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:现代溯源技术承诺通过简化召回、增加可见性或验证可持续供应商实践来改进供应链管理。领导实施溯源技术的倡议必须选择最具成本效益的一组企业 - 或种子集 - 以便进行早期采用。选择这种种子集很具挑战性,因为企业是相互链接在复杂网络中的供应链的一部分,从而产生内在的供应链效应:从溯源中获得的利益取决于产品供应链的一部分企业的技术采用情况。我们证明在供应链网络中选择最具成本效益的种子集是难以解决的,甚至无法在对数多项式因子内进行近似。然而,我们提供了一种基于线性规划的新型算法来识别最具成本效益的种子集。该算法在供应链网络的树宽参数是固定可计算的,在实际供应链网络中表现出较低的树宽度。该算法还使我们能够推断出关于选择最佳种子集的成本的易于计算的界限。最后,我们利用我们的算法进行大规模的数值实验,为了解供应链网络结构如何影响扩散提供了见解。这些见解可以帮助管理者优化他们的技术扩散策略。