On the modeling and solution algorithm for the reverse logistics recycling flow equilibrium problem

This paper presents a study that characterizes, formulates, and solves the reverse logistic recycling flow equilibrium (RLRFE) problem. The RLRFE problem is concerned with the recycling channel in which recyclable collectors, processors, landfills, and demand markets form a multi-tiered network to process the recycled material flows from sources destined either for landfills or demand markets. Motivated by a government policy making or enterprise conglomerate recycling system design and operation needs, the RLRFE problem is elaborated from a system-optimal perspective using the variational inequality (VI) approach. For each origin–destination (OD) pair, the corresponding equilibrium conditions are established as a variation of the Wardrop second principle. In light of demand and cost function interactions, a nested diagonalization solution (ND) algorithm is proposed that gradually transforms the RLRFE problem into a traffic assignment model. To address multiple landfills in the recycling network and to understand how a variable-demand problem can be analyzed as a fixed-demand problem, we propose a supernetwork representation of the RLRFE problem. A numerical analysis on a test case illustrates the model formulation and the proposed algorithm.