A new method for the measurement of robustness in reverse logistics supply chains based on entropy and nodal importance

This paper proposes a new methodology for measuring robustness in Reverse Logistics (RL) supply chains. First, an integer-mixed linear programming model is proposed to design an RL network and analyze its robustness. It uses a new method based on entropy and the importance of each node that has been adapted from measurement in electrical systems. The entropy of a node allows for determining important fault dynamics in the distribution network. Similarly, the node's importance is considered a measure of centrality by quantifying its importance in the network in the context of possible disturbances. In particular, when a disturbance occurs in a flow that originates in one of the nodes, leaving it disabled, the flow must be redistributed to the rest of the network echelons. A company producing animal feed has tested the proposed methodology in a case study applied to recovering wooden pallets and big bags. A validation with 500 scenarios has been carried out to evaluate the robustness metric's adaptation and group the solutions into up to 16 types. This classification has been performed to compare them in a set of 5000 new scenarios and to select the one that provides the most excellent robustness for the logistics system under study. The results obtained show the efficiency of the proposed methodology.