(Extended Abstract) Stochastic programming is an optimization technique that incorporates random variables as parameters. Because it better reflects the uncertain real world than its traditional deterministic counterpart, stochastic programming has drawn increasingly more attention among decision-makers, and its applications span many fields including financial engineering , health care, commun...

We study a class of chance-constrained two-stage stochastic optimization problems where second-stage feasible recourse decisions incur additional cost. In addition, we propose a new model, where “recovery” decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second-stage problem. We develop decomposition algorithms with specialized optimality and feasibility...

Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two peaked systems. Significant influence is demonstrated when a bare growth rate ...

this paper presents a probabilistic confidence-interval based method for optimal placement of shunt capacitors in distribution networks by considering probabilistic characteristics of loads. the main objective function are reducing loss and improving the voltage profile. backward forward sweep method has been employed to obtain the power flow results in distribution system. in addition, integer...

We introduce a new optimization framework to maximize the expected spread of cascades in networks. Our model allows a rich set of actions that directly manipulate cascade dynamics by adding nodes or edges to the network. Our motivating application is one in spatial conservation planning, where a cascade models the dispersal of wild animals through a fragmented landscape. We propose a mixed inte...

We consider a general adversarial stochastic optimization model. Our model involves the design of a system that an adversary may subsequently attempt to destroy or degrade. We introduce SPAR, which utilizes mixed-integer programming for the design decision and a Markov decision process (MDP) for the modeling of our adversarial phase. © 2005 Elsevier B.V. All rights reserved.

The Poisson process is one of the most widely used models of a continuous time stochastic process. Along with Brownian motion, it can be considered as a fundamental example of such processes. The Poisson process is a counting process Nt, t ≥ 0, (a non-decreasing integer-valued process which counts the number of ‘points’ or ‘events’ up to time t) indexed by the time parameter t, which will be po...

We review convex approximations for stochastic programs with simple integer recourse. Both for the case of discrete and continuous random variables such approximations are discussed, and representations as continuous simple recourse problems are given.

We consider the problem of optimally allocating the seats on a single flight leg to the demands from multiple fare classes that arrive sequentially. It is well-known that the optimal policy for this classical problem is characterized by a set of protection levels. In this paper, we propose a stochastic approximation method to compute the optimal protection levels under the assumption that the d...