Generalized Network Inequalities for Fixed-Charge Network Polyhedra

We propose valid inequalities for fixed-charge networks that contain the well-known network inequalities as special cases. We show the relationship between the generalized network inequalities and submodular inequalities. We develop efficient separation algorithms to identify violated generalized network inequalities. We implement a branch-and-cut algorithm to show the effectiveness of the proposed inequalities.

Probabilistic Inventory Control and Mixed-Integer Programming Under Uncertainty

We consider inventory control problems with stochastic demand in which a specific service level must be met. Unlike earlier models, we assume that the discrete demand distribution over the planning horizon is non-stationary. We formulate this problem as a chance-constrained MIP, or equivalently, a large-scale deterministic MIP. We study the structure of the formulations and develop methods to solve them effectively. Our goal is to extend our findings to solve general uncertain mixed-integer programs effectively. Joint work with Kai Huang.

State-Based Emergency Vehicle Location

We propose a model for maximizing the performance of emergency services based on the the number of idle vehicles available. We formulate this problem as a large scale mixed-integer program. We further propose additional constraints to ensure that the location plans only differ by a single location from one state to the next, thus easing the workload on the emergency crews. We study the structure of the various formulations and develop methods to solve them effectively. Joint work with Rashid Al Jalahema and Jeff Goldberg.

Reliable Network Design

Many critical network design problems must account for the probability of failures on their arcs and nodes. These problems, arising in applications such as communications, emergency management, power distribution and border security, require the design of networks that are reliable. We propose various formulations for reliable network design (including chance-constrained MIP, deterministic nonlinear MIP and exponential-size MIP) and develop methods to solve them effectively.