Formulation of integer and combinatorial optimization problems. Optimality conditions and relaxation. Polyhedral theory and integer polyhedra. Computational complexity. The theory of valid inequality, strong formulations. Duality and relaxation of integer programming problems. General and special purpose algorithms including branch and bound, decomposition and cutting-plane algorithms.
Theory and practice of dynamic programming, sequential decision making over time; the optimal value function and Bellman's functional equation for finite and infinite horizon problems; Introduction of solution techniques: policy iteration, value iteration, and linear programming; General stochastic formulations, Markov decision processes; application of dynamic programming to network flow, resource allocation, inventory control, equipment replacement, scheduling and queueing control.
Introduction to scheduling: examples of scheduling problems, role of scheduling, terminology, concepts, classifications; solution methods: enumerative methods, heuristic and approximation algorithms; single machine completion time, lateness and tardiness models; single machine sequence dependent setup models; parallel machine models; flow-shop models; flexible flow-shop models; job-shop models; shifting bottleneck heuristic; open-shop models; models in computer systems; survey of other scheduling problems; advanced concepts.
Constructive heuristics; improving heuristics; metaheuristics: simulated annealing, genetic algorithms, tabu search, scatter search, path relinking, ant colony
Markovian queues: M/M/1, M/M/C, M/M/C/K systems and applications. Phase-type distributions and matrix-geometric methods: PH/PH/1 systems. Queueing networks: reversibility and productform solutions. General arrival or service time distributions: embedded Markov Chains, M/G/1 and G/M/c queues, G/G/1 queues and the Lindley recursion, approximations. Stochastic comparisons of queues: stochastic orders, sample path properties.
Basic concepts and definitions of system reliability. Series, parallel, k-out-of n systems. Structure functions, coherent systems, min-path and min-cut representations. System reliability assessment and computing reliability bounds. Parametric families of distributions, classes of life distributions and their properties. Shock and wear models. Maintenance, replacement and repairmodels. Current issues on stochastic modelling of hardware and software reliability.
Investments and cash flows, present value and internal rate of return; fixed income securities, yield, duration and immunization; portfolio optimization, mean-variance models, Capital Asset Pricing Model and Arbitrage Pricing Theory; forwards, futures, swaps and risk hedging; pricing derivative securities and options, binomial market models, continuous market models and Black-Scholes equation.
Review of basic stochastic concepts; binomial market models and pricing of derivative securities; Wiener process and Brownian motion; martingales; stochastic integrals and differential equations; Its calculus; pricing of derivative securities in continuous markets; Black-Scholes model; foreign exchange, bond and interest rate markets.
Dynamic inventory policies for single-stage inventory systems: concepts of optimality and optimal policies. Multi-Echelon Systems: uncapacitated models and optimal policies, capacitated models: different control mechanisms. Multiple locations and multiple items: inventory and capacity allocation. Decentralized control and the effects of competition on the supply chain: coordination and contracting issues.
Application and development of mathematical modeling tools for the analysis of strategic, tactical, and operational supply-chain problems. Mathematical programming formulations for integrated planning of capacity and demand in a supply chain. Planning and managing inventories in multi-level systems, centralized versus decentralized control of supply chain inventories. Models and algorithms for transportation and logistics systems design and analysis. Supply chain coordination issues and achieving coordination through contracts. The role of information technology and enterprise resource planning (ERP) and Advanced Planning and Optimization software.
Formulation of integer and combinatorial optimization problems Introduction to logistics systems; logistics network design, location models; warehouse design, tactical decisions, operational decisions; transportation management; planning and managing freight transportation; fleet management, vehicle routing problem.
Principles of logistics and supply chain operations in the humanitarian context and health care systems. Broad understanding of how Operations Research techniques can be used in humanitarian operations and response functions by case studies. Mathematical modeling and solution of decision making problems in disaster mitigation, response and recovery operations that involve planning and design functions. Logistic problems arising in the healthcare sector such as ambulance assignment and routing in medical emergency response, blood collection and inventory management. Location of public service facilities such as hospitals and fire stations for long-term development.
A series of lectures given by faculty or outside speakers. Participating students must also make presentations during the semester.
Independent research towards MS degree.
Fundamental laws of information systems; computer hardware and software basics; SaaS (software-as-a-service) and open-source systems; Internet security and safety; innovative business models in electronic commerce; applications of SEO/SEM (search engine optimization / marketing) for enhanced profitability in real-world businesses.
Provides hands-on teaching experience to graduate students in undergraduate courses. Reinforces students' understanding of basic concepts and allows them to communicate and apply their knowledge of the subject matter.
Review of electromagnetism; geometrical optics, analysis of optical systems; wave properties of light, Gaussian beams, beam optics; interaction of light with matter, spontaneous and stimulated emission, optical amplification, theory and applications of lasers, optical interactions in semiconductors, light emitting diodes and diode lasers; detectors, noise in detection systems; light propagation in anisotropic crystals, Pockels and Kerr effect, light modulators; nonlinear optics, second harmonic generation, phase matching, nonlinear optical materials.
Introduction to Microsystems, MEMS and its integration with optics; Microfabrication and process integration; MEMS Modeling and design; Actuator and sensor design; Mechanical structure design; Optical system design basics; Packaging; Optical MEMS application case studies; Scanning systems (Retinal Scanning Displays, Barcode scanners); Projection display systems (DMD and GLV); Infrared imaging cameras; Optical switching for telecommunications.
Survey of the properties and applications of photonic materials and devices; semiconductors; photon detectors, light emitting diodes, noise in light detection systems; light propagation in anisotropic media, Pockels and Kerr effects, light modulators, electromagnetic wave propagation in dielectric waveguides, waveguide dispersion; nonlinear optical materials, second harmonic generation, Raman converters.
The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.
Crystal structure, reciprocal lattice, determination of crystal structure by x-ray diffraction, energy levels of a periodic potential, Bloch theorem, band theory of solids, crystal defects, lattice vibrations and phonons; electrical conductivity, metals, dielectrics, and semiconductors; magnetic effects, paramagnets, diamagnets, ferromagnets, and superconductors; optical properties of materials, refractive index, dispersion, absorption and emission of light, nonlinear optical materials, high harmonic generation, Raman effect.
Classical thermodynamics: enthalpy, entropy, free energies, equilibria; introduction to statistical thermodynamics to describe the properties of materials; kinetic processes; diffusion of mass, heat, energy; fundamentals of rate processes in materials, kinetics of transformations.
Thermal and mechanical properties of metals, polymers, ceramics and composites in relation to their structure & morphology; change in microstructural mechanisms and macroscopic behaviour with temperature; crystallization, melting & glass transition, stress-strain behaviour; elastic deformation, yielding, plastic flow; viscoelasticity; strengthening mechanisms, fracture, fatigue, creep
Nomenclature, tacticity, molecular weight, physical state: amorphous/crystalline, properties & applications: elastomers, fibers, plastics; Synthesis of polymers: step growth polymerization, chain growth polymerization; Special materials: supramolecular structures, liquid crystalline materials.