Optimal control and cooperative game theory based analysis of a by-product synergy system

In this paper, we propose a framework to analyse the setting up of an industrial symbiosis system. The establishment of such a system entails implementation of expensive technologies by the companies so as to convert wastes into energy and other mutually beneficial materials. Much of the literature on modeling industrial symbiosis do not consider this important aspect of high conversion costs. Further, such a cooperative effort will be sustainable only if the high cost of implementing technologies is compensated by sharing of the benefits in a fair and satisfactory manner. Towards this end, first at a general level, we addres the issue of the optimal design of an industrial symbiosis network of companies in a given region. The materials processing rates depend on the choice of the new technology. We first propose an optimal control problem to determine the best choice of technology for the companies. Then, we recommend the nucleolus-based cooperative game theory approach to determine the best share of the benefits among the participating companies as this method minimizes the unhappiness of the members. A hypothetical numerical example of three companies is provided to illustrate the model. Each company has a choice of 3 technology options. The planning horizon is assumed to be 5 years. The numerical example brings out clearly the benefit of cooperation. The benefit of by-product synergy is that companies 1, 2 and 3 can realize an increase in their NPVs by 44%, 33% and 21% respectively. The nucleolus based sharing of NPVs guarantees the acceptance by companies of the distribution of the additional profits.