A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations

We present a scenario decomposition framework based on Lagrangean decomposition for the multi-product, multi-period, supply investment planning problem considering network design and discrete capacity expansion under demand uncertainty. We also consider a risk measure that allows us to reduce the probability of incurring in high costs while preserving the decomposable structure of the problem. To solve the resulting large-scale two-stage mixed-integer stochastic linear programming problem, we propose a novel Lagrangean decomposition scheme. In this context, we compare different formulations for the non-anticipativity conditions. In addition to that, we present a new hybrid algorithm for updating the Lagrangean multiplier set, based on the combination of cutting-plane, subgradient and trust-region strategies. Numerical results suggests that different formulations of the non-anticipativity conditions have a significant effect on the performance of the algorithm. Moreover, we observe that the proposed hybrid approach has superior performance when compared with the traditional subgradient algorithm in terms of faster computational times for the problem addressed in this work.