Various applications in reliability and risk management give rise to optimization problems with constraints involving random parameters, which are required to be satisfied with a pre-specified probability threshold. There are two main difficulties with such chance-constrained problems. First, checking feasibility of a given candidate solution exactly is, in general, impossible since this requir...

Uncertainty issues associated with a multi-site, multi-product supply chain planning problem has been analyzed in this paper using the chance constraint programming approach. In literature, such problems have been addressed using the two stage stochastic programming approach. While this approach has merits in terms of decomposition, computational complexity even for small size planning problem ...

In this paper, “chance optimization” problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective of developing systematic numerical procedures to solve such problems, a sequence of convex relaxations based on the theory of measures and moments is provided...

Deterministic optimization approaches have been well developed and widely used in the process industry to accomplish off-line and on-line process optimization. The challenging task for the academic research currently is to address large-scale, complex optimization problems under various uncertainties. Therefore, investigations on the development of stochastic optimization approaches are necessi...

This work considers the resolution of the system of fuzzy integer inequalities. It is shown that a system of fuzzy integer inequalities with concave membership functions can be reduced to a regular convex integer programming problem. A modified solution algorithm of the -th power Lagrangian method is introduced to deal with the resulting convex integer programming problem as a sequence of linea...

The wide applicability of chance–constrained programming, together with advances in convex optimization and probability theory, has created a surge of interest in finding efficient methods for processing chance constraints in recent years. One of the successes is the development of so–called safe tractable approximations of chance–constrained programs, where a chance constraint is replaced by a...