Application of Markov chain model to calculate the average number of times of use of a material in society: An allocation methodology for open-loop recycling - Part 1: Methodology development

Hiroyuki Yamada, Ichiro Daigo, Yasunari Matsuno, Yoshihiro Adachi, Yasushi Kondo

    Research output: Contribution to journalArticle

    26 Citations (Scopus)


    Goal, Scope and Background. It has been recognized that LCA has a limitation in assessing open cycle recycling of materials because of inevitable subjective judgments in setting system boundary. According with the enforcement of recycling laws, there has been a rapid increase in recycling ratio of materials at the end-of-life of products in many industrialized countries. So, materials' life cycle is getting more complicated, which makes it difficult to quantify the environmental impacts of materials used in a product in an appropriate way. The purpose of this paper is to develop a methodology to calculate the average number of times a material is used in a society from cradle to grave. The method developed in this paper derives the average number of times material is used; this value could be used for allocation of environmental burdens of virgin material as well as an indicator for assessing the state of material use in a certain year, based on material flow of material in that year. Main Features. Our methodology is based on Markov chain model using matrix-based numerical analysis. A major feature of this method is that it creates transition probability matrices for a material from the way in which the material is produced, consumed, and recycled, making it possible to simply elicit indicators that assess the status of material use in products in society. Our methodology could be an alternative method to derive the average number of times material is used, which could be used for allocation of environmental burdens of virgin material. Results and Discussions. The methodology was applied to hypothetical examples of material flows, in which a virgin material was produced and used in products, recycled and finally landfilled. In some cases, closed loop and open loop recycling of materials existed. The transition probability matrix was created for each material flow, and how many times a virgin material is used in products until all of the elements are ultimately landfilled. Conclusions. This methodology is applicable to a complicated material flow if the status of residence of a material and its flow in a society can be figured out. All the necessary data are the amount of virgin material production, amount of the material used in products, recycling rate of the material at the end of life of each product, the amount of scrap of the material that are used for products. In Part 2 of this paper, case studies for steel were conducted.

    Original languageEnglish
    Pages (from-to)354-360
    Number of pages7
    JournalInternational Journal of Life Cycle Assessment
    Issue number5
    Publication statusPublished - 2006 Sep



    • Markov chain
    • Material flow
    • Number of times of use
    • Open loop recycling management

    ASJC Scopus subject areas

    • Environmental Engineering
    • Environmental Science(all)
    • Environmental Chemistry

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