Sustainable closed-loop supply chain for dairy industry with robust and heuristic optimization

•Reduction in run time using the heuristic for large-scale problems.•Using a robust optimization approach and an augmented ε-constraint method.•Higher profit for products with a longer lifetime under the worst-case scenario. This paper supplements the augmented ε-constraint approach with linearization using robust optimization and heuristics with an improved algorithm to maximize the total profit and minimize the environmental effects of a sustainable closed-loop supply chain (CLSC) in the dairy industry. The resultant mixed-integer linear programming (MILP) model is applied to a case from the dairy industry and evaluated against several test problems. The pessimistic, optimistic, and worst-case scenarios are considered along with the sensitivity analysis on the profitability of the CLSC concerning the product lifetimes. Our results inform that applying the heuristic on large-scale problems yields a 25% improvement in runtime. Furthermore, products with a longer lifetime under the worst-case scenario yield greater profit than those products with a shorter lifetime under an optimistic scenario.