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...

This paper deals with knapsack problem in fuzzy nature, where both the objective function and constraints are considered to be fuzzy. Three different models for proposed including, expected value model, chance-constrained dependent-chance model. Credibility ranking method is applied convert into a crisp equivalent linear one considering triangular trapezoidal numbers. The solution of obtained r...

This paper is devoted to develop an approximation method for scheduling refinery crude oil operations by taking into consideration the demand uncertainty. In the stochastic model the demand uncertainty is modeled as random variables which follow a joint multivariate distribution with a specific correlation structure. Compared to deterministic models in existing works, the stochastic model can b...

We consider the issue of modeling service level measures in stochastic decision making via chance constraints. More specifically we focus on service level measures in production/inventory control under stochastic demand and α service level constraints, which are constraints enforcing a prescribed non-stockout probability for the system. We introduce multiple ways of expressing these chance cons...

Resource allocation for secondary users is an important issue in cognitive radio networks. In our article, we introduce a resource allocation scheme for secondary users to share spectrum in a cognitive radio network. Secondary users can exploit the spectrum owned by primary links when the interference level does not exceed certain requirements. Uncertainties of channel gains pose a great impact...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1 Motion Planning with Chance Constraints . . . . . . . . . 1 1.

Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation limits for joints parameterized with the unit quaternion. Joint constrains constructed with our method are adeq...

We consider a chance constrained problem, where one seeks to minimize a convex objective over solutions satisfying, with a given close to one probability, a system of randomly perturbed convex constraints. Our goal is to build a computationally tractable approximation of this (typically intractable) problem, i.e., an explicitly given deterministic optimization program with the feasible set cont...