wind power generation is variable and uncertain. in the power systems with high penetration of wind power, determination of equivalent operating reserve is the main concern of systems operator. in this paper, a model is proposed to determine operating reserves in simultaneous market clearing of energy and reserve by stochastic programming based on scenarios generated via monte carlo simulation ...

A number of methods for solving multistage stochastic linear programs with recourse decompose the deterministic equivalent [4] to form subproblems based on scenarios (e.g., Rockafellar and Wets [6] and Mulvey and Ruszczyński [5]). Other methods use forms of Benders decomposition to form subproblems based on nodes of the scenario tree (e.g., Birge [1] and Gassmann [2]). Both types of algorithms ...

We consider a dynamic vehicle routing problem with time windows and stochastic customers (DS-VRPTW), such that customers may request for services as vehicles have already started their tours. To solve this problem, the goal is to provide a decision rule for choosing, at each time step, the next action to perform in light of known requests and probabilistic knowledge on requests likelihood. We i...

The design and analysis of efficient approximation schemes is of fundamental importance in stochastic programming research. Bounding approximations are particularly popular for providing strict error bounds that can be made small by using partitioning techniques. In this article we develop a powerful bounding method for linear multistage stochastic programs with a generalized nonconvex dependen...

We present a stochastic model for capacity-expansion planning of electricity distribution networks subject to uncertain demand (CEP). We formulate CEP as a multistage stochastic mixed-integer program with a scenario-tree representation of uncertainty. At each node of the scenario-tree, the model determines capacity-expansions, operating con guration, and power ows. A “super-arc” representation ...

We formulate and solve a new stochastic integer programming model for dynamic sequencing and scheduling of appointments to a single stochastic server. We assume that service durations and the number of customers to be served on a particular day are uncertain. Customers are sequenced and scheduled dynamically (on-line) one at a time as they request appointments. We present a two-stage stochastic...

We consider a dynamic vehicle routing problem with time windows and stochastic customers (DS-VRPTW), such that customers may request for services as vehicles have already started their tours. To solve this problem, the goal is to provide a decision rule for choosing, at each time step, the next action to perform in light of known requests and probabilistic knowledge on requests likelihood. We i...

a linear programming model has been presented for finding an appropriate planning in order to maximize hotel revenue. in this model, a special planning horizon has been considered that includes several busy days of a year. there are several reservation periods that may start a few months earlier. each period of reservation may have different prices and so result different incomes. hotel custome...