A Carbon-Conscious Closed-Loop Bi-Objective p-hub Location Problem

Closed-loop supply chains (CLSC) though present for decades, have seen significant research in optimization only in the last five years. Traditional sustainable CLSCs have generally implemented a Carbon Cap Trading (CCT), Carbon Cap (CC), or Carbon Taxes methodology to set carbon emissions limits but fail to minimize these emissions explicitly. Moreover, the traditional CCT model discourages investment in greener technologies by favoring established logistics over eco-friendly alternatives. This research tackles the sustainable CLSC problem by proposing a mixed-integer linear programming (MILP) carbon-conscious textit{p}-hub location model having the objective of minimizing emissions subject to profit constraints. The model is then extended to incorporate multi-periodicity, transportation modes, and end-of-life periods with a bi-objective cost and emissions function. Additionally, the model accounts for long-term planning and optimization, considering changes in demand and returns over time by incorporating a time dimension. The model's robustness and solving capabilities were tested for the case of electric vehicle (EV) battery supply chains. Demand for EVs is projected to increase by 18% annually, and robust supply chain designs are crucial to meet this demand, making this sector an important test case for the model to solve. Two baseline cases with minimum cost and minimum emissions objectives were tested, revealing a significant gap in emissions and underlining the need for an emissions objective. A sensitivity analysis was conducted on key parameters focusing on minimizing emissions; the analysis revealed that demand, return rates, and recycling costs greatly impact CLSC dynamics. The results showcase the model's capability of tackling real-world case scenarios, thus facilitating comprehensive decision-making goals in carbon-conscious CSLC design.