Organic waste resulting from fishing—consisting primarily of inedible fish parts and bycatch (non-target species) discarded during on-shore processing—is a source of substantial ecological concern. Researchers and practitioners are increasingly exploring how fishing supply chains can convert such waste into profitable products, towards benefiting the environment and the economy. The current study puts forward an optimal control model that addresses interactions between fishing practices, fish populations, and waste streams from fishing operations, with the aim of understanding how to achieve profitable and environmentally sustainable fishing practices. Although numerous models have been proposed for optimizing fish population management, ours is among the first to incorporate waste-processing dynamics, providing insight into how dynamic interactions between main-stream and side-stream supply chain operations can affect fishing policies and the overall ecosystem. We derive a necessary condition for sustainability of a “green” supply chain (i.e., one that incorporates side-stream processing) and determine the maximum fishing effort to ensure that a steady-state fish stock exists. We prove that when the cost of fish harvesting is negligible, a green supply chain (vs. a supply chain without side-stream processing) significantly reduces the rate of waste disposal but does not improve the stock of fish biomass. In a numerical analysis, we show that this result holds even when harvesting costs are high. The numerical analysis also shows that a sufficient increase in the marginal cost of fishing eliminates potential multiplicity of the steady states, thereby improving fish stock stability and ecosystem health.

中文翻译：

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具有有机废物侧流的供应链中的捕捞政策

捕捞产生的有机废物（主要由不可食用的鱼类部分和岸上加工过程中丢弃的副渔获物（非目标物种）组成）是重大生态问题的根源。研究人员和从业者越来越多地探索渔业供应链如何将这些废物转化为有利可图的产品，从而造福环境和经济。当前的研究提出了一种最佳控制模型，该模型解决了捕捞作业、鱼类种群和捕捞作业废物流之间的相互作用，旨在了解如何实现有利可图且环境可持续的捕捞作业。尽管已经提出了许多模型来优化鱼类种群管理，但我们的模型是最早纳入废物处理动态的模型之一，可以深入了解主流和侧流供应链运营之间的动态相互作用如何影响捕捞政策和整个生态系统。我们得出了“绿色”供应链（即包含侧流加工的供应链）可持续性的必要条件，并确定了最大捕捞努力量，以确保存在稳态鱼类种群。我们证明，当鱼类捕捞成本可以忽略不计时，绿色供应链（与没有侧流加工的供应链相比）会显着降低废物处理率，但不会提高鱼类生物量的存量。在数值分析中，我们表明即使收获成本很高，这一结果也成立。数值分析还表明，捕捞边际成本的充分增加消除了稳态的潜在多重性，从而改善了鱼类种群的稳定性和生态系统的健康。