Course Syllabus: Management Science Seminars
Table of contents (5)
Instructor: Dr. Luping Zhang
Institution: Southwestern University of Finance and Economics
Level: Undergraduate Course (4 Credits / 51 Lecture Hours)
Schedule Format: 17 Weeks × 3 Hours / Week
Official Syllabus Download: Management_Science_Seminars_Syllabus.pdf
1. Course Description and Objectives
This course equips undergraduate students with a solid foundational understanding of Management Science and its analytical applications in managerial decision-making. By combining mathematical programming, network optimization, and systems thinking, students learn to model and solve complex resource allocation challenges across modern organizations.
By the end of this course, students will be able to:
- Formulate and Solve Quantitative Models: Build mathematical representations using linear programming, integer programming, and network flows.
- Apply Principles to Real-World Challenges: Systematically address operational problems in production planning, inventory control, logistics distribution, and capital budgeting.
- Perform Post-Optimality and Sensitivity Diagnostics: Interpret dual variables, shadow prices, and allowable coefficient ranges to guide strategic decision-making.
- Communicate Analytical Insights: Articulate mathematical logic and executive recommendations effectively to decision-makers.
- Rigorously Evaluate Assumptions: Critique the validity and limitations of linear and discrete optimization models across diverse business contexts.
2. Textbooks and Academic References
- Core Textbook:
- Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Martin, R. K. An Introduction to Management Science: Quantitative Approaches to Decision Making. Cengage Learning.
- Supplementary Readings:
- Stanford University MS&E 111 / ENGR 62: Introduction to Optimization (Chapter 4: Linear Programming Theory and Duality). Stanford University.
- Bradley, S. P., Hax, A. C., & Magnanti, T. L. (1977). Applied Mathematical Programming. Addison-Wesley.
- Academic Journal Literature:
- Seminal articles from Management Science, Operations Research, and INFORMS Journal on Applied Analytics.
3. Curriculum Modules and Weekly Schedule
| Week | Module / Topic | Methodological Focus | Key Materials & Readings |
|---|---|---|---|
| W1 | Introduction to Management Science | Quantitative decision-making processes, problem formulation, certain vs. uncertain environments | Lecture Notes, Textbook |
| W2 | Fundamentals of Systems and Modeling | Organizational systems, feedback loops, model abstraction, decision and state variables | Lecture Notes, Case Materials: system_case.zip |
| W3 | Linear Programming (LP) Modeling | LP formulation, fundamental assumptions (proportionality, additivity, divisibility), graphical solutions | Lecture Notes, Textbook |
| W4 | Sensitivity Analysis & Shadow Prices | Post-optimality diagnostics, economic meaning of dual prices, reduced costs, allowable ranges | Lecture Notes, Textbook |
| W5 | LP Applications: Operations & Marketing | Media selection, advertising budget allocation, aggregate production scheduling, workforce staffing | Lecture Notes, Textbook |
| W6 | LP Applications: Corporate Finance | Working capital planning, cash flow management, capital budgeting, make-or-buy decisions | Lecture Notes, Textbook |
| W7 | LP in Portfolios & Asset Allocation | Constrained portfolio optimization, index tracking, transaction cost bounds, risk budgeting | Lecture Notes, Textbook |
| W8 | The Simplex Method & Computation | Simplex algorithm mechanics, standard form conversion, tableau pivoting, Python optimization solvers | Lecture Notes, Python Code, Bradley et al. |
| W9 | Introduction to Duality Theory | Motivation, economic interpretation of duality, constructing dual programs from primal models | Lecture Notes, Stanford MS&E 111 |
| W10 | Duality Theorems & Hyperplanes | Weak and Strong Duality Theorems, separating and supporting hyperplane geometry | Lecture Notes, Stanford MS&E 111 |
| W11 | Farkas' Lemma & Duality Proofs | Convex polyhedra, cone theory, theorems of the alternative, rigorous proof of Strong Duality | Lecture Notes, Stanford MS&E 111 |
| W12 | Complementary Slackness & General Duals | Complementary slackness optimality conditions, general LP duals with equality and unconstrained variables | Lecture Notes, Textbook |
| W13 | Transportation & Assignment Problems | Network structure of transportation models, unimodularity property, Hungarian assignment algorithm | Lecture Notes, Textbook |
| W14 | Distribution & Network Models | Transshipment models, shortest-path algorithms, maximum flow, minimum-cost network flows | Lecture Notes, Textbook |
| W15 | Integer Linear Programming (ILP) Theory | Pure, mixed, and 0-1 binary ILP, LP relaxation, integrality gap, fixed-charge and logical constraints | Lecture Notes, Textbook |
| W16 | ILP Applications & Computational Solvers | Facility location, set covering/packing, traveling salesperson problem (TSP), computational workflows | Lecture Notes, Textbook |
| W17 | Student Project Presentations & Synthesis | Capstone group project oral defense, peer critique, comprehensive methodological synthesis | Student Presentations & Reports |
4. Evaluation and Grading System
Course assessment combines continuous formative evaluation with rigorous applied project deliverables:
- Final Capstone Project Report & Presentation (40%): A comprehensive group investigation addressing a complex real-world managerial decision problem. Deliverables include formal mathematical model formulation, computational solver implementation (Python / Gurobi / CPLEX / PuLP), sensitivity analysis, executive presentation, and final report.
- Midterm Progress Milestone (30%): Intermediate milestone documenting problem background, literature context, initial mathematical formulation, data structure, and preliminary results.
- Case Studies, Homework & Seminar Participation (30%): Quantitative modeling problem sets, active participation in case discussions, and constructive peer review.
5. Course Policies and Expectations
- Academic Integrity: All modeling formulations, computational code, and analytical reports must represent original student work. Appropriate citations are required when referencing external literature or datasets.
- Computational Tools: Students are strongly encouraged to implement and solve optimization models using Python (
scipy.optimize,PuLP,Pyomo) or commercial mathematical solvers (Gurobi,CPLEX) under academic licensing. - Case Studies: Students should download and review the assigned case materials (e.g. system_case.zip) prior to classroom discussion.