Solving chance-constrained combinatorial problems to optimality

The aim of this paper is to provide new efficient methods for solving general chance-constrained integer linear programs to optimality. Valid linear inequalities are given for these problems. They are proved to characterize properly the set of solutions. They are based on a specific scenario, whose definition impacts strongly on the quality of the linear … Read more

Sample Average Approximation of Expected Value Constrained Stochastic Programs

We propose a sample average approximation (SAA) method for stochastic programming problems involving an expected value constraint. Such problems arise, for example, in portfolio selection with constraints on conditional value-at-risk (CVaR). Our contributions include an analysis of the convergence rate and a statistical validation scheme for the proposed SAA method. Computational results using a portfolio … Read more

New Formulations for Optimization Under Stochastic Dominance Constraints

Stochastic dominance constraints allow a decision-maker to manage risk in an optimization setting by requiring their decision to yield a random outcome which stochastically dominates a reference random outcome. We present new integer and linear programming formulations for optimization under first and second-order stochastic dominance constraints, respectively. These formulations are more compact than existing formulations, … Read more

Stochastic Approximation approach to Stochastic Programming

In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of this paper is to compare two computational approaches based on Monte … Read more

A Sample Approximation Approach for Optimization with Probabilistic Constraints

We study approximations of optimization problems with probabilistic constraints in which the original distribution of the underlying random vector is replaced with an empirical distribution obtained from a random sample. We show that such a sample approximation problem with risk level larger than the required risk level will yield a lower bound to the true … Read more

A General Heuristic Method for Joint Chance-Constrained Stochastic Programs with Discretely Distributed Parameters

We present a general metaheuristic for joint chance-constrained stochastic programs with discretely distributed parameters. We give a reformulation of the problem that allows us to define a finite solution space. We then formulate a novel neighborhood for the problem and give methods for efficiently searching this neighborhood for solutions that are likely to be improving. … Read more

Operations Risk Management by Planning Optimally the Qualified Workforce Capacity

Operational risks are defined as risks of human origin. Unlike financial risks that can be handled in a financial manner (e.g. insurances, savings, derivatives), the treatment of operational risks calls for a “managerial approach”. Consequently, we propose a new way of dealing with operational risk, which relies on the well known aggregate planning model. To … Read more

Tractable algorithms for chance-constrained combinatorial problems

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0-1 problems. Furthermore, its tractability is highlighted. Then, an optimization … Read more

Self-concordant Tree and Decomposition Based Interior Point Methods for Stochastic Convex Optimization Problem

We consider barrier problems associated with two and multistage stochastic convex optimization problems. We show that the barrier recourse functions at any stage form a self-concordant family with respect to the barrier parameter. We also show that the complexity value of the first stage problem increases additively with the number of stages and scenarios. We … Read more

Computations with Disjunctive Cuts for Two-Stage Stochastic Mixed Integer Programs

Two-stage stochastic mixed-integer programming (SMIP) problems with recourse are generally difficult to solve. This paper presents a first computational study of a disjunctive cutting plane method for stochastic mixed 0-1 programs that uses lift-and-project cuts based on the extensive form of the two-stage SMIP problem. An extension of the method based on where the data … Read more