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.
Convex analysis, optimality conditions, linear programming model formulation, simplex method, duality, dual simplex method, sensitivity analysis; assignment, transportation, and transshipment problems.
The basic theory of the Poisson process, renewal processes, Markov chains in discrete and continuous time, as well as Brownian motion and random walks are developed. Applications of these stochastic processes are emphasized by examples, which are drawn from inventory and queueing theory, reliability and replacement theory, finance, population dynamics and other biological models.
Topics on distribution fitting and generating random numbers and random variates will be covered as well as the statistical analysis of simulation output including some well-known analysis methods and variance reduction techniques. Recent developments in the area will also be discussed.
Review of descriptive statistics, importants populations statistics and their distributions. Point estimation, estimations methods and minimum-variance unbiased estimators. Testing hypothesis, Neyman-Pearson lemma and likelihood ratio tests. Estimation and testing in linear regression modes. Analysis of variance models. Nonparametric statistics methods. Bayesian testing and analysis.
Combinatorial optimization, structure of integer programs, pure integer and mixed integer programming problems, branch and bound methods, cutting plane and polyhedral approach, convexity, local and global optima, Newton-type, and conjugate gradient methods for unconstrained optimization, Karush-Kuhn-Tucker conditions for optimality, algorithms for constrained nonlinear programming problems, applications in combinatorial and nonlinear optimization.
Brief review of basic processes like Poisson, Markov and renewal processes; Markov renewal processes and theory, regenerative and semi-regenerative processes; random walk, Wiener process and Brownian motion; martingales; stochastic differential equations and integrals; applications in queueing, inventory, reliability and financial systems.
Network flow models and optimization problems. Algorithms and applications. Minimum spanning tree problem. Shortest path problems. Maximum flow problems, minimum cuts in undirected graphs and cut-trees. The minimum cost network flow problem. Matching problems. Generalized flows. Multicommodity flows and solution by Lagrangean relaxation, column generation and Dantzig-Wolfe decomposition. Network design problems including the Steiner tree problem and the multicommodity capacitated network design problem; their formulations, branch-and-cut approaches and approximation algorithms.
Tools, techniques, and skills needed to analyze decision-making problems characterized by uncertainty, risk, and conflicting objectives. Methods for structuring and modeling decision problems and applications to problems in a variety of managerial decision-making contexts. Structuring decision problems: Decision trees, model building, solution methods and sensitivity analysis; Bayes' rule, the value of information and using decision analysis software. Uncertainty and its measurement: Probability assessment. Utility Theory: Risk attitudes, single- and multiattribute utility theory, and risk management. Decision making with multiple objectives.
Analysis of selected models, algorithms, and applications from location theory. Study of deterministic and stochastic problems in continuous and discrete space. Capacitated and uncapacitated facility location. Covering problems. Center and median problems. The quadratic assignment problem and facility layout. Location and routing. Transportation of hazardous materials. Flow-interception. Voting and competitive location problems.
Topics will be announced when offered.
Methods for the solution of complex real world problems modeled as large-scale linear, nonlinear and stochastic programming, network optimization and discrete optimization problems. Solution methods include Decomposition Methods: Benders's, Dantzig-Wolfe, Lagrangian Methods; Meta-heuristics: Local search, simulated annealing, tabu search, genetic algorithms; Constraint Programming. Applications in transportation and logistics planning, pattern classification and image processing, data mining, design of structures, scheduling in large systems, supply-chain management, financial engineering, and telecommunications systems planning.
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.