----- Research Directions

Modeling and Mitigating Supply Chain Vulnerabilities

Funding Source:  National Science Foundation

PI:  Lawrence V. Snyder

This research project develops and solves models for designing and operating supply chains that are resilient to disruptions.  One set of models prescribes optimal strategies for coping with disruptions when the firm has advanced warning that a disruption may occur or that the probability and duration of a disruption has changed.  Another set of models examine alternate strategies available to firms facing disruptions, including dual sourcing, emergency sourcing, demand management, and capacity flexibility.  These models are formulated and solved using classical inventory theory and Markov decision processes.  In addition, this research studies the cascading effect of disruptions in a multi-echelon supply chain.  Using a combination of simulation and optimization techniques, the research identifies the vulnerabilities of such a system and develops strategies for placing safety stock inventory within the system to buffer against disruptions.  Many of the models developed will be integrated into a freely distributed software package that simulates a multi-echelon inventory system and may be used in both research and classroom settings.

Space-Time Inhomogeneity and Performance of Large Scale Ad hoc Networks

Funding Source:  National Science Foundation

PI:  Eugene Perevalov

The objective of this research is the study of the problem of efficiency, quality of service and robustness in space- and time-inhomogeneous large scale ad hoc wireless networks.  While some progress has been made in understanding the main factors affecting the performance of ad hoc networks, theoretical exploration of the fundamental performance characteristics of realistic networks that possess essential space- and time-inhomogeneity has been largely absent.  The simplest examples of space- and time-inhomogeneous systems are the networks with highly non-uniform node density and networks with changes in node membership both of which have practical importance.  This research attempts to close this gap and develop a theoretical framework for the analysis of fundamental limitations and performance of such complex large scale ad hoc networks.

Collaborative Research:  Exploiting Cyberinfrastructure to Solve Real-time Integer Programs

Funding Source:  National Science Foundation

PI:  Jeff Linderoth

Co-PIs:  Ted Ralphs, Lehigh University, S. Ahmed, G. Nemhauser,

M. Savelsbergh, Georgia Institute of Technology, A. Miller, M. Ferris, University of Wisconsin-Madison

In recent decades, stunning advances in theory, algorithms, and implementation have turned Integer Programming (IP) into a unique computational science – one that attempts routinely to solve problems that are fundamentally intractable.  IP’s modeling robustness has led to its application in industrial areas, such as supply-chain planning and telecommunication network design, as well as in basic scientific arenas such as statistics, molecular biology, and physics.  Due to its success in the area of planning and design, and the ever-increasing availability of real-time data, demand for IP technology that solves real-time operational problems with stringent runtime requirements is increasing rapidly.  Such technology has huge potential for addressing difficult operational problems.  Its tactical use may dramatically improve airlines’ ability to recover from disruptions, significantly enhance the quality of radiation therapy for cancer patients, or provide huge economic benefits by increasing the agility of supply chains.  A key characteristic of IPs arising in real-time environments is that consecutive instances typically differ only slightly, which indicates a need for novel IP technology that supports incremental problem solving.  Breakthroughs in high performance and distributed computing technology have made it possible to harness enormous computational power for the solution of specific problems.  Because of the stringent runtime requirements, it is natural to consider designing real-time IP systems that exploit modern cyberinfrastructure.  This cross-cutting research effort requires specialists in cyberinfrastructure (high performance and grid computing systems), operations research (integer programming methodology), and enterprise applications.  The project team has experts that span these disciplines. 

Optimization Under Nonconvexity and Uncertainty:  Algorithms and Software

Funding Source:  Department of Energy – Office of Science

PI:  Jeff Linderoth             

This project will advance the state-of-the-art in solving large-scale numerical optimization problems.  The project’s focus is on problem classes that have proven to be among the most challenging for practitioners:  those involving uncertainty and those involving nonconvexity.  Moreover, the algorithmic advances will be converted into practical software packages and engineered to run on modern, powerful computing platforms.

We focus on the following specific optimization problem classes:  Nonconvex Optimization:  mixed integer nonlinear programming (MINLP) and nonconvex quadratically constrained quadratic programs (NQP).  Stochastic Optimization:  two stage linear (2SLP) and integer (2SIP) recourse problems, variance reduction techniques for sample-path-based optimization (VRSP).

We attack these problems by developing new 1) Algorithms:  dynamic decomposition algorithms for 2SLP, trust-region algorithms and branch-and-price for 2SIP, outerapproximation and branch-and-cut for MINLP, and branch-and-bound for NQP, 2) Relaxations:  cutting planes for MINLP, nonlinear, second-order cone, relaxations for MINLP and NQP, and 3) Approximations:  quasi-Monte Carlo and randomized Quasi-Monte Carlo approximations for VRSP.

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----- Research through the Center for Value Chain 

       Research (CVCR)

          (Directors:  Lawrence V. Snyder, Ph.D., Mike D. Santoro, Ph.D.)

Strategies for Coping with Supply Chain Disruptions
Funding Source:   IBM Integrated Supply Chain
Ph.D. student:  Ying Rong

Faculty Supervisor:  Lawrence V. Snyder, Ph.D.

In this research, we develop an analytical model for a multi-location firm that faces a disruption risk that changes over time and that has information about the current risk level.   In particular, we develop a model for a multi-location inventory system in which the firm periodically determines its “threat level,” i.e., its estimate of the supplier’s probability of failure, which may be different at different locations. The firm can then react by increasing or decreasing inventory levels or by repositioning inventory among stocking locations.  Our model will serve both as a decision-support tool and as a vehicle for developing insights about the nature of supply uncertainty and strategies for coping with them.

Managing Capacity and Inventory in the High-Tech Manufacturing Industry
Funding Source:  Agere Systems
Ph.D. students:  Mehmet Atan, Berrin Aytac, Ying Rong, Amanda Schmitt

Faculty Supervisor:  Lawrence V. Snyder, Ph.D.

The objective of this project is to develop a model and efficient solution techniques for problems that the semiconductor manufacturing industry encounters in managing production, capacity and inventory. The high-tech industry is characterized by a high degree of demand uncertainty, short product/technology lifecycles, expensive investment requirements, multi-stage production processes, and yield uncertainty. Therefore, strategic decisions such as the placement of inventory buffers and their size, how much internal capacity to have and how to change it over time, and the setting of production rates and outsourcing quantities at each stage have quite an impact on the success of companies in achieving their business goals.  In our project, we model this system mathematically and construct algorithms with strong theoretical foundations to provide the answers to the critical questions mentioned above. We also implement the solution algorithm in a user-friendly software package for the use of planning personnel.  

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