- Markus Drouven, EQT
- Miles Lubin, Google
Talk: Polyhedral Approaches for Mixed-integer Convex Optimization (abstract)
- Can Zhang, Duke Fuqua School of Business
Talk: Blood Supply Chain Management: From Collection To Inventory Management
- David Abdul-Malak, Industrial Engineering, University of Pittsburgh
- David Huckleberry Gutman, Mathematical Sciences, Carnegie Mellon University
- Arash Haddadan, Tepper School of Business, Carnegie Mellon University
- Abhinav Maurya, Heinz College, Carnegie Mellon University
- Maria Ochoa, Chemical Engineering (postdoc), Carnegie Mellon University
- Mohammad Shahabsafa, Industrial and Systems Engineering, Lehigh University
- Lauren Steimle, Industrial and Operations Engineering, University of Michigan
- Vanitha Virudachalam, The Wharton School, University of Pennsylvania
David Huckleberry Gutman
In this talk we propose a novel proof of the $O(1/k)$ and $O(1/k^2)$ convergence rates of the proximal gradient and accelerated proximal gradient methods for composite convex minimization. The crux of the new proof is an upper bound constructed via the convex conjugate of the objective function.
We present a new algorithm for finding a feasible solution for a mixed integer linear program. The algorithm runs in polynomial time and is guaranteed to find a feasible integral solution provided the integrality gap is bounded. The algorithm computes convex decompositions and it provides a suite of integral solutions. The main application of our algorithm is to experimentally evaluate the integrality gap of IP formulations. We apply this technique to several network design problems such as 2-edge-connected subgraph problem (2EC).
Joint work with Robert Carr and Cynthia Phillips.
In this work, we address the scheduling problem under uncertainties in electricity price and product demand in an air separation plant. The operation of the plant is represented by an efficient discrete-time MILP model as a process state transition network in order to deal with short-term production scheduling. On the one hand, uncertainties in electricity are addressed with stochastic programming techniques to find a schedule that minimizes expected cost over a proposed set of scenarios. On the other hand, uncertainties in product demand are tackled as flexibility constraints in order to ensure flexible operation over the entire range of variation of this uncertain parameter.
The inmate assignment project, in close collaboration with the Pennsylvania Department of Corrections (PADoC), took five years from start to successful implementation. In this project, we developed the Inmate Assignment Decision Support System (IADSS), where the primary goal is simultaneous and system-wide optimal assignment of inmates to correctional institutions (CIs). We develop a novel hierarchical, multiobjective mixed-integer linear optimization (MILO) model, which accurately describes the inmate assignment problem (IAP). The IAP is the mathematical optimization formulation of the problem every correctional system faces, which is to assign inmates to CIs and schedule their programs, while considering all legal restrictions and best practice constraints. By using actual inmate data sets from the PADoC, we also demonstrate that the MILO model can be solved efficiently. IADSS enables the PADoC to significantly reduce the inmate population management costs and enhance public safety and security of the CIs. To the best of our knowledge, this is the first time that operations research methodologies have been incorporated into the routine business practice of a correctional system and used to optimize its operations. This successful project opens a rich and untouched area for the application of operations research.
Markov decision processes (MDPs) are commonly used to model sequential decision-making under uncertainty and derive optimal control policies. However, these policies can underperform if the true model parameters differ from the estimates used in the optimization process. To address this issue, the Multi-model MDP (MMDP) has been proposed as a way to find a policy that performs well with respect to multiple models of the MDP parameters. Policy evaluation for this problem is easy due to the decomposable nature of the MMDP; however, policy optimization for MMDPs is more challenging than for a standard MDP due to coupling constraints. In this talk, we present solution methods that take advantage of the decomposable nature of this problem to generate MDP policies that are robust to deviations in model parameters.
Joint work with Brian T. Denton.