optimization models for dynamic pricing and inventory control under uncertainty and competition

Problem Statement and Motivation

Key Achievements and Future GoalsTechnical Approach

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

Investigator: Elodie Adida, 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?

• 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.

• 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



Multi-Scale Simulations of Flames and Multiphase FlowSuresh 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

• “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.

(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.

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Heat-release, kJm-3s-1*10-3



Virtual Brain Surgery: Resident Training with ImmersiveTouch™ Haptic Augmented Virtual Reality System

Investigator: Pat Banerjee, MIE, CS and BioE DepartmentsPrime 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.

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UIC Mechatronics LabPI: Professor Sabri Cetinkunt, 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



Control Reconfiguration of Complex Discrete Event Dynamic Systems

Investigator: Houshang Darabi, 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.

• 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

• 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



Computational Intelligence for Diagnostics and PrognosticsInvestigators: David He and Pat Banerjee, MIE Department

Prime Grant Support: BF Goodrich (USA)

• 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.

• 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.

• 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 +

Prognostic Models

Optimal Data

Extraction

*Time domain *Frequency domain * Flight profiles

Sensor Signals

IntegratedComputational

Intelligence



Simulation of Multibody Railroad Vehicle/Track DyanmicsInvestigator: 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.

• 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.

• 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.

optimization models for dynamic pricing and inventory control under uncertainty and competition

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