{"title":"Non-renewable input and waste stock: optimal transition towards circularity","authors":"S. Bertarelli, C. Lodi, S. Ragni","doi":"10.12988/ams.2023.917446","DOIUrl":null,"url":null,"abstract":"Natural resource stocks are drastically shrinking and the contempo-rary debate on depletion of reserves highlights their crucial role over time. This paper deals with the management of exhaustible resources when recycling and extraction are employed, as well as the short-term effects of the economic transition towards circularity on consumption and welfare. Mathematical modeling may support effective plans for maximizing social welfare and protecting the environment. Concerning the production of a certain good, an optimal control model is studied to allocate labor between mining and recycling over a finite time horizon. A suit-able scrap value function allows for reducing waste and maintaining natural stock in the forthcoming future. Well-posedness of the problem is proved and some qualitative features of the optimal solution are stated.","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":"39 1","pages":""},"PeriodicalIF":3.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Models & Methods in Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12988/ams.2023.917446","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
Natural resource stocks are drastically shrinking and the contempo-rary debate on depletion of reserves highlights their crucial role over time. This paper deals with the management of exhaustible resources when recycling and extraction are employed, as well as the short-term effects of the economic transition towards circularity on consumption and welfare. Mathematical modeling may support effective plans for maximizing social welfare and protecting the environment. Concerning the production of a certain good, an optimal control model is studied to allocate labor between mining and recycling over a finite time horizon. A suit-able scrap value function allows for reducing waste and maintaining natural stock in the forthcoming future. Well-posedness of the problem is proved and some qualitative features of the optimal solution are stated.
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The purpose of this journal is to provide a medium of exchange for scientists engaged in applied sciences (physics, mathematical physics, natural, and technological sciences) where there exists a non-trivial interplay between mathematics, mathematical modelling of real systems and mathematical and computer methods oriented towards the qualitative and quantitative analysis of real physical systems.
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Special attention will be paid to the analysis of nonlinearities and stochastic aspects.
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Book reviews, announcements and tutorial articles will be featured occasionally.
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