Duality in Two-stage Adaptive Linear Optimization: Faster Computation and Stronger Bounds

During this talk we show how to derive and exploit duality in general two-stage adaptive linear optimization models. The equivalent dualized formulation we derive is again a two-stage adaptive linear optimization model. Therefore, all existing solution approaches for two-stage adaptive models can be used to solve or approximate the dual formulation. The new dualized model differs from the primal formulation in its dimension and uses a different description of the uncertainty set. The optimal primal affine policy can be directly obtained from the optimal affine policy in the dual formulation. We provide empirical evidence that the dualized model, in the context of two-stage lot-sizing on a network and two-stage facility location problems, solves an order of magnitude faster than the primal formulation with affine policies. We also provide an explanation and associated empirical evidence that offer insight on which characteristics of the dualized formulation make computations faster. Furthermore, the affine policy of the dual formulations can be used to provide stronger lower bounds on the optimality of affine policies. At the end of the talk we will discuss some potential future research directions based on this dualized formulation for adaptive optimization problems.

This research is based on joint work with Dimitris Bertsimas (MIT).

Registration to Remy Spliet, spliet@ese.eur.nl is required for availability of lunch.