This paper proposes a chance-constrained multi-objective goal programming model for supplier selection problem with uncertain factors. Considering uncertain factors of demand, capacity and lead time and several objectives, the proposed approach provides chance constraints leading to a order allocation decision-making result. The decision keeps the confidence and risk of constraints to a certain...

Introduction: A chance constrained optimization problem involves constraints with stochastic data that are required to be satisfied with a pre-specified probability. When the underlying distribution of the stochastic data is not known precisely, an often used model is to require the chance constraints to hold for all distributions in a given family. Such a problem is known as a distributionally...

In the paper we consider the chance-constrained version of an affinely perturbed linear matrix inequality (LMI) constraint, assuming the primitive perturbations to be independent with light-tail distributions (e.g., bounded or Gaussian). Constraints of this type, playing a central role in chance-constrained linear/conic quadratic/semidefinite programming, are typically computationally intractab...

We study joint chance constraints where the distribution of the uncertain parameters is onlyknown to belong to an ambiguity set characterized by the mean and support of the uncertaintiesand by an upper bound on their dispersion. This setting gives rise to pessimistic (optimistic)ambiguous chance constraints, which require the corresponding classical chance constraints to bes...

6 Chance constraints and the choice of uncertainty sets 15 6.1 Value at risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6.2 Safe convex approximations for chance constraints . . . . . . . . . . . . . . . 17 6.3 Tightest convex bounds and conditional value at risk . . . . . . . . . . . . . 18 6.4 Analytic approximation using moment generating functions . . . . . ....

This article considers the stochastic optimal control of discrete-time linear systems subject to (possibly) unbounded stochastic disturbances, hard constraints on the manipulated variables, and joint chance constraints on the states. A tractable convex second-order cone program (SOCP) is derived for calculating the receding-horizon control law at each time step. Feedback is incorporated during ...