In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant … Read more
We study a class of chance-constrained two-stage stochastic optimization problems where second-stage feasible recourse decisions incur additional cost. In addition, we propose a new model, where “recovery” decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second-stage problem. We develop decomposition algorithms with specialized optimality and feasibility cuts to solve … Read more
With stochastic integer programming as the motivating application, we investigate techniques to use integrality constraints to obtain improved cuts within a Benders decomposition algorithm. We compare the effect of using cuts in two ways: (i) cut-and-project, where integrality constraints are used to derive cuts in the extended variable space, and Benders cuts are then used … Read more
We study the problem of integrated staffing and scheduling under demand uncertainty. The problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules, well ahead in time. The wait-and-see decision is to adjust these schedules at a time epoch closer to the … Read more
This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely … Read more
Directional sensors are gaining importance due to applications, in- cluding surveillance, detection, and tracking. Such sensors have a limited fi eld-of-view and a discrete set of directions they can be pointed to. The Directional Sensor Control problem (DSCP) consists in assigning a direction of view to each sensor. The location of the targets is known with … Read more
We study a class of two-stage stochastic integer programs with general integer variables in both stages and finitely many realizations of the uncertain parameters. Based on Benders’ method, we propose a decomposition algorithm that utilizes Gomory cuts in both stages. The Gomory cuts for the second-stage scenario subproblems are parameterized by the first-stage decision variables, … Read more
We consider convex nonsmooth optimization problems whose objective function is known through a (fine) oracle together with some additional (cheap but poor) information – formalized as a second coarse oracle with uncontrolled inexactness. It is the case when the objective function is itself the output of an optimization solver, using a branch-and-bound procedure, or decomposing … Read more
Stochastic programming models are large-scale optimization problems that are used to facilitate decision-making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integral whose integrand … Read more
We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions, and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when applied to … Read more