Modelling and optimization of closed-loop supply chains with carbon policies under uncertainty

Abstract

Climate change, increased carbon regulations, globalized supply chains, volatile energy and material prices, and competitive marketing pressures are driving industry practitioners and supply chain decision makers to implement various carbon regulatory mechanisms to curb carbon emissions. One of the effective approaches to reduce carbon emissions is the adoption of closed-loop supply chain (CLSC). Optimal supply chain network design (SCND) is crucial to the success of industrial concerns nowadays because design decisions should be viable enough to function well under complex and uncertain business environments. Also, it plays a vital role in determining the total carbon footprint across the supply chain and the total cost. Therefore, it is essential to make decisions such a way that it could not only configure optimal network but also reduce supply chain total cost and carbon footprint in the presence of uncertainty. In this context, this research proposes optimization models for design and planning of a multi-period, multi-product CLSC network considering carbon footprint under uncertainty to quantify and compare both economic and environmental impacts of carbon emission policies, namely carbon cap, carbon tax, and carbon trade on SCND and planning decisions. This study involves extensive mathematical modelling where SCND considerations are formulated into mixed-integer linear programming (MILP). The proposed models address uncertainty in products demand, returned products, and processing costs. To overcome complexity in scenario-based stochastic programming approach for dealing uncertainty, robust optimization model is developed and validated using two test scenarios of different sizes. The proposed models capture trade-offs between supply chain total cost and carbon emissions. The results suggest that carbon cap policy is only favourable to certain carbon amount. Beyond this limit, there is no economic benefit. The number of opening various facilities is significantly reduced as carbon tax rate increases. The results indicate that carbon trade policy is the most flexible and efficient policy as compared to the other two policies. Moreover, this policy motivates firms to emit less carbon units even when the carbon allowance is available more than needed. Further, the results show that the stochastic model is constantly outperformed the deterministic model in terms of total cost. However, when considering robust optimization to deal with uncertainty, the total cost incurred by the robust models are greater than the values obtained from deterministic model. The additional costs are due to larger solution space to accommodate possible realization of uncertainties in a given uncertainty set. The findings of this study provide evidence that the decision makers are not only able to configure optimal SCND but also reduce carbon emissions without significantly increasing the total cost. Moreover, this study guides decision makers to decide which policy to be chosen well in advance to minimize the total cost and carbon emissions. Finally, the proposed optimization models with different carbon policies can be valuable to manufacturers, researchers, and decision makers to predict the impact of these policies on SCND, overall supply chain costs, and carbon emissions.