Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we introduce a new production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is NP-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the effectiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

垃圾填埋场中的废物堆积、全球变暖以及保护有限原材料的需要推动政府和行业转向循环经济。工业共生代表了一种共享资源并将不可避免的生产残留物转化为有用和附加值产品的可持续方式。在这种情况下，我们引入了工业共生中两个生产单位 (PU) 之间出现的新生产计划问题。在主要产品的生产过程中，第一个 PU 会产生生产残留物，随后将其用作第二个 PU 的原材料或进行处理。第二个 PU 也可以从外部供应商处采购原材料。由此产生的组合生产计划问题已被公式化为一个两级单项批量大小问题。NP -Hard 与生产残留物无关，即不可储存或可储存且容量有限。为了有效地解决这个问题，提出了一种基于拉格朗日分解的启发式算法。大量的数值实验突出了所提出的求解方法的有效性。通过对不同分散式和集中式协作政策的比较分析，研究了协作框架的影响，其中每个 PU 的生产计划汇集在一起​​。从此分析得出的宝贵见解随后用于讨论在副产品供应商与其接收者之间建立工业共生关系的管理意义。