ANION Environmental Ltd., 26 Lykoudi Str., Athens, GR 11141, Greece.
Waste Manag. 2011 Nov;31(11):2302-18. doi: 10.1016/j.wasman.2011.06.003. Epub 2011 Jul 23.
Explicit expressions for the end-of-life flows (EOL) of single and multiple cycle products (MCPs) are presented, including deterministic and stochastic EOL exit. The expressions are given in terms of the physical parameters (maximum lifetime, T, annual cycling frequency, f, number of cycles, N, and early discard or usage loss). EOL flows are also obtained for hi-tech products, which are rapidly renewed and thus may not attain steady state (e.g., electronic products, passenger cars). A ten-step recursive procedure for obtaining the dynamic EOL flow evolution is proposed. Applications of the EOL expressions and the ten-step procedure are given for electric household appliances, industrial machinery, tyres, vehicles and buildings, both for deterministic and stochastic EOL exit, (normal, Weibull and uniform exit distributions). The effect of the physical parameters and the stochastic characteristics on the EOL flow is investigated in the examples: it is shown that the EOL flow profile is determined primarily by the early discard dynamics; it also depends strongly on longevity and cycling frequency: higher lifetime or early discard/loss imply lower dynamic and steady state EOL flows. The stochastic exit shapes the overall EOL dynamic profile: Under symmetric EOL exit distribution, as the variance of the distribution increases (uniform to normal to deterministic) the initial EOL flow rise becomes steeper but the steady state or maximum EOL flow level is lower. The steepest EOL flow profile, featuring the highest steady state or maximum level, as well, corresponds to skew, earlier shifted EOL exit (e.g., Weibull). Since the EOL flow of returned products consists the sink of the reuse/remanufacturing cycle (sink to recycle) the results may be used in closed loop product lifecycle management operations for scheduling and sizing reverse manufacturing and for planning recycle logistics. Decoupling and quantification of both the full age EOL and of the early discard flows is useful, the latter being the target of enacted legislation aiming at increasing reuse.
提出了单循环和多循环产品（MCP）的终端寿命（EOL）的显式表达式，包括确定性和随机性 EOL 退出。这些表达式是根据物理参数（最大寿命 T、年循环频率 f、循环次数 N 和早期报废或使用损失）给出的。还为高科技产品（例如电子产品、乘用车）获得了 EOL 流量，这些产品更新速度很快，因此可能无法达到稳定状态。提出了一种十步递归程序，用于获得动态 EOL 流量演变。给出了 EOL 表达式和十步程序在电器、工业机械、轮胎、车辆和建筑物中的应用，包括确定性和随机性 EOL 退出（正态、威布尔和均匀退出分布）。在示例中研究了物理参数和随机特征对 EOL 流量的影响：结果表明，EOL 流量分布主要由早期报废动态决定；它还强烈依赖于寿命和循环频率：较高的寿命或早期报废/损失意味着较低的动态和稳定状态 EOL 流量。随机退出塑造了整体 EOL 动态分布：在 EOL 退出分布对称的情况下，随着分布方差的增加（从均匀到正态到确定性），初始 EOL 流量上升变得更陡峭，但稳定状态或最大 EOL 流量水平更低。最高的 EOL 流量分布，具有最高的稳定状态或最大水平，也对应于偏斜、提前转移的 EOL 退出（例如威布尔）。由于返回产品的 EOL 流量构成了再利用/再制造循环的汇流（汇流到回收），因此这些结果可用于闭环产品生命周期管理操作，用于安排和调整反向制造以及规划回收物流。完全年龄 EOL 和早期报废流量的解耦和量化是有用的，后者是旨在增加再利用的已颁布立法的目标。
