Interrelating physical and financial flows in a bi-objective closed-loop supply chain network problem with uncertainty

This paper presents a bi-objective logistic design problem integrating the financial and physical flows of a closed-loop supply chain in which the uncertainty of demand and the return rate described by a finite set of possible scenarios. The main idea of this paper consists of the joint integration of enterprise finance with the company operations model, where financial aspects are explicitly considered as exogenous variables. The model addressesthe company operationsdecisions as well as the finance decisions. Moreover, the change in equity is considered as objective function along with the profit to evaluate the business aspects.Since the logistic network design is a strategic problem and the change of configuration is not easy in the future,a bi-objective robust optimization with the max-min versionis extended to cope with the uncertainty of parameters. In addition, to obtain solutions with a better time, the scenario relaxation algorithm is adapted for the proposed approach. The numerical examples are presented to show the applicability of the model along with a sensitivity analysis on financial parameters. The obtained results illustrate the importance of such modelling systems leading to more overall earnings and expressingfurther insights on the interactions between operations and finances.