Closed‐loop supply chain network static equilibrium and dynamics under pollution permits system

Abstract

A closed‐loop supply chain network including multi‐manufacturing/remanufacturing firms and multi‐demand markets is considered. We present equilibrium conditions for decision‐makers in the network and develop a static model with marketable pollution permits and noncompliant behavior, using the variational inequality theory. We provide qualitative analysis of the model. Then, using the projected dynamical system, we propose a dynamic model. The results show that the set of stationary points of dynamic model coincides with the set of solutions of static model. Finally, numerical examples are proposed. The equilibrium results including production output of new products, the forward and reverse product flows, the prices of product, the prices of license, the number of licenses, and the possible noncompliant overflows and underflows of the waste are obtained. We find that increase in the unit penalty cost contributes to decrease in waste emission from firms in the network, and when the unit penalty cost increase to a certain level, they no longer choose excess emission of waste. © 2018 American Institute of Chemical Engineers Environ Prog, 38:e13021, 2019