In this talk, we present two research results: 1) a new framework that integrates lower-bound and upper-bound methods into the Nested Partitions (NP) method. We have applied this method to a very difficult lot sizing problem-- the Multi-Item Capacitated Lot-Sizing Problems with Set-Up Times. The problem is to schedule N different items with given machine capacities over a finite horizon of T periods.  Computational results based on benchmark test problems show that our method is computationally tractable and outperforms all other state-of-the-art approaches found in the literature.2) our ongoing work on the development of Stochastic Lower Bound with Extreme Value theory. We propose statistical promising indexes for Nested Partitions based on the implementation of the extreme value theory. We further develop an approach to estimate the correctness of NP moves, which can be very useful in determining a good algorithm setting. An additional benefit of using the statistical promising index in NP is that statistical bounds can be obtained with little computational burden. These bounds are problem-independent and can be handy to use when traditional bounding techniques are ineffective. Initial results are also presented to demonstrate the effectiveness of the proposed method.

Biography of Prof. Leyuan Shi

Professor of Department of Industrial and Systems Engineering, University of Wisconsin-Madison.

BS 1982, mathematics, Nanjing Normal University, Nanjing, China

MS 1985, applied mathematics, Tsinghua University, Beijing, China

MS 1990, applied mathematics, Harvard University

PhD 1992, applied mathematics, Harvard University

Professor Shi's research has been in developing theory and methodology for design and optimization of complex systems such as supply chain networks, manufacturing systems and communication networks. Her interest in this area has spanned three levels: semantic modeling and design of systems, sensitivity analysis via discrete-event simulation, and control and optimization. Research interests: simulation modeling, large-scale optimization, supply chain optimization, production planning and scheduling computational efficiency, and opens up a new door to re-examine old methods and create new ones.