We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chanceconstrained game using worst-case chance constraint. We consider two types of distributional u...

In this paper, we address the problem of maximizing expected return subject to a worst case return constraint by composing a portfolio that may consist of cash, holdings in a stock market index and options on the index. We derive properties of optimal and feasible portfolios and present a linear programming model to solve the problem. The optimal portfolios have pay-off functions that reflect a...

An algorithm is presented for solving nonlinear optimization problems with chance 5 constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at 6 least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained 7 nonlinear optimization problems that arise in sample average approximations of chance-constrained 8 ...

This paper considers a balance-constrained stochastic bottleneck spanning tree problem (BCSBSTP) in which edge weights are independently distributed but may follow arbitrary random distributions. The problem minimizes a scalar and seeks a spanning tree, of which the maximum edge weight is bounded by the scalar for a given certain probability, and meanwhile the minimum edge weight is lower bound...

We propose a new framework to address feasibility analysis and optimal design problems under uncertainty. This approach is based on nonlinear chance constrained programming. The feasibility analysis problem is defined as the maximization of the achievable confidence level of satisfying all constraints for a given design. The solution can provide clear information about the dependence of the rel...

Chance constraints are an important modeling tool in stochastic optimization, providing probabilistic guarantees that a solution “succeeds” in satisfying a given constraint. While they control the probability of “success,” they provide no control whatsoever in the event of a “failure.” That is, they do not distinguish between a slight overor under-shoot of the bounds, and more catastrophic viol...

We present a stochastic programming framework for finding the optimal vaccination policy for controlling infectious disease epidemics under parameter uncertainty. Stochastic programming is a popular framework for including the effects of parameter uncertainty in a mathematical optimization model. The problem is initially formulated to find the minimum cost vaccination policy under a chance-cons...

In this paper, the chance-constraint joint single vendor-single buyer inventory problem is considered in which the demand is stochastic and the lead time is assumed to vary linearly with respect to the lot size. The shortage in combination of back order and lost sale is considered and the demand follows a uniform distribution. The order should be placed in multiple of packets, the service rate ...

Most approaches of chance–constrained robust MPC utilise an open– loop model for uncertainty prediction; this results in conservative control. To avoid this some approaches propose robust MPC (RMPC) based on closed–loop prediction, and these often give improved dynamic performance at a small expense to constraint handling performance. The aim of this paper is to extend the methodology of (Warre...

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities subsume existing inequalities for this problem, and they are facet-defining under certain conditions. In addition, we show that they give the convex hull descr...