On the polyhedral structure of a multi-capacity mixing set
Mixed integer programming is a very powerful modeling and decision making tool. It finds applications in many areas of economic and social impact such as supply chain, energy and healthcare management. Unfortunately, solving mixed integer programming problems is challenging due to the inherent non-convexity of their feasible regions. Therefore there is an ever increasing need to improve our understanding of convex (polyhedral) relaxations of such problems. This understanding can then be used to produce better formulations and cutting-plane schemes that help solve these problems efficiently. In this talk, we study the polyhedral structure of a generalized mixing set that we refer to as the multi capacity mixing set. This set arises as part of the formulation of production planning and logistics problems either naturally or as part of a relaxation. We derive two families of facet-defining inequalities for the set under consideration by lifting mixing inequalities. We discuss the properties of the associated lifting function and show that lifting can be performed efficiently. Our results are analogous to earlier results of 1998 - Marchand and Wolsey
Bio: Ayşe Nur Arslan is a Ph.D. candidate at University of Florida's Industrial and Systems Engineering Department. Her Ph.D. advisors are Dr. Jean-Philippe P. Richard and Dr. Yongpei Guan. She received her bachelor's degree in Industrial Engineering from Bogazici University in 2010. Ayşe Nur's research efforts revolve around developing new theory and methodologies for the efficient solution of mixed integer programming problems both deterministic and stochastic. She is especially interested in polyhedral/cutting-plane approaches and their computational applications. Her Ph.D. thesis develops polyhedral results for production planning and logistics problems and investigates the use of these results in a computational framework.