Centralized Collaborative Planning of an Industrial Symbiosis: Mixed-integer linear model

Currently, the production, distribution and consumption modes disrupt ecosystems. To preserve the environ-ment, circular economy (CE) proposes to reduce the environmental footprint in a social approach. Among the principles of CE, industrial ecology seeks to limit the impact of industries on the environment by involving them in collaboration schemes through industrial symbioses (IS). IS enables the upcycling of a company's waste, called by-products, by another company as raw material. In this context, the goal of this study is to optimize the production planning of supply chains involved in an IS. We formulate this problem as a multi-level collaborative lot-sizing problem applied to industrial symbiosis. Thus, we introduce and define a new problem class: Centralized Collaborative Planning of an Industrial Symbiosis with N actors (CCP-IS-N). First, a new mixed-integer linear (MILP) model is presented, and then the complexity of the problem is studied. Finally, the proposed model is analyzed to understand its behavior and draw some key properties allowing to identify situation(s) in which IS is economically interesting or not.