An Adjusted Robust Optimization Method to an Integrated Production-Distribution Planning Problem in Closed-Loop Supply Chains under Uncertainty

In the last decade, planning of closed-loop supply chains in different strategic, tactical, and operational levels has attracted many interests due to economic reasons, environmental challenges, and government legislations. This paper presents a novel linear programming model for the integrated production and distribution planning in closed-loop supply chains under uncertainty. The proposed model involves multi-product and multi-period which considers multiple transportation modes, direct or indirect shipments, advertising costs, and several customer zones for different types of products and also attempts to integrate production and distribution plans in the forward and reverse sides of the closed-loop supply chain, simultaneously. To deal with uncertain input data, a robust optimization counterpart based on polyhedral uncertainty set is developed to obtain optimal solutions immunizing the problem for any realization of uncertain parameters in the given polyhedral uncertainty set. Computation results for a numerical example under different scenarios are discussed to give insights about the features of the proposed robust optimization model in handling the uncertainty of parameters. Finally, some sensitivity analyses are performed to show the behaviour of the robust and deterministic models respect to changes of uncertainty levels of parameters as well as the amounts of important parameters such as demands and returns.