TITLE: Optimization under Partitioned Information: Supply-Chain Applications
SPEAKER: Dr. V. Jorge Leon, Allen-Bradley Professor
Texas A&M University
DATE / TIME: Tuesday, December 11, 2007 / 2:30 – 3:45 p.m.
LOCATION: Room 451 Mohler Lab, 200 W. Packer Avenue
ABSTRACT: A linear optimization problem can be expressed as:
Minimize cx
subject to Bx ≥ b.
Where, the n-dimensional vectors x = (x1, …, xn) and c are the variables and objective function coefficients, respectively. Further, the constraints are defined in terms of an m-dimensional vector b is, and an m × n matrix B. An instance of the linear program is specified by the data (c, B, b). If the variables and data in (x, c, B, b) are partitioned a priori into p information subsets, Pi = (xi, ci, Bi, bi), i = 1,…, p, such that the information in different subsets cannot be directly combined to solve the problem, then the resulting problem is termed optimization under partitioned information (PI).
The study of PI is important because it manifests in a variety of real life scenarios. The ubiquitous information networks and their multiple applications for remote collaborations and interactions among multiple enterprises exacerbate the importance of PI problems. For instance, supply-chain inventory management requires that the overall inventory costs are minimized. Companies in the supply chain are usually heterogeneous, possibly competitors, and most likely in different countries. Under these circumstances, it may be unrealistic to require that all participants in the supply chain openly provide sensitive cost and capacity information. More realistically, the companies would like to operate efficiently as a supply chain but without disclosing private information. Similar examples are observed in the contexts of scheduling, resource allocation, design, and many other scenarios involving collaborating entities. This line of research has potential for implementations in virtual enterprises, web-based applications, and other distributed environments.
This talk will apply PI in the context of supply-chain inventory management. Specifically, we will describe a method developed to solve the single-product, dynamic demand, multi-echelon lot-sizing problem, where the objective functions and cost parameters are private information to the corresponding facility, and the replenishment policies are shared only between adjacent facilities. Experimental results suggest that the proposed methodology performs similar to competing methods that have unrestricted access to information.
BIOGRAPHY: Dr. Leon is the Allen-Bradley Professor at Texas A&M University (Texas-USA) where he holds a joint appointment in the departments of Industrial and Systems Engineering, and Engineering Technology and Industrial Distribution. His interests are in the areas of operations modeling and applied optimization. Dr. Leon’s research work has been sponsored by the National Science Foundation, the U.S. Army, the National Aeronautical and Space Agency (NASA), and high-tech industry, among others. Dr. Leon has received several recognitions at Texas A&M University including the Halliburton Professorship Award, the 3M Fellowship, the Ford Faculty Fellowship, and the Center for Teaching Excellence Award. Dr. Leon is the Program Director of the Manufacturing and Mechanical Engineering Technology program at TAMU (2000-present), and has served as the Editor of the Journal of Manufacturing Systems (2004-2007). Dr. Leon is a member of ASEE, IEE, INFORMS, and SME.
