Optimization Models for Dynamic Pricing and Inventory Control under Uncertainty and Competition

1. Optimization Models for Dynamic Pricing and Inventory Control under Uncertainty and Competition Investigator: ElodieAdida, Mechanical and Industrial Engineering • A small improvement in pricing and revenue management strategy may yield significant profits. • What are the optimal prices and production levels over time? How to allocate capacity among multiple products? • What is the impact of demand uncertainty? • What is the impact of competition? Can we predict the state of equilibrium? • Is there a realistic and yet computationally tractable way to model the dynamic problem? • Modeling the optimal decision-making problem as a nonlinear, constrained, dynamic program • Robust optimization technique incorporates the presence of uncertainty with limited probabilistic information • Dynamic aspect with feedback (closed-loop) or without feedback (open-loop) • Game theoretical framework and determination of Nash equilibria encompasses competitors’ interactions • Price of anarchy: loss of efficiency due to competition in the system • Heuristic algorithm to determine the optimal pricing and allocation of available production capacity among products • Under data uncertainty, equivalent robust formulation is of the same order of complexity; involves safety stock levels • In a duopoly with uncertain demand, a relaxation algorithm converges to a particular unique Nash equilibrium • A good trade-off between performance (closed-loop) and tractability (open-loop) is to let controls be linearly dependent with the uncertain data realizations • Design of incentives (such as a contract) to reduce the loss of efficiency when suppliers compete on prices.

2. Multi-Scale Simulations of Flames and Multiphase Flow Suresh K. Aggarwal, Mechanical and Industrial Engineering Sponsors: NASA, NSF, Argonne National Laboratory • Application of the advanced computational fluid dynamics (CFD) methods using detailed chemistry and transport models • Simulation of flame structure, extinction and fire suppression • Multi-scale modeling of combustion and two-phase phenomena • Extensive use of computer graphics and animation (See flame images above.) The image on the left shows a comparison of simulated and measured triple flames that are important in practical combustion systems, while the five images on the right depict a simulated flame propagating downward in a combustible mixture. • “A Numerical Investigation of Particle Deposition on a Square Cylinder Placed in a Channel Flow," Aerosol Sci. Technol. 34: 340, 2001. • “On Extension of Heat Line and Mass Line Concepts to Reacting Flows Through Use of Conserved Scalars," J. Heat Transfer 124: 791, 2002. • “A Molecular Dynamics Simulation of Droplet Evaporation," Int. J. Heat Mass Transfer 46: 3179, 2003. • “Gravity, Radiation and Coflow Effects on Partially Premixed Flames,” Physics of Fluids 16: 2963, 2004.

3. Virtual Brain Surgery: Resident Training with ImmersiveTouch™ Haptic Augmented Virtual Reality System Investigator: Pat Banerjee, MIE, CS and BioE Departments Prime Grant Support: NIST-ATP; NIBIB; NINDS • NOTE: PAT BANERJEE HAS ASKED DAN BAILEY TO WRITE A NEW QUAD CHART. IN THE MEANTIME, THE OLD ONE CAN BE USED. • PAT WANTS THE NEW CHART TO FOCUS ON VENTRICULOSTOMY • Text • Text • SubText • Text • Text • Text • SubText • Text • Text • Text • SubText

4. UIC Mechatronics Lab PI: Professor SabriCetinkunt, Mechanical and Indusrial Engineering Prime Grant Support: Caterpillar, NSF, Motorola • The world needs more affordable, reliable, energy efficient, environmentally friendly construction and agricultural equipment. Energy efficiency improvements can help overcome poverty in developing world. • Embedded computer control and information technology applications in construction and agricultural equipment: closed loop controls, GPS, autonomous vehicles. • Developed a new steer-by-wire EH system (for wheel loaders) • Developed a new closed center EH hydraulic implement control system • Developed semi-active joystick controls • Developed payload monitoring systems • Closed loop control for graders, site planning with GPS • Three US patents awarded (fourth filed) • 12+ former graduate students employed by CAT

5. Control Reconfiguration of Complex Discrete Event Dynamic Systems Investigator: HoushangDarabi, Mechanical and Industrial Engineering; Prime Grant Support: NIST, Motorola, IVRI • Today’s manufacturing and service information systems (IS) contain complex decision making processes. • These processes can be modeled as supervisory control problems with dynamic control specifications. • Many theoretical results and software tools are already available to analyze supervisory control problems. • Discrete manufacturing IS, hospital IS and supply chain IS are governed by the same control principals. • Control specifications of these system change over time and require reconfiguration of their control rules. • Modeling of systems by Petri Nets and Finite Automata • Modular and hierarchical decomposition of control • Formal verification and validation of system properties • Classification of reconfiguration needs and triggers • Cost/benefit modeling of reconfiguration response • Simulation modeling and analysis of systems based regular events and reconfiguration events • Supervisory control of discrete event systems • Systematic methods for modeling of manufacturing IS • Automatic procedures to reconfigure PLC programs subject to sensor failures • Systematic procedures for modeling hospital IS • Modeling and analysis tools assisting medical service control systems during mass casualty situations • Simulation models for hospital resource assignment • Adaptive mixed integer programming models for reconfiguring supply chain controllers • Standard supply chain agent models for distributed decision making and peer to peer communication

6. Computational Intelligence for Diagnostics and Prognostics Investigators: David He and Pat Banerjee, MIE Department Prime Grant Support: BF Goodrich (USA) Sensor Signals *Time domain *Frequency domain * Flight profiles • Develop innovative computational intelligence for diagnostic and prognostic applications of complex systems such as helicopters. • The computational intelligence developed can be used to accurately diagnose the failure conditions of the complex systems and predict the remaining useful life or operation of the systems. • The developed diagnostic and prognostic computational intelligence will be tested and validated with the data collected by Goodrich’s IMD- HUMS units that are currently used in US Army’s helicopters. Optimal DataExtraction Integrated Computational Intelligence Diagnostic + Prognostic Models • Innovative probabilistic approaches will be integrated with wavelet analysis to develop integrated diagnostic and prognostic computational intelligence. • Different failure modes of left generator shafts in UH-60 will be identified and failure conditions will be used to predict the remaining useful life of the system. • Diagnostic and prognostic algorithms are currently being developed and tested for different helicopters. • The developed algorithms will be eventually integrated into the Goodrich’s IMD-HUMs for different military and commercial applications.

7. Simulation of Multibody Railroad Vehicle/Track Dyanmics Investigator: Ahmed A. Shabana, Department of Mechanical Engineering, College of Engineering Prime Grant Support: Federal Railroad Administration (USA) • Develop new methodologies and computer algorithms for the nonlinear dynamic analysis of detailed multi-body railroad vehicle models. • The computer algorithms developed can be used to accurately predict the wheel/rail interaction, derailment, stability and dynamic and vibration characteristics of high speed railroad vehicle models. • Develop accurate small and large deformation capabilities in order to be able to study car body flexibility and pantograph/ catenary systems. • Methods of nonlinear mechanics are used to formulate the equations of motion of general multi-body systems; examples of which are complex railroad vehicles. • Small and large deformation finite element formulations are used to develop the equations of motion of the flexible bodies. • Numerical methods are used to solve the resulting system of differential and algebraic equations. • Computer graphics and animation are used for the visualization purpose. • Fully nonlinear computational algorithms were developed and their use in the analysis of complex railroad vehicle systems was demonstrated. • The results obtained using the new nonlinear algorithms were validated by comparison with measured data as well as the results obtained using other codes. • Advanced large deformation problems such as pantograph/catenary systems have been successfully and accurately solved for the first time. • The tools developed at UIC are currently being used by federal laboratories and railroad industry.