Research
Interests
- Mixed-Integer Programming (MIP)
- Large-Scale Optimization
- Optimization under Uncertainty
- Applications of MIP in:
- Communications network design
- Supply chain management and logistics
- Emergency management
- Power distribution
Funding
- National Science Foundation Award # 0917952, 2008-2011.
Current Projects
- 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.
- 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.
- Convex Hull of General Mixed Integer Programs
We give a finite disjunctive procedure to obtain the convex hull of general mixed integer programs. We propose an algorithm to construct a linear program that has the same optimal solution as the associated mixed integer program. We also give extensions to convex mixed integer programs. Joint work with Suvrajeet Sen.
Last updated on 17 May 2009
