... with right-hand side stochasticity. A Lagrangian relaxation-based heuristic method is applied to address the NP-hard nature of the problem. Findings The efficacy of the proposed model is illustrated through a numerical example, demonstrating its capability to optimize material flows across the supply...

.... As the proposed model is an non-deterministic polynomial-time-hard model, the Lagrangian relaxation algorithm is used to solve it. Findings The proposed model is applied to a real supply chain in the aftermarket automotive service industry. The results of the model and the current status of the company under...

... of the mathematical model, a solution approach based on a Lagrangian relaxation (LR) heuristic is developed which provides good-quality upper and lower bounds. Findings The model output is discussed through various examples. The introduction of some enhancements and using some heuristics results in better outputs...

..., the authors introduced a Lagrangian relaxation solution methodology to facilitate and improve the solving process of the model. Then, the evaluation of the results enabled us to demonstrate the model validity, and underscore its utility to deal with problems with more sophisticated used product collection...