Topics

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Column Generation

Gilmore, P.C., and Gomory, R.E. "A linear programming approach to the cutting-stock problem." Operations research 9.6 (1961): 849-859.

Gilmore, P.C., and Gomory, R.E. "A linear programming approach to the cutting stock problem—Part II." Operations research 11.6 (1963): 863-888.

Additional material:

Gilmore, P.C., and Gomory, R.E. "Multistage cutting stock problems of two and more dimensions." Operations research 13.1 (1965): 94-120.

Cutting Planes

Dantzig, G., Fulkerson D.R., and Johnson S.M. "Solution of a large-scale traveling-salesman problem." Journal of the Operations Research Society of America 2.4 (1954): 393-410.

Dantzig, G., Fulkerson, D.R., and Johnson, S.M. "On a linear-programming, combinatorial approach to the traveling-salesman problem." Operations Research 7.1 (1959): 58-66.

Additional material:

Chvátal V., Cook W., Dantzig G.B., Fulkerson D.R., Johnson S.M. (2010) Solution of a Large-Scale Traveling-Salesman Problem. In: Jünger M. et al. (eds) 50 Years of Integer Programming 1958-2008. Springer, Berlin, Heidelberg

Grötschel, M., Nemhauser G.L. "George Dantzig’s contributions to integer programming", Discrete Optimization, Volume 5, Issue 2, 2008, Pages 168-173, ISSN 1572-5286

Network Flows and Project Scheduling

Ford, L.R., and Fulkerson, D.R. "Maximal flow through a network." Canadian journal of Mathematics 8.3 (1956): 399-404.

Fulkerson, D.R. "Scheduling in project networks". No. RM-4137-PR. RAND CORP SANTA MONICA CA, 1964.

Additional material:

Ahuja, R.K., Magnanti, T.L., and Orlin, J.B. Network flows. Pearson Education, 2014.

Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C. (2001). "Section 26.2: The Ford–Fulkerson method". Introduction to Algorithms (Second ed.). MIT Press and McGraw–Hill. pp. 651–664. ISBN 0-262-03293-7.

Scheduling Rules

Johnson, S.M. "Optimal two‐and three‐stage production schedules with setup times included." Naval Research Logistics (NRL) 1.1 (1954): 61-68.

Jackson, J.R. "Scheduling a production line to minimize maximum tardiness". CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH, 1955.

Smith, W.E. "Various optimizers for single‐stage production." Naval Research Logistics (NRL) 3.1‐2 (1956): 59-66.

Additional material:

Pinedo, M.L. Scheduling: theory, algorithms, and systems. Springer, 2016. (Chapters 3.1-3.2)

Panwalkar, S.S. and Koulamas, C. (2015), Scheduling research and the first decade of NRLQ: A historical perspective. Naval Research Logistics, 62: 335–344.

Stable Marriage

Gale, D., and Shapley, L.S. “College Admissions and the Stability of Marriage.” The American Mathematical Monthly, vol. 69, no. 1, 1962, pp. 9–15.

Irving, R.W. "An efficient algorithm for the “stable roommates” problem." Journal of Algorithms 6.4 (1985): 577-595.

Additional material:

Gusfield, D., and Irving, R.W. The stable marriage problem: structure and algorithms. MIT press, 1989.

Knuth, D.E. Stable marriage and its relation to other combinatorial problems: An introduction to the mathematical analysis of algorithms. Vol. 10. American Mathematical Soc., 1997.