An efficient matheuristic algorithm for bi-objective sustainable closed-loop supply chain networks

This paper develops an optimization model for a sustainable closed-loop supply chain network with two conflicting objectives, namely, the minimization of the total logistic costs and the total amount of carbon emissions. The first objective relates to financial benefits, whereas the second represents the wider goal of guaranteeing cleaner air and hence a greener and healthier planet. The problem is first modelled as a mixed integer linear programming based-model. The aim is to determine the location of distribution centres and recycling centres, their respective numbers and the type of vehicles assigned to each facility. Vehicle type consideration, not commonly used in the literature, adds another dimension to this practical and challenging logistic problem. A matheuristic using compromise programming is put forward to tackle the problem. The proposed matheuristic is evaluated using a variety of newly generated datasets which produces compromise solutions that demonstrate the importance of an appropriate balance of both objective functions. The robustness analysis considering fluctuations in customer demand is assessed using Monte Carlo simulation. The results show that if the standard deviation of the demand falls within 10% of its average, the unsatisfied demand is insignificant, thus demonstrating the stability of supply chain configuration. This invaluable information is key towards helping senior management make relevant operational and strategic decisions that could impact on both the sustainability and the resilience of their supply chain networks.