We describe a two-stage robust optimization approach for solving network flow and design problems with uncertain demand. In optimization, one defers subset of the decisions until after realization Availability such recourse action allows to come up less conservative solutions compared single-stage optimization. However, this advantage often comes at price: is, in general, significantly harder than For under demand uncertainty, we give characterization first-stage an exponential number...

We study several joint facility location and inventory management problems with stochastic retailer demand. In particular, we consider cases uncapacitated facilities, capacitated correlated demand, lead times, multicommodities. show how to formulate these as conic quadratic mixed-integer problems. Valid inequalities, including extended polymatroid cover cuts, are added strengthen the formulations improve computational results. Compared existing modeling solution methods, new integer...

Airline operations are subject to frequent disruptions typically due unexpected aircraft maintenance requirements and undesirable weather conditions. Recovery from a disruption often involves propagating delays in downstream flights increasing cruise stage speed when possible an effort contain the delays. However, there is critical trade-off between fuel consumption (and its adverse impact on air quality greenhouse gas emissions) speed. Here we consider caused by such propose flight...

We consider the constrained assortment optimization problem under mixed multinomial logit model. Even moderately sized instances of this are challenging to solve directly using standard mixed-integer linear formulations. This has motivated recent research exploring customized strategies and approximation techniques. In contrast, we develop a novel conic quadratic formulation. new formulation, together with McCormick inequalities exploiting capacity constraints, enables solution large...

The fundamental question encountered in acquiring capacity to meet nonstationary demand over a multiperiod horizon is how balance the trade-off between having insufficient some periods and excess others. In former situation, part of subcontracted while, latter, that has been paid for rendered idle. Capacity subcontracting decisions arise many economic activities ranging from production planning semiconductor fabs leasing communication networks, transportation contracts staffing call centers....

Given a finite ground set N and value vector $${a \in \mathbb{R}^N}$$ , we consider optimization problems involving maximization of submodular utility function the form $${h(S)= f \left(\sum_{i S} a_i \right ), S \subseteq N}$$ where is strictly concave, increasing, differentiable function. This appears frequently in combinatorial when modeling risk aversion decreasing marginal preferences, for instance, risk-averse capital budgeting under uncertainty, competitive facility location,...

We consider the Alternating Current Optimal Power Flow (ACOPF) problem, formulated as a nonconvex Quadratically-Constrained Quadratic Program (QCQP) with complex variables. ACOPF may be solved to global optimality semidefinite programming (SDP) relaxation in cases where its QCQP formulation attains zero duality gap. However, when there is positive gap, no optimal solution SDP feasible for ACOPF. One way find optimum partition problem using spatial branch-and-bound method. Tightening upper...

Lifting is a procedure for deriving valid inequalities mixed-integer sets from suitable restrictions of those sets. has been shown to be very effective in developing strong linear integer programming and it successfully used solve such problems with branch-and-cut algorithms. Here we generalize the theory lifting conic programming, i.e., programs constraints. We show how derive program its lower-dimensional restrictions. In order simplify computations, also discuss sequence-independent...

We show that superadditive lifting functions lead to sequence independent of inequalities for general mixed-integer programming. As an application, we note rounding (MIR) may be viewed as lifting. Consequently, obtain facet conditions MIR knapsacks.

We investigate the polyhedral structure of lot-sizing problem with inventory bounds. consider two models, one linear cost on inventory, other and fixed costs inventory. For both we identify facet-defining inequalities that make use bounds explicitly give exact separation algorithms. also describe a programming formulation when order satisfy Wagner-Whitin nonspeculative property. present computational experiments show effectiveness results in tightening relaxations costs.

Purpose: Many planning methods for high dose rate (HDR) brachytherapy treatment require an iterative approach. A set of computational parameters are hypothesized that will give a plan meets dosimetric criteria. is computed using these parameters, and if any criteria not met, the process iterated until suitable found. In this way, distribution controlled by abstract parameters. The purpose study to improve HDR developing new approach directly optimizes based on Method: We develop Inverse...