Optimal distribution of power among generating units to meet a specific demand subject to system constraints is an ongoing research topic in the power system community. The problem, even in a static setting, turns out to be hard to solve with conventional optimization methods owing to the consideration of valve-point effects, which make the cost … Read more
We describe a simulation-based optimization method that allocates additional capacity to transmission lines in order to minimize the expected value of the load shed due to a cascading blackout. Estimation of the load-shed distribution is accomplished via the ORNL-PSerc-Alaska (OPA) simulation model, which solves a sequence of linear programs. Key to achieving an effective algorithm … Read more
The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing quality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF) prob- lem, the semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack … Read more
Scheduling elective surgeries is a complicated task due to the coupled effect of multiple sources of uncertainty and the impact of the proposed schedule on the downstream units. In this paper, we propose an adaptive robust optimization model to address the existing uncertainty in surgery duration and length-of-stay in the surgical intensive care unit. The … Read more
We study the polyhedron of the unit commitment problem, and consider a relaxation involving the ramping constraints. We study the three-period ramp-up polytope, and describe the convex-hull using a new class of inequalities. Citation[1] J. Ostrowski, M. F. Anjos, and A. Vannelli, \Tight mixed integer linear programming formulations for the unit commitment problem,” Power Systems, … Read more
The automated real time control of an electrical network is achieved through the estimation of its state using Phasor Measurement Units (PMUs). Given an undirected graph representing the network, we study the problem of finding the minimum number of PMUs to place on the edges such that the graph is fully observed. This problem is … Read more
In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded $L^{1}$-costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing a priori a global variable $s$ heuristically, we show that there exist optimal policies for the infinite horizon problem. To … Read more
We study two-stage stochastic mixed integer programs (TSS-MIPs) with integer variables in the second stage. We show that under suitable conditions, the second stage MIPs can be convexified by adding parametric cuts a priori. As special cases, we extend the results of Miller and Wolsey (Math Program 98(1):73-88, 2003) to TSS-MIPs. Furthermore, we consider second … Read more
In many real-world transportation systems, passengers are often required to make a number of interchanges between different modes of transport. As cities continue to grow, a greater number of these connections tend to occur within centrally located Transport Hubs. In order to encourage the uptake of public transport in major cities, it is important for … Read more
In this note we show that multiple solutions exist for the production-inventory example in the seminal paper on adjustable robust optimization in [2]. All these optimal robust solutions have the same worst-case objective value, but the mean objective values differ up to 21.9% and for individual realizations this difference can be up to 59.4%. We … Read more