Integrating production, replenishment and fulfillment decisions for supply chains: a target-based robust optimisation approach

In this paper, a three-echelon supply chain problem under demand uncertainty is considered. The problem is formulated as a multiperiod two-stage stochastic optimisation model. The first stage, consisting of production and replenishment decisions, is integrated with the second stage, which comprises reactive fulfillment decisions, allowing seamless determination as demands are revealed over time. The demand in each period is characterised by an uncertainty set based on the nominal value and demand bounds. We propose a target-based robust optimisation (TRO) approach to determine the most robust planning with respect to a pre-specified cost target. The proposed TRO approach can trade off the total cost (performance) and model feasibility in the presence of demand perturbation (robustness) by fine-tuning the cost target. The robust counterpart is converted to a quadratically constrained linear programming (QCLP) problem, which can be solved by commercial solvers. Numerical experiments demonstrate that the TRO approach can outperform traditional robust optimisation methods in terms of both cost and feasibility against demand uncertainty by enabling precise adjustment of the cost target. Importantly, the TRO approach provides a flexible means to strike a balance between performance and robustness metrics, making it a valuable tool for supply chain planning under uncertain conditions.