Featured Speakers:

  • 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

Invited Speakers:

  • 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


Miles Lubin

Title: Polyhedral Approaches for Mixed-integer Convex Optimization

Abstract: Mixed-integer convex optimization problems (MICPs) are problems that become convex when all integrality constraints are relaxed. I will present recent advances in solving these problems to global optimality by constructing polyhedral relaxations in a higher-dimensional space. This work develops significant new connections between MICP and modeling with symmetric and nonsymmetric convex cones, a discovery that influenced the development of MOSEK version 9 with their support for exponential and power cones. I will present our own implementation of an iterative outer approximation algorithm and a branch-and-cut variant in the open-source MICP solver Pajarito.

This is joint work with Russell Bent, Chris Coey, Juan Pablo Vielma and Emre Yamangil.

David Abdul-Malak
Title: Maintaining Systems with Heterogeneous Spare Parts
A common assumption in maintenance models is that spare parts come from a population with negligible variability in component reliability. In this talk, we will present a periodic maintenance model for systems whose replacement parts come from a lot with multiple system qualities each of which are visually indistinguishable from one another. At inspection points, a failed system can be reactively repaired or replaced, and a working system can be preventively repaired, replaced, or allowed to continue operating. Crucially, repairs place the same system back into service allowing the system operator to update their belief about the active system’s quality and utilize this information in their decision making. The problem is modeled as a mixed observability Markov decision process (MOMDP) and structural results, as well as numerical illustrations, are discussed.

David Huckleberry Gutman

Title: Convergence Rates of Proximal Gradient Methods via the Convex Conjugate

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.

Arash Haddadan

Title: Finding Feasible Solutions To Integer Programs With Bounded Integrality Gap In Polynomial Time

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.

Maria Ochoa

Title: Optimal Production Scheduling of Industrial Gases under Uncertainty with Flexibility Constraints

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.

Mohammad Shahabsafa

Title: The Inmate Assignment and Scheduling Problem and its Application in the Pennsylvania Department of Corrections

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.

Lauren Steimle

Title: Leveraging problem structure to solve robust Markov decision processes

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.