Endüstri Mühendisliği Yüksek Lisans Programı (Tezli)

Mathematical algorithms: random numbers, polynomials, matrices, integration. Sorting and searching. String processing. Geometric algorithms. Graph algorithms: connectivity weighted and directed graphs, network flow. Dynamic programming. Algorithms will be studied using object-oriented approach as much as possible.

A survey of mathematical and numerical methods used in IE and OR related studies presented in a unified structure based upon the theory of computation with special emphasis given to the development of computer codes and design of database.

The objective of this course is to explore the effects of environmental conditions on the human performance. The topics to be covered are effects of control-display design, environmental conditions (illumination, climate, noise and motion), shift-work, human error, accidents and safety.  Moreover, the students will be asked to conduct research projects either in the human factors laboratory or in a real field.  The Statistical Package for Social Sciences (SPSS) will be used in the project work.

This course is designed to introduce the student with the principles of safety and health hazards in industrial environment. It provides students with fundamentals of measurement, evaluation, regulation, and control of hazardous conditions, toxic substances, physical agents, and dangerous processes in the industrial environment. Skills development in record keeping, risk assessment and accident cause analysis will also be emphasized. This course will prepare the student for workplace safety and management.

Convex analysis; optimality conditions; generalized linear programming; revised simplex, matrix representation; integer programming; computer applications. Extensions of linear programming: quadratic programming; dynamic programming; geometric programming; methods for unconstrained and constrained non-linear optimization; multi-objective optimization methods.

Geometry of LP and Simplex Method. Duality and its implications. Sensitivity. Simplex forms: Revised Simplex, dual Simplex etc. LU factorization. Transportation and transshipment problems, assignment problem. Decomposition Methods. Networks. Problems with upper bounds. Numerical stability and computational efficiency. Karmarkar's method.

Axiomatic approach to probability; conditional probability; Random variable. Commonly used discrete and continuous distributions. Expectation of a random variable; jointly distributed random variables; Marginal and conditional distributions; independent random variables. Multinomial and multivariate normal distributions. Functions of random variables, moments, conditional expectation, m.g.f. and p.g.f., Markov inequality, Law of large numbers, Central Limit Theorem. Discrete-time Markov chains, Kolmogorov-Chapman equations, classification of states, steady-state probabilities. Applications from different areas.

Analysis of birth and death processes. Development of elements of queuing theory. Single and multiple server queues for Markovian and non-Markovian arrival and service time distributions (M/M/1, M/M/c, G/M/c, M/G/1, PH/PH/1). Bulk arrival and service systems. Networks of Markovian queues. Lindley's equation for the G/G/1 queue. Applications of queuing theory in manufacturing and service systems.

Network representation and terminology. Network flow problems such as shortest path, minimal spanning tree and maximal flow problems. Graph Theory.

The course covers the basic solution methods: dynamic programming, implicit enumeration, branch and bound, cutting plane and polyhedral approach. It also gives an introduction to heuristic methods as the use of Lagrange multipliers and local search. Traveling Salesperson Problem (TSP) and optimization in graphs are also discussed. The course aims to provide tools for students dealing with integer programming models for developing their own algorithms for their special problems.

In practice Multi-Criteria Decision Making (MCDM) methods are very popular in addressing complex problems involving multiple and typically conflicting criteria as well as several stakeholders or decision makers with different preferences with respect to the evaluation criteria. This course aims at training students in the field of MCDM with emphasis on rating, ranking and classification problems and methods with applications in business. Quantitative decision analysis. Multi-criteria benefit and utility theories. Decision making under uncertainty. Decision tree. Structuring of objectives and value hierarchies, and determination of value functions. Multi-objective decision making with mutually exclusive alternatives. Multi-objective ranking and classification. Multi-objective mathematical programming. Interactive methods and applications.

Bayesian decision models; decision trees; value of information; utility theory, use of judgmental probability, study of strategies; economics of sampling; risk sharing and decisions; implementation of decision models.

The meaning of investment process in general and for creating systems to produce products and services in particular. Classification of investment decision problems with respect to context and the precision of informational support, i.e. certainty, risk and uncertainty. A general mathematical structure for modeling for investment decisions. Deterministic, stochastic, combinatorial, sequential and dynamic investment decision models, and optimization techniques used for their solutions. A mathematical basis for deriving suitable value measures for evaluating investment alternatives and derivation of such measures. Types of risk taking as the fundamental dimension of a class of investment decision making situations.

This course is designed to enable students to understand and conceptualize basics of modern financial markets in the form of mathematical models. Several models of risk free assets and dynamics of risky assets will be discussed. Optimal portfolio management in risky environments will be analyzed. Call and put options of securities in discrete and continuous time settings will be explained. This part includes the famous work of Black-Scholes.

Analysis of some specific problem areas within the context of planning and scheduling of production activities. Definition, formulation and available solution procedures for aggregate planning, lot sizing, material requirements planning, cutting stock, line balancing, single processor scheduling, multi processor scheduling problems are studied.

Study of inventory systems. Deterministic and stochastic models. Fixed versus variable reorder intervals. Dynamic and multistage models. Selection of optimal inventory policies for single and multi-item dynamic inventory models, with convex and concave cost functions, known and uncertain requirements. Myopic policies. Multi-echelon models. Heuristic algorithms.

Terminology, characteristics and classification of sequencing and scheduling problems. An overview of computational complexity theory. Single Machine Scheduling. Parallel Machine Scheduling. Shop Scheduling: open shop, flow shop, job shop, and mixed shop. Batching.  Scheduling under Resource Constraints. Due-Date Scheduling. Scheduling in Flexible Manufacturing Systems.

Introduction to CIM (Computer Integrated Manufacturing) systems. Computer process interfacing. Computer control. Industrial robots. Flexible manufacturing systems. CIM systems. CIM systems selection criteria.

Supply chain management; New product development; Management and control of purchasing and logistics management systems. Strategic orientation toward the design and development of the supply chain for purchasing, materials, and logistics systems. Total Quality Management to assess and assure customer satisfaction. Global strategies. Expert systems for continuous improvement of the supply chain.

Single or multiple facilities location in the plane with minisum or minimax criteria. Discrete or continuous layout optimization. Single facility network location. Applications in public service, production, distribution, warehousing, emergency service, flexible manufacturing.

The design and performance issues in production, transfer lines, production/inventory systems, network of production/inventory systems, and flexible manufacturing systems. Phase type processing times, failures and service completion processes. Buffering and blocking issues. Decomposition methods. Control policies in pure inventory and production/inventory systems.

The course covers a discussion of the major aspects of advanced manufacturing and process technologies, selection and implementation of new technologies, and the management of technological and organizational changes.  

The design and analysis of simulation models. The use of simulation for estimation, comparison of policies, and optimization. Variance estimation techniques including the regenerative methods, time series methods, and batch means. Variance reduction. Statistical analysis of output of simulations, applications to modeling stochastic systems in Industrial Engineering and Operations Research.

The simple comparative experiments, experiments with a single factor, fixed effect and random effect models, model adequacy checking, choice of sample size, randomized blocks and latin squares design, incomplete block design, factorial designs, rules for sums of squares and expected mean squares, fractional factorial designs and regression analysis. Moreover, the statistical package for social sciences (SPSS) will be introduced.

Sampling distributions; Point estimation; Measures of goodness estimators; Methods of estimation; Sample size determination; Confidence intervals; Sufficient Statistics; Rao-Blackwell theorem; Hypothesis testing; Errors of type I & II; power of a test; p-values; Neyman-Pearson Theory; Likelihood ratio test; Some commonly used tests for means, variances and for ratio of variance etc.; Method of least squares; Curve fitting; Regression analysis; Some commonly used non-parametric tests for randomness, independence etc.; Goodness-of-fit tests; Sequential tests of hypothesis; Use of order statistics to find statistical intervals etc. Use of computer packages.

This course is designed to introduce a conceptual and practical notion of advanced quality control in engineering. It also provides students with methods and philosophy of statistical process control. The course contents include introduction to advanced quality control and improvement concepts in production processes, control charts for variable and attributes, cumulative sum control charts, economic design of control charts, fractional factorial experiments for process design, process optimization with designed experiments, advanced acceptance sampling techniques and lot-by-lot acceptance sampling for attributes. 

Planning and forecasting; Measures of forecast errors; Correlation, covariances, autocorrelations and autocorrelation function and their use pattern recognition; Smoothing methods; Decomposition methods and seasonal indices; Methods for trend and seasonal patterns including differences, double smoothing, Holt & Winter methods; Fourier series forecast analysis; Box-Jenkins ARIMA methods and their applications; ARIMA intervention analysis and transfer functions; Econometric methods; Multiple regression; Cyclic methods; Technological forecasting; Use of neural networks, expert systems and genetic algorithm in forecasting. Mini-case studies and  software packages.

Reliability and maintainability. Basic reliability  models. Maintainability. Availability. Reliability testing. Implementation and Case studies.

Recent advances in selected topics in industrial engineering will be covered. The topics and the contents of the course will depend on the course instructor and will be announced in the beginning of each semester.

This course is designed to orient the students for research by emphasizing reading, comprehension, discussion and performing exercises on IE/OR problem areas. For this purpose, each student is required to choose an IE/OR topic that is suitable to his/her academic background and interests, study this topic under the guidance of faculty members, make a literature survey, and point out the relevant further research areas. Throughout this course each student is also required to read and study some technical papers and give a series of seminars.