page":"6081-6110","source":"Crossref","is-referenced-by-count":4,"title":["An inventory-routing optimization model for pharmaceutical supply\u00a0chain with time-dependent travel time on a multi-graph network: a\u00a0case study"],"prefix":"10.1108","volume":"54","author":[{"given":"Seyed Mohammad Hadi","family":"Baghdadi","sequence":"first","affiliation":[{"name":"School of Industrial Engineering, Iran University of Science and Technology , ,","place":["Tehran, Islamic Republic of Iran"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5992-1730","authenticated-orcid":true,"given":"Ehsan","family":"Dehghani","sequence":"additional","affiliation":[{"name":"School of Industrial Engineering, Iran University of Science and Technology , ,","place":["Tehran, Islamic Republic of Iran"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3205-2804","authenticated-orcid":true,"given":"Mohammad Hossein","family":"Dehghani Sadrabadi","sequence":"additional","affiliation":[{"name":"School of Industrial Engineering, Iran University of Science and Technology , ,","place":["Tehran, Islamic Republic of Iran"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mahdi","family":"Heydari","sequence":"additional","affiliation":[{"name":"School of Industrial Engineering, Iran University of Science and Technology , ,","place":["Tehran, Islamic Republic of Iran"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-9715-3053","authenticated-orcid":true,"given":"Maryam","family":"Nili","sequence":"additional","affiliation":[{"name":"School of Industrial Engineering, Iran University of Science and Technology , ,","place":["Tehran, Islamic Republic of Iran"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2024,6,13]]},"reference":[{"key":"2025102701195381100_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/j.seps.2021.101126","article-title":"A multi-objective model for optimizing the socio-economic performance of a pharmaceutical supply chain","volume":"79","author":"Ahmad","year":"2022","journal-title":"Socio-Economic Planning Sciences"},{"key":"2025102701195381100_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2023.109590","article-title":"Multi-objective optimization of two-echelon vehicle routing problem: vaccines distribution as a case study","volume":"187","author":"Al Theeb","year":"2024","journal-title":"Computers and Industrial Engineering"},{"key":"2025102701195381100_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.111012","article-title":"A fuzzy multi-objective optimization model for sustainable healthcare supply chain network design","volume":"150","author":"Ala","year":"2024","journal-title":"Applied Soft Computing"},{"key":"2025102701195381100_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2021.104509","article-title":"On the accuracy of ARIMA based prediction of COVID-19 spread","volume":"27","author":"Alabdulrazzaq","year":"2021","journal-title":"Results in Physics"},{"key":"2025102701195381100_ref005","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2022\/4526641","article-title":"Providing a mathematical routing-inventory model for the drug supply chain considering the travel time dependence and perishability on multiple graphs","volume":"2022","author":"Ali","year":"2022","journal-title":"Discrete Dynamics in Nature and Society"},{"key":"2025102701195381100_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/j.renene.2024.120626","article-title":"An optimization-based design methodology to manage the sustainable biomass-to-biodiesel supply chain under disruptions: a case study","volume":"228","author":"Bahmani","year":"2024","journal-title":"Renewable Energy"},{"key":"2025102701195381100_ref007","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s40199-016-0144-y","article-title":"A novel approach for inventory problem in the pharmaceutical supply chain","volume":"24","author":"Candan","year":"2016","journal-title":"DARU Journal of Pharmaceutical Sciences"},{"issue":"14","key":"2025102701195381100_ref008","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/00207543.2023.2283566","article-title":"Sustainable collaborative strategy in pharmaceutical refrigerated logistics routing problem","volume":"62","author":"Chen","year":"2023","journal-title":"International Journal of Production Research"},{"issue":"01","key":"2025102701195381100_ref009","first-page":"32","article-title":"A data-driven approach to inventory control under uncertain demand for pharmaceutical products using continuous review policy","volume":"7","author":"Chowdhury","year":"2024","journal-title":"GPH-International Journal of Business Management"},{"issue":"3","key":"2025102701195381100_ref010","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1080\/03155986.2023.2226896","article-title":"Closed-form (R, S) inventory policies for perishable inventory systems with supply chain disruptions","volume":"61","author":"Czerniak","year":"2023","journal-title":"INFOR: Information Systems and Operational Research"},{"key":"2025102701195381100_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.110357","article-title":"A fuzzy robust stochastic model for designing a pharmaceutical supply chain with sustainability and resiliency dimensions","volume":"143","author":"Daryanian","year":"2023","journal-title":"Applied Soft Computing"},{"key":"2025102701195381100_ref012","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/j.compchemeng.2018.01.013","article-title":"Resilient solar photovoltaic supply chain network design under business-as-usual and hazard uncertainties","volume":"111","author":"Dehghani","year":"2018","journal-title":"Computers and Chemical Engineering"},{"key":"2025102701195381100_ref013","doi-asserted-by":"publisher","DOI":"10.1108\/k-04-2023-0547","article-title":"An integrated optimization model for planning supply chains' resilience and business continuity under interrelated disruptions: a case study","author":"Dehghani Sadrabadi","year":"2023","journal-title":"Kybernetes"},{"key":"2025102701195381100_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2024.109899","article-title":"A Bi-objective stochastic blood type supply chain configuration and optimization considering time-dependent routing in post-disaster relief logistics","volume":"188","author":"Entezari","year":"2024","journal-title":"Computers and Industrial Engineering"},{"key":"2025102701195381100_ref015","first-page":"424","article-title":"The consistent vehicle routing problem: an application to the pharmaceutical supply chain","author":"Eus\u00e9bio","year":"2024"},{"issue":"6","key":"2025102701195381100_ref016","doi-asserted-by":"publisher","first-page":"1921","DOI":"10.1108\/jm2-03-2022-0080","article-title":"Designing a multi-objective mathematical model of a perishable supply chain (PSC) in a state of uncertainty","volume":"18","author":"Fallah","year":"2023","journal-title":"Journal of Modelling in Management"},{"issue":"1","key":"2025102701195381100_ref017","doi-asserted-by":"publisher","DOI":"10.1177\/21582440221149717","article-title":"Inventory management and pharmaceutical supply chain performance of hospital pharmacies in Bahrain: a structural equation modeling approach","volume":"13","author":"George","year":"2023","journal-title":"SAGE Open"},{"key":"2025102701195381100_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2022.108880","article-title":"Two-stage stochastic programming model and algorithm for mitigating supply disruption risk on aircraft manufacturing supply chain network design","volume":"175","author":"Hu","year":"2023","journal-title":"Computers and Industrial Engineering"},{"issue":"2","key":"2025102701195381100_ref019","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/s0377-2217(02)00147-9","article-title":"Vehicle dispatching with time-dependent travel times","volume":"144","author":"Ichoua","year":"2003","journal-title":"European Journal of Operational Research"},{"key":"2025102701195381100_ref020","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2023.108481","article-title":"Designing a sustainable disruption-oriented supply chain under joint pricing and resiliency considerations: a case study","volume":"180","author":"Jafari-Nodoushan","year":"2024","journal-title":"Computers and Chemical Engineering"},{"key":"2025102701195381100_ref021","doi-asserted-by":"publisher","DOI":"10.1016\/j.seps.2023.101602","article-title":"Supply chain planning of vaccine and pharmaceutical clusters under uncertainty: the case of COVID-19","volume":"87","author":"Kochakkashani","year":"2023","journal-title":"Socio-Economic Planning Sciences"},{"issue":"3","key":"2025102701195381100_ref022","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1287\/trsc.26.3.185","article-title":"Time dependent vehicle routing problems: formulations, properties and heuristic algorithms","volume":"26","author":"Malandraki","year":"1992","journal-title":"Transportation Science"},{"key":"2025102701195381100_ref023","doi-asserted-by":"publisher","DOI":"10.1016\/j.rser.2021.111428","article-title":"A multi-objective optimization model to sustainable closed-loop solar photovoltaic supply chain network design: a case study in Iran","volume":"150","author":"Nili","year":"2021","journal-title":"Renewable and Sustainable Energy Reviews"},{"issue":"14","key":"2025102701195381100_ref024","doi-asserted-by":"publisher","first-page":"3069","DOI":"10.3390\/math11143069","article-title":"An overview of forecast analysis with ARIMA models during the COVID-19 pandemic: methodology and case study in Brazil","volume":"11","author":"Ospina","year":"2023","journal-title":"Mathematics"},{"key":"2025102701195381100_ref025","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2022.108597","article-title":"Modeling and solving a multi-trip multi-distribution center vehicle routing problem with lower-bound capacity constraints","volume":"172","author":"Pham","year":"2022","journal-title":"Computers and Industrial Engineering"},{"key":"2025102701195381100_ref026","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2024.108675","article-title":"Designing a green-resilient closed-loop supply chain to preserve business continuity under interrelated disruptions (a case study of the automotive battery industry)","volume":"185","author":"Sadrabadi","year":"2024","journal-title":"Computers and Chemical Engineering"},{"key":"2025102701195381100_ref027","doi-asserted-by":"publisher","DOI":"10.1016\/j.est.2024.111423","article-title":"Optimal pricing strategy in the closed-loop supply chain using game theory under government subsidy scenario: a case study","volume":"87","author":"Sadrabadi","year":"2024","journal-title":"Journal of Energy Storage"},{"issue":"2","key":"2025102701195381100_ref028","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40819-024-01678-9","article-title":"Inventory management in a retail pharmaceutical industry during COVID-19 pandemic","volume":"10","author":"Sahoo","year":"2024","journal-title":"International Journal of Applied and Computational Mathematics"},{"key":"2025102701195381100_ref029","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2023.109826","article-title":"Designing a sustainable vaccine supply chain by considering demand substitution and value-added function during a pandemic outbreak","volume":"187","author":"Salari","year":"2024","journal-title":"Computers and Industrial Engineering"},{"key":"2025102701195381100_ref030","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1016\/j.cherd.2018.09.008","article-title":"A possibilistic location-inventory model for multi-period perishable pharmaceutical supply chain network design","volume":"138","author":"Savadkoohi","year":"2018","journal-title":"Chemical Engineering Research and Design"},{"key":"2025102701195381100_ref031","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.jmsy.2014.11.016","article-title":"A time-dependent vehicle routing problem in multigraph with FIFO property","volume":"35","author":"Setak","year":"2015","journal-title":"Journal of Manufacturing Systems"},{"issue":"2","key":"2025102701195381100_ref032","doi-asserted-by":"publisher","first-page":"1149","DOI":"10.1007\/s10479-023-05620-y","article-title":"Healthcare inventory management in the presence of supply disruptions and a reliable secondary supplier","volume":"331","author":"Shourabizadeh","year":"2023","journal-title":"Annals of Operations Research"},{"key":"2025102701195381100_ref033","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/978-3-319-52452-8_3","article-title":"ARIMA models","volume":"1","author":"Shumway","year":"2017","journal-title":"Time Series Analysis and Its Applications: With R Examples"},{"key":"2025102701195381100_ref034","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2022.135474","article-title":"Closed-loop supply chain inventory model in the pharmaceutical industry toward a circular economy","volume":"383","author":"Suhandi","year":"2023","journal-title":"Journal of Cleaner Production"},{"issue":"3","key":"2025102701195381100_ref035","doi-asserted-by":"publisher","first-page":"996","DOI":"10.1016\/j.ejor.2023.07.028","article-title":"Split-demand multi-trip vehicle routing problem with simultaneous pickup and delivery in airport baggage transit","volume":"312","author":"Zhang","year":"2024","journal-title":"European Journal of Operational Research"}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/K-12-2023-2547\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/k\/article-pdf\/54\/10\/6081\/10388477\/k-12-2023-2547en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/k\/article-pdf\/54\/10\/6081\/10388477\/k-12-2023-2547en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T05:19:57Z","timestamp":1761542397000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/k\/article\/54\/10\/6081\/1259872\/An-inventory-routing-optimization-model-for"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,13]]},"references-count":35,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2025,10,28]]}},"URL":"https:\/\/doi.org\/10.1108\/k-12-2023-2547","relation":{},"ISSN":["0368-492X","1758-7883"],"issn-type":[{"value":"0368-492X","type":"print"},{"value":"1758-7883","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,13]]}}}