On the use of risk-based Shapley values for cost sharing in interplant heat integration programs

The heat exchanger network (HEN) is traditionally used for optimal heat recovery in a single chemical plant, while the multi-plant counterparts have been studied in recent years primarily for the purpose of reaping additional overall energy savings. Since all these works focused primarily upon minimization of the total energy cost, the resulting interplant heat integration arrangements were often infeasible due to the fact that the individual savings are not always acceptable to all participating parties. Although a few studies addressed this cost-sharing issue, the existing methodologies are still not mature enough for realistic applications. The present paper outlines a rigorous model-based two-stage procedure to handle this practical problem in the spirit of a cooperative game. The minimum total annual cost (TAC) of each and every potential coalition was first determined with a conventional MINLP model, while the core and the risk-based Shapley values of all players were then computed with explicit formulas derived in this work to settle the benefit allocation issues. A simple example is presented at the end of this paper to demonstrate the feasibility of the proposed approach.