Designing a reverse biomass supply chain network under uncertainty conditions using robust programming and Lagrangian relaxation algorithm

Researchers have studied solutions for reducing pollution and resource waste caused by increases in environmental pollution and resource waste. Moreover, increased productivity, reduced energy generation costs, decreased dependence on fossil fuels and use of biogas in supply chain networks have attracted interest from many industrialists. This research designed a biomass-based reverse supply chain network under conditions of uncertainty about capacity, demand and raw material quality that focused on increased profits and reduced biomass waste. For this purpose, a two-stage stochastic mixed-integer programming model was developed and robust optimisation was used to cope with the uncertainty about the parameters of quality, demand and capacity. In addition, a Lagrangian relaxation (LR) algorithm for simplification of the complicated constraints of the NP-hard problem was developed that could solve large-scale problems with a competitive convergence rate. [Submitted: 6 July 2022; Accepted; 4 December 2023]