Modification of Recourse Data for Mixed-Integer Recourse Models

We consider modification of the recourse data, consisting of the second-stage parameters and the underlying distribution, as an approximation technique for solving two-stage recourse problems. This approach is applied to several specific classes of mixed-integer recourse problems; in each case, the resulting recourse problem is much easier to solve

Contingency-Constrained Unit Commitment with Post-Contingency Corrective Recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-e reliability criterion. This reliability criterion is a generalization of the well-known $N$-$k$ criterion, and dictates that at least $(1-e_ j)$ fraction of the total system demand must be met following the failures of $k$ or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art

Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen's inequality that extends the one for stochastic program. To solve this challenging problem, we present a variant of Benders decomposition method in bilinear form, which actually provides an easy-to-use algorithm framework for further improvements, along with a few enhancement strategies based on structural properties or Jensen's inequality. Computational study shows that the presented Benders decomposition method, jointly with appropriate enhancement techniques, outperforms a commercial solver by an order of magnitude on solving chance constrained program or detecting its infeasibility

An integer L-shaped algorithm for the integrated location and network restoration problem in disaster relief

Being prepared for potential disaster scenarios enables government agencies and humanitarian organizations to respond effectively once the disaster hits. In the literature, the two-stage stochastic programming models are commonly employed to develop preparedness plans before anticipated disasters. These models can be very difficult to solve as the complexity increases by several sources of uncertainty and interdependent decisions. In this study, we propose an integer L-shaped algorithm to solve the integrated location and network restoration model, which is a two-stage stochastic programming model determining the number and locations of the emergency response facilities and restoration resources under uncertainty. Our algorithm accommodates the second-stage binary decision variables which are required to indicate undamaged and restored roads of the network that can be used for relief distribution. Our computational results show that our algorithm outperforms CPLEX for the larger number of disaster scenarios as the solution time of our algorithm increases only linearly as the number of scenarios increases