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For the exponential lead time model, we provide some analytical properties of the cost function. Using numerical results, an optimal cost analysis is performed and some remarks are made as to the optimality of cost function with respect to each of decision variables.<\/jats:p>","DOI":"10.1051\/ro\/2025079","type":"journal-article","created":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T14:45:33Z","timestamp":1750171533000},"page":"1959-1980","source":"Crossref","is-referenced-by-count":1,"title":["Continuous-review (<i>s, S<\/i>) inventory system with lost sales and variable lead times"],"prefix":"10.1051","volume":"59","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4180-0808","authenticated-orcid":false,"given":"Preethi","family":"Kumaresan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7062-4252","authenticated-orcid":false,"given":"Sivakumar","family":"Balasubramanian","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0000-0847-5295","authenticated-orcid":false,"given":"Arivarignan","family":"Gunaseelan","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2025,7,29]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1287\/mnsc.27.10.1171","volume":"27","author":"Archibald","year":"1981","journal-title":"Manage. 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