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Management Science (also called Decision Science, Operations Research, and Systems Analysis) is offered as a minor field of study only and focuses upon the methodological and modeling technologies that form the foundations for analyzing systems. All students in the Quantitative Methods Core obtain substantial training in methodological skills and advanced modeling issues.

Program

Students must take the two-year Quantitative Methods Core, including six PhD seminars in Computers and Information Systems or Operations Management (CIS or OMG 501 503 the first year; CIS or OMG 521 523 in year two and beyond). Specific course work and reading assignments for the minor must be submitted to the Management Science area coordinator for approval in advance.

The First Year: Foundation

Typical first-year courses for the Management Science minor are listed below. The first year culminates with the Quantitative Methods Core Exam given in June.

Fall Quarter	AEC 511 Advanced Price Theory I
Winter Quarter	AEC 512 Advanced Price Theory II MSM522 Optimization MSM 504 Theory of Prob. and Stochastic Processes I
Spring Quarter	AEC 513 Advanced Price Theory III MSM 535 Integer Programming MSM 505 Theory of Prob. and Stochastic Processes II
Fall Semester	ECO 483/484 (2 hrs. each) Intro Math Stats/Econometrics MTH 265H (4 hrs.) Real AnalysisBST 401 Probability Theory
Spring Semester	ECO 485 (4 hrs.) Econometrics

The Second Year: Depth

The Qualifying Exam may include a take-home research exam or required course work, which has been previously approved by the Management Science area coordinator, the majority of which must be at the PhD level. A 3.75 GPA in 15 hours of that course work must be maintained.The Third Year: Breadth

Current faculty research in other functional areas includes a strong element of management science. Recent relevant faculty research includes:

• Computational methods for large Markov chains
• Stochastic models of equipment reliability
• Large-scale scheduling theory
• Queueing network models of computer telecommunication and manufacturing systems
• Optimization of manufacturing systems
• Performance modeling of storage and material handling systems
• Information systems design for large-scale systems
• Systems control for computer-integrated manufacturing
• Large-scale mathematical programming
• Aggregation methodologies
• Markovian decision processes

Faculty and Research Interests Simon School faculty who do research and sometimes teach in Management Science include:

• Gregory Dobson
• Harry Groenevelt
• Edieal J. Pinker
• Abrahm Seidmann

Courses and Descriptions

Listed below are titles of M.B.A.-level courses (for descriptions see the Simon Information Guide), and descriptions of Ph.D.-level courses in Management Science.

• MSM 400  Mathematics Review
• MSM 491  Math for Management
• MSM 501  Quantitative Methods Colloquium (non-credit). A forum for the presentation of recent and current research. Faculty, Ph.D. students, and outside speakers present papers on their current research and/or discuss recent work by others in the field. Ph.D. students are expected to actively participate.
• MSM 502  Linear Algebra and Linear Programming. Provides an introduction to linear programming and is designed to help incoming PhD students better prepare for later course work. The topics covered are definitions and examples, introduction to linear algebra, the simplex method, starting solution and convergence, the revised simplex method, duality and sensitivity analysis, and (if time permits) the structure of convex polyhedral sets.
• MSM 504  Theory of Probability and Stochastic Processes I. The course will study probability spaces; univariate and multivariate distributions, moments; transforms and generating functions, univariate and multivariate central limit theorems, Markov chains and processes in discrete and continuous time, autoregressive and moving average time series, Poisson process, Wiener process, discrete and continuous time renewal theory, properties of Markov chains.
• MSM 505  Theory of Probability and Stochastic Processes II. The course will study birth-death processes; M/M/1 and M/M/S queuing systems; transient behavior in time-reversible chains; stochastic systems; delay and loss in M/G/1; queues with interrupted service; Markov diffusion processes; applications.
• MSM 509  Informational Sciences and Large-Scale Algorithms (prerequisite: MSM 535 or permission of the instructor). The course consists of a set of advanced topics in optimization and artificial intelligence. Topics include numerical linear algebra, decomposition methods in optimization such as Dantzig-Wolfe, partitioning, relaxation, projection, inner and outer linearization aggregation and price and resource directive decomposition; heuristic methods for combinatorial optimization such as genetic algorithms, simulated annealing, neural networks, beam search and tabu search; and parallel computing, systolic and data-flow algorithms.
• MSM 522  Optimization (prerequisites: MSM 502 and College Courses MTH 235 and MTH 265). An introduction to unconstrained and constrained optimization in RN. Theoretical topics include convexity, Kuhn-Tucker conditions, and Lagrangian duality. Algorithms include equation-solving (Newton), primal methods (gradient, variable metric, penalty and barrier, successive quadratic programming), dual-ascent methods, and primal-dual methods (augmented Lagrangian).
• MSM 535  Network and Integer Programming. The course covers the solution of network problems and integer programs. Shortest path, minimum spanning tree, maximum flow, minimum-cost flow, and matching are some of the network problems covered. Algorithms for linear-integer and mixed-integer problems include branch and bound, implicit enumeration, primal and dual cutting planes, group theoretic methods, Lagrangian relaxation, and surrogate relaxation. These algorithms are illustrated on classical integer problems such as the knapsack, set covering/partitioning, and traveling salesman.
• MSM 542  Queuing Theory and Applications (prerequisite: MSM 504 or Medical School Course BST 402 or permission of the instructor). The study of queues and networks of queues, including single and multiserver queues, Markovian models of phase-type systems, open and closed networks of queues, product-form solutions and local balance, bottleneck analysis, approximations and computational aspects; applications to scheduling, resource allocation and capacity-expansion decisions in service systems, computer systems and job shops.
• MSM 549  Stochastic Models (prerequisites: MSM 504 or Medical School course BST 402 or permission of the instructor). The course reviews applications of stochastic processes to business problems drawn from reliability, inventory and production control, queueing models of computers, telecommunications, manufacturing and service systems; applications of stochastic control theory and Markov-decision processes; modeling techniques, including aggregation, hierarchical modeling, decomposition, approximations, bottleneck detection and elimination, simulation and sensitivity analyses; and economic issues in the design, performance evaluation, and management of stochastic systems.