Operations Research with Engineering

Degrees Offered

  • Master of Science in Operations Research with Engineering (Non-Thesis)
  • Doctor of Philosophy in Operations Research with Engineering

Program Description

Operations Research (OR) involves mathematically modeling physical systems (both naturally occurring and man-made) with a view to determining a course of action for the system to either improve or optimize its functionality. Examples of such systems include, but are not limited to, manufacturing systems, chemical processes, socio-economic systems, mechanical systems (e.g., those that produce energy), and mining systems.

Program Requirements

Master of Science in Operations Research with Engineering (Non-Thesis)

Core Courses18.0
ORWE courses not taken as core and/or track courses12.0
Total30.0

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

MATH530STATISTICAL METHODS I3.0
MATH531STATISTICAL METHODS II3.0
ORWE586LINEAR OPTIMIZATION3.0
or ORWE585 NETWORK MODELS
MATH438/538STOCHASTIC MODELS Course may be substituted with Math 4XX Computational Linear Albebra3.0
ORWE587NONLINEAR OPTIMIZATION3.0
or ORWE588 INTEGER OPTIMIZATION
MEGN502ADVANCED ENGINEERING ANALYSIS3.0
or CSCI406 ALGORITHMS
or CEEN405 NUMERICAL METHODS FOR ENGINEERS
or CEEN505 NUMERICAL METHODS FOR ENGINEERS

The remaining 12 hours 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:  (i) operations research methodology; (ii) systems engineering; (iii) computer science; (iv) finance and economics; and (v) 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 hours of ORWE-labeled coursework can "mix and match" from the ORwE coursework and coursework mentioned in the tables below with consultation 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 hours from the course list below)

MEGN461THERMODYNAMICS II3.0
MEGN567HVAC AND BUILDING ENERGY SYSTEMS3.0
MEGN591ADVANCED ENGINEERING DESIGN METHODS3.0
MEGN583/AMFG501ADDITIVE MANUFACTURING3.0
MEGN570ELECTROCHEMICAL SYSTEMS ENGINEERING3.0
MEGN560DESIGN AND SIMULATION OF THERMAL SYSTEMS3.0

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

*Subject to approval by graduate council

AMFG511DATA DRIVEN ADVANCED MANUFACTURING3.0
MEGN583/AMFG501ADDITIVE MANUFACTURING3.0
AMFG531MATERIALS FOR ADDITIVE MANUFACTURING3.0
AMFG421/521DESIGN FOR ADDITIVE MANUFACTURING3.0

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

MATH500LINEAR VECTOR SPACES3.0
MATH532SPATIAL STATISTICS3.0
MATH536ADVANCED STATISTICAL MODELING3.0
MATH537/538MULTIVARIATE ANALYSIS3.0
MATH438/538STOCHASTIC MODELS3.0
MATH551COMPUTATIONAL LINEAR ALGEBRA3.0
EENG511CONVEX OPTIMIZATION AND ITS ENGINEERING APPLICATIONS3.0

Economics Track (12 hours 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 hours from the course list below)

ORWE559SUPPLY CHAIN MANAGEMENT3.0
EBGN560DECISION ANALYSIS3.0
EBGN571MARKETING ANALYTICS3.0
EBGN562STRATEGIC DECISION MAKING3.0

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

CSCI542SIMULATION3.0
CSCI562APPLIED ALGORITHMS AND DATA STRUCTURES3.0
CSCI571ARTIFICIAL INTELLIGENCE3.0
CSCI575MACHINE LEARNING3.0
CSCI555GAME THEORY AND NETWORKS3.0

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

CEEN506FINITE ELEMENT METHODS FOR ENGINEERS3.0
CEEN5XX Risk Assessment in Geotechnical Engineering3.0
CEEN510ADVANCED SOIL MECHANICS3.0
CEEN511UNSATURATED SOIL MECHANICS3.0
CEEN512SOIL BEHAVIOR3.0
CEEN515HILLSLOPE HYDROLOGY AND STABILITY3.0

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

CEEN506FINITE ELEMENT METHODS FOR ENGINEERS3.0
CEEN530ADVANCED STRUCTURAL ANALYSIS3.0
CEEN531STRUCTURAL DYNAMICS3.0
CEEN533MATRIX STRUCTURAL ANALYSIS3.0
CEEN543CONCRETE BRIDGE DESIGN BASED ON THE AASHTO LRFD SPECIFICATIONS3.0
CEEN545STEEL BRIDGE DESIGN3.0

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

MNGN5XX Big Data Analytics for Earth Resources Sciences and Engineering3.0
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 & Business, Mining Engineering, Mechanical Engineering, and Metallurgical & Materials Engineering.

Specialty Requirements

Doctoral students develop a customized curriculum to fit their needs. The degree requires a minimum of 72 graduate credit hours that includes coursework and a thesis. Coursework is valid for nine years towards a Ph.D. 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 24.0 hours of 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 Ph.D., ORwE specialty.  Qualifying Exam I  is generally taken no later than three semesters after entry into the Ph.D. program, and Qualifying Exam II follows no more than two semesters after having passed Qualifying Exam I. The proposal defense should be completed within ten months of passing Qualifying Exam II.

Transfer Credits

Students may transfer up to 24.0 hours 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 doctoral thesis committee 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
MATH530STATISTICAL METHODS I3.0
CSCI406ALGORITHMS3.0

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 Ph.D. 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
CSCI/MATH406ALGORITHMS3.0
MEGN502ADVANCED ENGINEERING ANALYSIS3.0
ORWE586LINEAR OPTIMIZATION3.0
MATH530STATISTICAL METHODS I3.0
MATH438STOCHASTIC MODELS3.0
ORWE585NETWORK MODELS3.0
ORWE588INTEGER OPTIMIZATION3.0
ORWE587NONLINEAR OPTIMIZATION3.0
Total Semester Hrs24.0

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

Area of Specialization Courses
EBGN528INDUSTRIAL SYSTEMS SIMULATION3.0
or MATH542 SIMULATION
or CSCI542 SIMULATION
CSCI555GAME THEORY AND NETWORKS3.0
MATH532SPATIAL STATISTICS3.0
MATH537MULTIVARIATE ANALYSIS3.0
MATH582STATISTICS PRACTICUM3.0
MEGN592RISK AND RELIABILITY ENGINEERING ANALYSIS AND DESIGN3.0
ORWE688ADVANCED INTEGER OPTIMIZATION3.0
MTGN450/MLGN550STATISTICAL PROCESS CONTROL AND DESIGN OF EXPERIMENTS3.0
EBGN560DECISION ANALYSIS3.0
EENG517THEORY AND DESIGN OF ADVANCED CONTROL SYSTEMS3.0
CSCI562APPLIED ALGORITHMS AND DATA STRUCTURES3.0
ORWE686ADVANCED LINEAR OPTIMIZATION3.0
MNGN536OPERATIONS RESEARCH TECHNIQUES IN THE MINERAL INDUSTRY3.0
MNGN538GEOSTATISTICAL ORE RESERVE ESTIMATION3.0
EBGN509MATHEMATICAL ECONOMICS3.0
MNGN538GEOSTATISTICAL ORE RESERVE ESTIMATION3.0
EBGN509MATHEMATICAL ECONOMICS3.0
EBGN575ADVANCED MINING AND ENERGY ASSET VALUATION3.0
MATH531STATISTICAL METHODS II3.0
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 (meaning uninterrupted registration from the time the student earns a Mines undergraduate degree to the time the student begins a Mines graduate degree) may double count up to six hours of credits which were used in fulfilling the requirements of their undergraduate degree at Mines, towards their graduate program. Any 400+ level courses that count towards the undergraduate degree requirements as "Elective Coursework" or any 500+ level course, may be used for the purposes of double counting at the discretion of the graduate advisor. These courses must have been passed with a "B-" or better, not be substitutes for required coursework, and meet all other University, Department, Division, and Program requirements for graduate credit.

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.

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.

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.

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.

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.

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.

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.