As an essential substructure underlying a large class of chance-constrained programming problems with finite discrete distributions, the mixing set with 0 − 1 knapsack has received considerable attentions in recent literature. In this study, we present a family of strong inequalities that subsume known inequalities for this set. We also find many other inequalities that can be explained by lift...

In decision making problems where uncertainty plays a key role and decisions have to be taken prior to observing uncertainty, chance constraints are a strong modelling tool for defining safety of decisions. These constraints request that a random inequality system depending on a decision vector has to be satisfied with a high probability. The characteristics of the feasible set of such chance c...

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem ...

In this paper, we discuss linear programs in which the data that specify the constraints are subject to random uncertainty. A usual approach in this setting is to enforce the constraints up to a given level of probability. We show that for a wide class of probability distributions (i.e. radial distributions) on the data, the probability constraints can be explicitly converted into convex second...

We consider a two player bimatrix game where the entries of the payoff matrices are random variables. We formulate this problem as a chance-constrained game by considering that the payoff of each player is defined using a chance constraint. We consider the case where the entries of the payoff matrices are independent normal/Cauchy random variables. We show a one-to-one correspondence between a ...

The aim of this paper is to solve the portfolio problem when security returns are birandom variables. Two types of portfolio selection based on chance measure are provided according to birandom theory. Since the proposed optimization problems are difficult to solve by traditional methods, a hybrid intelligent algorithm by integrating birandom simulation and genetic algorithm is designed. Finall...

In this paper we develop convex relaxations of chance constrained optimization problems in order to obtain lower bounds on the optimal value. Unlike existing statistical lower bounding techniques, our approach is designed to provide deterministic lower bounds. We show that a version of the proposed scheme leads to a tractable convex relaxation when the chance constraint function is affine with ...