To model combinatorial decision problems involving uncertainty and probability, we have proposed “stochastic constraint programming” [3]. This extends constraint programming with stochastic variables, chance constraints and optimized expectations. We propose extending the OPL modelling language [1] with these features, and show how they can be compiled away using some simple rules.

Abstract Renewable energy has unpredictable intermittency and variability, increasing the complexity of grid dispatch. Fuzziness theory is introduced under uncertainty large-scale intermittent power supply. characterized by fuzziness parameters. Meanwhile, conventional deterministic unit commitment model transformed into a chance-constraint with The explicit equivalence classes chance constrain...

Crash frequency and crash severity are two major aspects of transportation safety. In this paper, we propose a decision-making scheme combining statistical analysis optimization modeling to be used in safety study. We conduct analysis, travel speed an develop two-stage decision minimize while mitigating severity, using data collected urban environments Lincoln, Nebraska. the study impact lane w...

We consider an n-player strategic game with finite action sets and random payoffs. We formulate this as a chance-constrained game by considering that the payoff of each player is defined using a chance-constraint. We consider that the components of the payoff vector of each player are independent normal/Cauchy random variables. We also consider the case where the payoff vector of each player fo...

A joint chance constrained optimization problem involves multiple uncertain constraints, i.e., constraints with stochastic parameters, that are jointly required to be satisfied with probability exceeding a prespecified threshold. In a distributionally robust joint chance constrained optimization problem (DRCCP), the joint chance constraint is required to hold for all probability distributions o...

We study approximations of chance constrained problems. In particular, we consider the Sample Average Approximation (SAA) approach and discuss convergence properties of the resulting problem. A method for constructing bounds for the optimal value of the considered problem is discussed and we suggest how one should tune the underlying parameters to obtain a good approximation of the true problem...

In this article, a fast chance-constrained trajectory generation strategy incorporating convex optimization and approximation of chance constraints is designed so as to solve the unmanned vehicle path planning problem. A path-length-optimal model constructed with consideration pitch angle constraint, curvature radius probabilistic control actuation collision avoidance constraint. Subsequently, ...

Coordination of market decisions with other aspects of operations management such as production and inventory decisions has long been a meticulous research issue in supply chain management. Generally, changes to the original lot-sizing policy stimulated by market prices may impose remarkable deviation revenue throughout the supply and demand chain system. This paper examines how to set the chan...

We study an n-player game with random payoffs and continuous strategy sets. The payoff function of each player is defined by its expected value the set a joint chance constraint. constraint vectors defining are dependent follow elliptically symmetric distributions. Archimedean copula used to capture dependence among vectors. propose reformulation player. Under mild assumptions on players’ funct...