Operations Research with Engineering

Program Director

Alexandra Newman, Professor, Mechanical Engineering

Program Requirements

Master of Science in Operations Research with Engineering (non-thesis)

Core Courses18.0
ORWE courses not taken as core courses12.0
Total30.0

All master's students are required to take a set of core courses (18 credits) that provides basic tools for the more advanced and specialized courses in the program as specified below. 

MEGN502ADVANCED ENGINEERING ANALYSIS3.0
or ORWE598 ALGORITHMS FOR OPERATIONS RESEARCH
or CEEN505 NUMERICAL METHODS FOR ENGINEERS
EBGN526STOCHASTIC MODELS IN MANAGEMENT SCIENCE3.0
or MATH538 STOCHASTIC MODELS
EBGN528INDUSTRIAL SYSTEMS SIMULATION3.0
MATH530INTRODUCTION TO STATISTICAL METHODS3.0
ORWE586LINEAR OPTIMIZATION3.0
or ORWE585 NETWORK MODELS
ORWE587NONLINEAR OPTIMIZATION3.0
or ORWE588 INTEGER OPTIMIZATION

The remaining 12 credits of coursework can be completed with any ORWE-labeled course not taken as core.  Or specialty tracks can be added in areas, for example, including:  1) operations research methodology, 2) systems engineering, 3) computer science, 4) finance and economics, and 5) an existing engineering discipline that is reflected in a department name such as electrical, civil, environmental, or mining engineering. 

Students who do not wish to specialize in a track mentioned in the table below and do not wish to complete 12 additional credits of ORWE-labeled coursework can mix and match from the ORWE coursework and coursework mentioned in the tables below in consultation with and approval from their academic advisers. 

Examples of specialty tracks from various departments across campus are given below:

Energy Systems within Mechanical Engineering Track (12 credits from the course list below)

MEGN567PRINCIPLES OF BUILDING SCIENCE3.0
MEGN583/AMFG501ADDITIVE MANUFACTURING3.0
MEGN570ELECTROCHEMICAL SYSTEMS ENGINEERING3.0
MEGN560DESIGN AND SIMULATION OF THERMAL SYSTEMS3.0
MEGN561ADVANCED ENGINEERING THERMODYNAMICS3.0

Additive Manufacturing Track (12 credits from the course list below)*

*Subject to approval by graduate council

AMFG511DATA DRIVEN ADVANCED MANUFACTURING3.0
AMFG521DESIGN FOR ADDITIVE MANUFACTURING3.0
AMFG531MATERIALS FOR ADDITIVE MANUFACTURING3.0
MEGN583/AMFG501ADDITIVE MANUFACTURING3.0

Applied Mathematics and Statistics Track (12 credits from the course list below)

MATH500LINEAR VECTOR SPACES3.0
MATH532SPATIAL STATISTICS3.0
MATH536ADVANCED STATISTICAL MODELING3.0
MATH537/538MULTIVARIATE ANALYSIS3.0
MATH551COMPUTATIONAL LINEAR ALGEBRA3.0
EENG511CONVEX OPTIMIZATION AND ITS ENGINEERING APPLICATIONS3.0

Economics Track (12 credits from the course list below)

EBGN509MATHEMATICAL ECONOMICS3.0
EBGN510NATURAL RESOURCE ECONOMICS3.0
EBGN530ECONOMICS OF INTERNATIONAL ENERGY MARKETS3.0
EBGN535ECONOMICS OF METAL INDUSTRIES AND MARKETS3.0
EBGN590ECONOMETRICS I3.0
EBGN645COMPUTATIONAL ECONOMICS3.0
CSCI555GAME THEORY AND NETWORKS3.0

Business Track (12 credits from the course list below)

ORWE559SUPPLY CHAIN MANAGEMENT3.0
EBGN560DECISION ANALYTICS3.0
EBGN571MARKETING ANALYTICS3.0
EBGN562STRATEGIC DECISION MAKING3.0

Computer Science Track (12 credits from the course list below)

CSCI542SIMULATION3.0
CSCI562APPLIED ALGORITHMS AND DATA STRUCTURES3.0
CSCI571ARTIFICIAL INTELLIGENCE3.0
CSCI575ADVANCED MACHINE LEARNING3.0
CSCI555GAME THEORY AND NETWORKS3.0

Civil Engineering - Geotechnics Track (12 credits from the course list below)

CEEN506FINITE ELEMENT METHODS FOR ENGINEERS3.0
CEEN510ADVANCED SOIL MECHANICS3.0
CEEN519RISK ASSESSMENT IN GEOTECHNICAL ENGINEERING3.0
CEEN511UNSATURATED SOIL MECHANICS3.0
CEEN512SOIL BEHAVIOR3.0
CEEN515HILLSLOPE HYDROLOGY AND STABILITY3.0

Civil Engineering-Structures Track (12 credits from the course list below)

CEEN506FINITE ELEMENT METHODS FOR ENGINEERS3.0
CEEN530ADVANCED STRUCTURAL ANALYSIS3.0
CEEN531STRUCTURAL DYNAMICS3.0
CEEN533MATRIX STRUCTURAL ANALYSIS3.0
CEEN543ADVANCED DESIGN OF STEEL STRUCTURES3.0
CEEN545STEEL BRIDGE DESIGN3.0

Nuclear Engineering Track (12 credits from the course list below) 

NUGN506NUCLEAR FUEL CYCLE3.0
NUGN510INTRODUCTION TO NUCLEAR REACTOR PHYSICS3.0
NUGN520INTRODUCTION TO NUCLEAR REACTOR THERMAL-HYDRAULICS3.0
NUGN580NUCLEAR REACTOR LABORATORY3.0
NUGN590COMPUTATIONAL REACTOR PHYSICS3.0
NUGN585/586NUCLEAR REACTOR DESIGN I2.0

Electrical Engineering-Antennas and Wireless Communications Track (12 credits from the course list below)

EENG525ANTENNAS3.0
EENG527WIRELESS COMMUNICATIONS3.0
EENG530PASSIVE RF & MICROWAVE DEVICES3.0
EENG526ADVANCED ELECTROMAGNETICS3.0
EENG528COMPUTATIONAL ELECTROMAGNETICS3.0

Electrical Engineering-Energy Systems and Power Electronics Track (12 credits from the course list below)

EENG570ADVANCED HIGH POWER ELECTRONICS3.0
EENG580POWER DISTRIBUTION SYSTEMS ENGINEERING3.0
EENG581POWER SYSTEM OPERATION AND MANAGEMENT3.0
EENG583ADVANCED ELECTRICAL MACHINE DYNAMICS3.0

Electrical Engineering-Information and Systems Sciences Track (12 credits from the course list below)

EENG509SPARSE SIGNAL PROCESSING3.0
EENG511CONVEX OPTIMIZATION AND ITS ENGINEERING APPLICATIONS3.0
EENG515MATHEMATICAL METHODS FOR SIGNALS AND SYSTEMS3.0
EENG517THEORY AND DESIGN OF ADVANCED CONTROL SYSTEMS3.0
EENG519ESTIMATION THEORY AND KALMAN FILTERING3.0
EENG527WIRELESS COMMUNICATIONS3.0
EENG589DESIGN AND CONTROL OF WIND ENERGY SYSTEMS3.0
MEGN544ROBOT MECHANICS: KINEMATICS, DYNAMICS, AND CONTROL3.0

Mining and Earth Systems Track (12 credits from the course list below)

MNGN502GEOSPATIAL BIG DATA ANALYTICS3.0
MNGN512SURFACE MINE DESIGN3.0
MNGN516UNDERGROUND MINE DESIGN3.0
MNGN536OPERATIONS RESEARCH TECHNIQUES IN THE MINERAL INDUSTRY3.0
MNGN539ADVANCED MINING GEOSTATISTICS3.0

Doctor of Philosophy in Operations Research with Engineering

The ORWE PhD allows students to complete an interdisciplinary doctoral degree in Operations Research with Engineering by taking courses and conducting research in eight departments/divisions: Applied Mathematics and Statistics, Electrical Engineering, Computer Sciences, Civil and Environmental Engineering, Economics and Business, Mining Engineering, Mechanical Engineering, and Metallurgical and Materials Engineering.

Specialty Requirements

Doctoral students develop a customized curriculum to fit their needs. The degree requires a minimum of 72 graduate credits that includes coursework and a thesis. Coursework is valid for nine years toward a PhD degree; any exceptions must be approved by the director of the ORWE program and by the student's adviser.

Credit requirements

Core Courses24.0
Area of Specialization Courses12.0
Any Combination of Specialization Courses or Research12.0
Research Credits24.0
Total Semester Hrs72.0

Research Credits

Students must complete at least 24 research credits. The student's faculty adviser and the doctoral thesis committee must approve the student's program of study and the topic for the thesis.

Qualifying Examination Process and Thesis Proposal

Upon completion of the appropriate core coursework, students must pass Qualifying Exams I (written, over four courses) and II (oral, consisting of a report and research presentation) to become a candidate for the PhD, ORWE specialty.  Qualifying Exam I  is generally taken no later than three semesters after entry into the PhD program, and Qualifying Exam II follows no more than two semesters after passing Qualifying Exam I. The proposal defense should be completed within ten months of passing Qualifying Exam II.

Transfer Credits

Students may transfer up to 24 credits of graduate-level coursework from other institutions toward the PhD degree subject to the restriction that those courses must not have been used as credit toward a bachelor's degree. The student must have achieved a grade of B or better in all graduate transfer courses and the transfer must be approved by the student's doctoral thesis committee and the Director of the ORWE program.

Although most doctoral students will only be allowed to transfer up to 24 credits, with approval from the student’s doctoral committee, exceptions may be made to allow students who have earned a specialized thesis-based master’s degree in operations research or other closely related field from another university to transfer up to 36 credits in recognition of the degree. Students should consult with their academic advisors and ORWE director for details. 

Unsatisfactory Progress

In addition to the institutional guidelines for unsatisfactory progress as described elsewhere in this bulletin, unsatisfactory progress will be assigned to any full-time student who does not pass the following prerequisite and core courses in the first three semesters of study:

CSCI262DATA STRUCTURES3.0
ORWE586LINEAR OPTIMIZATION3.0
ORWE598ALGORITHMS FOR OPERATIONS RESEARCH3.0
EBGN526STOCHASTIC MODELS IN MANAGEMENT SCIENCE3.0

Unsatisfactory progress will also be assigned to any students who do not complete requirements as specified in their admission letters. Any exceptions to the stipulations for unsatisfactory progress must be approved by the ORWE committee. Part-time students develop an approved course plan with their advisor.

Prerequisites

Students must complete the following undergraduate prerequisite courses with a grade of B or better:

CSCI261PROGRAMMING CONCEPTS3.0
CSCI262DATA STRUCTURES3.0

Required Course Curriculum

All PhD students are required to take a set of core courses that provides basic tools for the more advanced and specialized courses in the program.

Core Courses
ORWE598ALGORITHMS FOR OPERATIONS RESEARCH3.0
MEGN502ADVANCED ENGINEERING ANALYSIS3.0
ORWE586LINEAR OPTIMIZATION3.0
MATH530INTRODUCTION TO STATISTICAL METHODS3.0
ORWE585NETWORK MODELS3.0
ORWE588INTEGER OPTIMIZATION3.0
ORWE587NONLINEAR OPTIMIZATION3.0
EBGN526STOCHASTIC MODELS IN MANAGEMENT SCIENCE3.0
Total Semester Hrs24.0

Students are required to take four courses from the following list: 

Area of Specialization Courses
CSCI555GAME THEORY AND NETWORKS3.0
CSCI562APPLIED ALGORITHMS AND DATA STRUCTURES3.0
EBGN509MATHEMATICAL ECONOMICS3.0
EBGN528INDUSTRIAL SYSTEMS SIMULATION3.0
or CSCI542 SIMULATION
EBGN560DECISION ANALYTICS3.0
EBGN575ADVANCED MINING AND ENERGY ASSET VALUATION3.0
EENG517THEORY AND DESIGN OF ADVANCED CONTROL SYSTEMS3.0
MATH531THEORY OF LINEAR MODELS3.0
MATH532SPATIAL STATISTICS3.0
MATH537MULTIVARIATE ANALYSIS3.0
MATH582STATISTICS PRACTICUM3.0
MEGN592RISK AND RELIABILITY ENGINEERING ANALYSIS AND DESIGN3.0
MNGN536OPERATIONS RESEARCH TECHNIQUES IN THE MINERAL INDUSTRY3.0
MNGN538GEOSTATISTICAL ORE RESERVE ESTIMATION3.0
ORWE688ADVANCED INTEGER OPTIMIZATION3.0
ORWE686ADVANCED LINEAR OPTIMIZATION3.0
5XX/6XX Special Topics (Requires approval of the advisor and OrwE program director)3.0

Mines’ Combined Undergraduate/Graduate Degree Program

Students enrolled in Mines’ combined undergraduate/graduate program may double count up to 6 credits of graduate coursework to fulfill requirements of both their undergraduate and graduate degree programs. These courses must have been passed with B- or better, not be substitutes for required coursework, and meet all other university, department, and program requirements for graduate credit.

Students are advised to consult with their undergraduate and graduate advisors for appropriate courses to double count upon admission to the combined program.

Courses

ORWE559. SUPPLY CHAIN MANAGEMENT. 3.0 Semester Hrs.

(II) Due to the continuous improvement of information technology, shorter life cycle of products, rapid global expansion, and growing strategic relationships, supply chain management has become a critical asset in today?s organizations to stay competitive. The supply chain includes all product, service and information flow from raw material suppliers to end customers. This course focuses on the fundamental concepts and strategies in supply chain management such as inventory management and risk pooling strategies, distribution strategies, make-to-order/make-to-stock supply chains, supplier relationships and strategic partnerships. It introduces quantitative tools to model, optimize and analyze various decisions in supply chains as well as real-world supply chain cases to analyze the challenges and solutions. 3 hours lecture; 3 semester hours.

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View Course Learning Outcomes
  • Understand fundamental supply chain management concepts such as inventory management, supply chain planning, integration, distribution and coordination"
  • Understand challenges that arise in supply chains
  • Understand the role of optimization models that are used to model supply chain operations and solve them using AMPL
  • Analyze supply chains of different businesses and discuss possible solutions to their problems.

ORWE585. NETWORK MODELS. 3.0 Semester Hrs.

(I) We examine network flow models that arise in manufacturing, energy, mining, transportation and logistics: minimum cost flow models in transportation, shortest path problems in assigning inspection effort on a manufacturing line, and maximum flow models to allocate machine-hours to jobs. We also discuss an algorithm or two applicable to each problem class. Computer use for modeling (in a language such as AMPL) and solving (with software such as CPLEX) these optimization problems is introduced. 3 hours lecture; 3 semester hours.

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View Course Learning Outcomes
  • 1. Understand how to differentiate spanning tree, shortest path, maximum flow and minimum cost flow models.
  • 2. Understand how to graphically depict and mathematically model spanning tree, shortest path, maximum flow and minimum cost flow models.
  • 3. Understand algorithms that solve model spanning tree, shortest path, maximum flow and minimum cost flow models.
  • 4. Understand the difference between network and non-network optimization models

ORWE586. LINEAR OPTIMIZATION. 3.0 Semester Hrs.

(I) We address the formulation of linear programming models, linear programs in two dimensions, standard form, the Simplex method, duality theory, complementary slackness conditions, sensitivity analysis, and multi-objective programming. Applications of linear programming models include, but are not limited to, the areas of manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with software such as CPLEX) these optimization problems is introduced. Offered every other year. 3 hours lecture; 3 semester hours.

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View Course Learning Outcomes
  • Understand how to formulate linear optimization models
  • Understand how to solve linear optimization models, both by hand and with the computer through an algebraic modeling language and a state-of-the-art solver.
  • Understand the special structure underlying linear optimization models and how this affects their ability to be solved.
  • Understand sensitivity and post-optimality analysis.

ORWE587. NONLINEAR OPTIMIZATION. 3.0 Semester Hrs.

(I) This course addresses both unconstrained and constrained nonlinear model formulation and corresponding algorithms (e.g., Gradient Search and Newton's Method, and Lagrange Multiplier Methods and Reduced Gradient Algorithms, respectively). Applications of state-of-the-art hardware and software will emphasize solving real-world engineering problems in areas such as manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with an algorithm such as MINOS) these optimization problems is introduced. Offered every other year. 3 hours lecture; 3 semester hours.

View Course Learning Outcomes

View Course Learning Outcomes
  • Understand how to formulate nonlinear optimization models.
  • Understand how to solve nonlinear optimization models, both by hand and with the computer through an algebraic modeling language and a state-of-the-art solver.
  • Understand the special structure underlying nonlinear optimization models and how this affects their ability to be solved.

ORWE588. INTEGER OPTIMIZATION. 3.0 Semester Hrs.

(I) This course addresses the formulation of integer programming models, the branch-and-bound algorithm, total unimodularity and the ease with which these models are solved, and then suggest methods to increase tractability, including cuts, strong formulations, and decomposition techniques, e.g., Lagrangian relaxation, Benders decomposition. Applications include manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with software such as CPLEX) these optimization problems is introduced. Offered every other year. 3 hours lecture; 3 semester hours.

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View Course Learning Outcomes
  • Understand how to formulate linear-integer optimization models.
  • Understand how to solve linear-integer optimization models, both by hand and with the computer through an algebraic modeling language and a state-of-the-art solver.
  • Understand the special structure underlying linear-integer optimization models and how this affects their ability to be solved.
  • Understand decomposition techniques to aid in solution.

ORWE598. ALGORITHMS FOR OPERATIONS RESEARCH. 6.0 Semester Hrs.

Reasoning about algorithm correctness (proofs, counterexamples). Analysis of algorithms: asymptotic and practical complexity. Review of dictionary data structures (including balanced search trees). Priority queues. Advanced sorting algorithms (heapsort, radix sort). Advanced algorithmic concepts illustrated through sorting (randomized algorithms, lower bounds, divide and conquer). Dynamic programming. Backtracking. Algorithms on unweighted graphs (traversals) and weighted graphs (minimum spanning trees, shortest paths, network flows and bipartite matching); NP-completeness and its consequences. Prerequisite: CSCI220 with a grade of C- or higher or CSCI262 with a grade of C- or higher, MATH213 or MATH223 or MATH224, MATH300 or MATH358 or CSCI358.

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  • Same as existing CSCI406.

ORWE598. SIMULATION FOR OPERATIONS RESEARCH. 3.0 Semester Hrs.

A first course in computer simulation using formal learning groups and emphasizing the rigorous development of simulation applications. Topics will include random number generation, Monte Carlo simulation, discrete event simulation, and the mathematics behind their proper implementation and analysis (random variates, arrival time modeling, infinite horizon statistics, batch means and sampling techniques). The course uses learning group assignments, quizzes, programming projects (using Linux) and exams for assessment. Prerequisite: (CSCI210 or CSCI274) AND CSCI306 AND (MATH201 or MATH334).

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  • same as existing course CSCI423

ORWE686. ADVANCED LINEAR OPTIMIZATION. 3.0 Semester Hrs.

(II) As an advanced course in optimization, we expand upon topics in linear programming: advanced formulation, the dual simplex method, the interior point method, algorithmic tuning for linear programs (including numerical stability considerations), column generation, and Dantzig-Wolfe decomposition. Time permitting, dynamic programming is introduced. Applications of state-of-the-art hardware and software emphasize solving real-world problems in areas such as manufacturing, mining, energy, transportation and logistics, and the military. Computers are used for model formulation and solution. Offered every other year. Prerequisite: MEGN586. 3 hours lecture; 3 semester hours.

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  • Understand how to formulate complicated linear optimization models.
  • Dual Simplex Method and Interior Point Method
  • Algorithmic Tuning
  • Column Generation and Dantzig-Wolfe Decomposition

ORWE688. ADVANCED INTEGER OPTIMIZATION. 3.0 Semester Hrs.

(II) As an advanced course in optimization, we expand upon topics in integer programming: advanced formulation, strong integer programming formulations (e.g., symmetry elimination, variable elimination, persistence), in-depth mixed integer programming cuts, rounding heuristics, constraint programming, and decompositions. Applications of state-of-the-art hardware and software emphasize solving real-world problems in areas such as manufacturing, mining, energy, transportation and logistics, and the military. Computers are used for model formulation and solution. Prerequisite: MEGN588. 3 hours lecture; 3 semester hours. Offered every other year.

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View Course Learning Outcomes
  • Know how to formulate advanced integer optimization models 2. Be familiar with advanced algorithms to solve these models 3. Be able to use software, including scripting, to model and solve these models 4. Understand the theory behind and mathematical tenants of advanced integer optimization models