Modern traceability technologies promise to improve supply chain management by simplifying recalls, increasing visibility, or verifying sustainable supplier practices. Initiatives leading the implementation of traceability technologies must choose the least-costly set of firms - or seed set - to target for early adoption. Choosing this seed set is challenging because firms are part of supply chains interlinked in complex networks, yielding an inherent supply chain effect: benefits obtained from traceability are conditional on technology adoption by a subset of firms in a product's supply chain. We prove that the problem of selecting the least-costly seed set in a supply chain network is hard to solve and even approximate within a polylogarithmic factor. Nevertheless, we provide a novel linear programming-based algorithm to identify the least-costly seed set. The algorithm is fixed-parameter tractable in the supply chain network's treewidth, which we show to be low in real-world supply chain networks. The algorithm also enables us to derive easily-computable bounds on the cost of selecting an optimal seed set. Finally, we leverage our algorithms to conduct large-scale numerical experiments that provide insights into how the supply chain network structure influences diffusion. These insights can help managers optimize their technology diffusion strategy.

翻译：现代溯源技术有望通过简化召回、提高可见性或验证可持续供应商实践来改善供应链管理。实施溯源技术的倡议必须选择成本最低的企业集合（即种子集）作为早期采纳目标。选择该种子集极具挑战性，因为企业是相互关联的复杂供应链网络的一部分，由此产生固有的供应链效应：从溯源中获得的收益取决于产品供应链中部分企业对技术的采纳。我们证明，在供应链网络中选择成本最低的种子集问题难以求解，甚至无法在多项式对数因子内近似。尽管如此，我们提出了一种基于线性规划的新型算法来识别成本最低的种子集。该算法在供应链网络的树宽（我们证明实际供应链网络的树宽较低）上具有固定参数可解性。该算法还能使我们推导出选择最优种子集成本的易计算边界。最后，我们利用该算法开展大规模数值实验，揭示供应链网络结构如何影响技术扩散。这些见解可帮助管理者优化技术扩散策略。