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In the actual era of the international trade, global warming and depletion of Earth's natural resources, the willingness to generate sustainable and competitive benefits determines us to stop thinking linearly (produce, consume and dispose) and to shift towards a circular approach by closing material loops. The latter falls within the concept of circular economy that, in turn, derives from reverse logistics. This paper proposes a comprehensive state-of-the-art review around the topic of circular economy and reverse logistics with a particular emphasis on mid-term production planning under discrete time settings. The broad spectrum of reviewed publications is categorized and discussed with respect to the main recovery operations, namely: (i) disassembly for recycling, (ii) from product to raw material recycling, and (iii) by-products and co-production. For each of the aforementioned recovery options, this paper elucidates the related definitions, reviews the mathematical formulations jointly with a structured overview of the solution methods, and discusses their industrial implications. Given the legislative pressure to mitigate environmental impacts caused by production processes, a special attention is paid to the greenhouse gas emissions and energy consumption. A cross-cutting analysis of the reviewed literature brought forward a number of research gaps and revealed multiple research opportunities to support the development of the circular economy. The key findings show an ever growing interest in making sustainable the traditional linear industrial processes within a circular economy context.

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The high pace of waste accumulation in landfills and the depletion of scarce natural resources lead us to seek pathways for converting unavoidable production outputs into useful and high added-value products. In this context, we formalize and propose a model for the single-item lot-sizing problem, which integrates the management of unavoidable production residues classified as by-products. During the production process of a main product, a by-product is generated, stored in a limited capacity and transported with a fixed transportation cost. This problem is investigated for two cases of the by-product inventory capacity: time-dependent and constant. We prove the problem with inventory capacities is NP-Hard. To solve it optimally, we develop a pseudo-polynomial time dynamic programming algorithm. For the case with stationary inventory capacities, a polynomial time dynamic programming algorithm is proposed.

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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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