Robust Multi-Objective Optimization of Supply Chain Resources Under Stochastic Demand Constraints

Abstract

The supply chain planner is often faced with the situation of making investments in network systems that are resilient to demands, capacity constraints and carbon goals. While many robust optimization (RO) models have adopted demand inclusion in box or ellipsoid shapes for tackling uncertainties, this model misses out on one critical aspect, which is the fact that while a positive demand shock is risky, a negative shock usually creates slack in capacity. Furthermore, they frequently ignore the phenomenon that local markets tend to react in a correlated way rather than independently. In order to overcome these drawbacks, in this paper, we present a bi objective, two-stage robust integer programming model for the four-level supply chain including suppliers, plants, distribution centers, and demand nodes, using an uncertainty set which we call Asymmetric Covariance aware Ellipsoidal Budget Model. The uncertainty set allows setting individual upper and lower bounds for demand increases and decreases, respectively, while strong duality transforms the resulting model into a tractable second order cone program. The cost–emissions trade-off is obtained using the augmented ε-constraint method (AUGMECON2), and the formulation is benchmarked against the classical Soyster, Bertsimas–Sim and Ben Tal–Nemirovski approaches on a network containing ten suppliers, fifteen plants, thirty distribution centers and one hundred demand zones. The proposed uncertainty set reduces capital expenditure by up to 14.2 percent relative to these benchmark formulations while maintaining full feasibility under worst-case demand and avoiding the substantial runtime increase often associated with richer uncertainty representations. The paper concludes with practical guidance on the cost of protection and discusses the limitations that remain.