In [2], a family of stochastic flows of kernels on S 1 called " sticky flows " is described. Sticky flows are defined by their " moments " which are consistent systems of transition kernels on S 1. In this note, a discrete version of sticky flows is presented in the case the sticky flows are associated with a system of Brownian particles on S 1. This discrete model is defined by products of Bet...

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service ...

This work describes a stochastic approach for the optimal placement of sensors in municipal water networks to detect maliciously injected contaminants. The model minimizes the expected fraction of the population at risk. Our work explicitly includes uncertainties in attack risks and population density, so that the resulting problem involves optimization under uncertainty. In our formulation, we...

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and sto...