Risk-averse joint facility location-inventory optimisation for green closed-loop supply chain network design under demand uncertainty

This paper considers a joint facility location-inventory optimisation for green closed-loop supply chain network design under demand uncertainty. Under the uncoordinated inventory policy, we propose a chance-constrained risk-averse bi-objective 0-1 mixed-integer nonlinear stochastic programming to minimise the total expected cost and CO2 emissions. To solve the model, we first present an equivalent reformulation with a single objective based on distributionally robust optimisation. Then, we provide a linear reformulation with some valid inequalities. We also provide a greedy heuristic decomposition searching rule to solve the large-scale problem. We finally present a numerical analysis to show the performance of our methods. Results illustrate that the risk-averse joint model can effectively improve service capability and reliability than independent and risk-neutral location and inventory problems. We also recommend that the incompletely uncoordinated strategy for the joint optimisation can be more cost-effective and generate fewer workloads. Besides, the proposed algorithm achieves a more desirable performance than CPLEX for large-scale problems. [Submitted: 10 December 2020; Accepted: 15 January 2022]