This article considers two versions of the stochastic bin packing problem with chance constraints. In the first version, we formulate the problem as a two-stage stochastic integer program that considers item-to-bin allocation decisions in the context of chance constraints on total item size within the bins. Next, we describe a distributionally robust formulation of the … Read more
We consider the problem of computing optimal traffic light programs for urban road intersections using traffic flow conservation laws on networks. Based on a Partial Outer Convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or differential algebraic equations, we develop a computationally tractable two-stage solution … Read more
We consider the problem of measuring risk of a portfolio com- prising loans, bonds, and financial instruments, which is caused by possible default of its obligors. Specifically, we are interested in esti- mating probability that a portfolio incurs large loss over a fixed time horizon. One crucial concern of such problem is how to measure … Read more
Free-floating bike sharing (FFBS) is an innovative bike sharing model. FFBS saves on start-up cost, in comparison to station-based bike sharing (SBBS), by avoiding construction of expensive docking stations and kiosk machines. FFBS prevents bike theft and offers significant opportunities for smart management by tracking bikes in real-time with built-in GPS. However, like SBBS, the … Read more
Power generation planning in large-scale hydrothermal systems is a complex optimization task, specially due to the high uncertainty in the inflows to hydro plants. Since it is impossible to traverse the huge scenario tree of the multi-stage problem, stochastic dual dynamic programming (SDDP) is the leading optimization technique to solve it, originally from an expected-cost … Read more
We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversi cation. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation … Read more
We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all arcs, and the location of sources and sinks. The concave cost over each arc is assumed to be evaluated … Read more
This paper points out the impact of opportunity cost of time (high discount rate or high rate of time preference, time-dependent profits, etc.) in designing real-world Steiner trees like electricity, gas, water, or telecommunications networks. We present the Steiner Tree Scheduling Problem which consists of finding a Steiner tree in an activity-on-arc graph that spans … Read more
Implied volatility expansions allow calibration of sophisticated volatility models. They provide an accurate fit and parametrization of implied volatility surfaces that is consistent with empirical observations. Fine-grained higher order expansions offer a better fit but pose the challenge of finding a robust, stable and computationally tractable calibration procedure due to a large number of market … Read more
This paper considers the risk-constrained stochastic traveling salesman problem with random arc costs. In the context of stochastic arc costs, the deterministic traveling salesman problem’s optimal solutions would be ineffective because the selected route might be exposed to a greater risk where the actual cost can exceed the resource limit in extreme scenarios. We present … Read more