Egon Balas

PHONE

412-268-2285

OFFICE

POS - Posner Hall - Room 232B

AREA OF EXPERTISE

Operations Research

EDUCATION

University of Paris - Ph D - 1968
University of Brussels - Ph D - 1967
Bolyai University - - 1949

USEFUL LINKS

PUBLICATIONS

• On the relationship between standard intersection cuts, lift-and-project cuts and generalized intersection cuts

(author(s): Egon Balas, Tamas Kis) Mathematical Programming A, 2016

• Integer (Linear) Programming
  Advances and Trends in Optimization with Applications to Engineering

(author(s): Egon Balas, Matteo Fischetti) Chaper in SIAM volume to appear

• Integer Programming
  Wiley’s StatsRef: Statistics Reference Online

Wiley, StatsRef Online, 2015

• Intersection cuts--standard versus restricted

(author(s): Egon Balas, Tamas Kis) Discrete Optimization 18, 2015; 189-192

• Der Wille zur Freiheit (paperback edition of the German translation of Will to Freedom)

Springer, 2014

• Generalized intersection cuts and a new cut generating paradigm

(author(s): Egon Balas, François Margot) Mathematical Programming A 137, 2013; 19-35

• Combining lift-and-project and reduce-and-split

(author(s): Egon Balas, Gerard Cornuejols, Tamas Kis, Giacomo Nannicini) INFORMS Journal on Computing 25(3), 2013; 475-487

• Intersection cuts from multiple rows: A disjunctive programming approach

(author(s): Egon Balas, Andrea Qualizza) European Journal of Computational Optimization 1(1), 2013; 3-49

• A hard integer program made easy by lexicography

(author(s): Egon Balas, M. Fischetti, A. Zanette) Mathematical Programming A 135, 2012; 500-514

• Der Wille zur Freiheit (German translation of Will to Freedom)

Springer, 2012; 418

• Monoidal cut strengthening revisited

(author(s): Egon Balas, Andrea Qualizza) Discrete Optimization 9(1), 2012; 40-49

• Disjunctive programming
  The Wiley Encyclopedia of Operations Research and Management Science

John Wiley & Sons, 2011

• Lexicography and degeneracy: Can a pure cutting plane algorithm work?

(author(s): Arrigo Zanette, Matteo Fischetti, Egon Balas) Mathematical Programming 130(1), 2011; 153-176

• Projecting systems of linear inequalities with binary variables

Annals Of Operations Research 188(1), 2011; 19-31

• Disjunctive Programming
  50 Years of Integer Programming 1958-2008: From the Early Years to the State-of-the-Art

Springer-Verlag, 2010; 283-340

• On the enumerative nature of Gomory''s dual cutting plane method

(author(s): Egon Balas, M. Fischetti, A. Zanette) Mathematical Programming B 125(2), 2010; 325-351

• Generating lift-and-project cuts from the LP simplex tableau: open source implementation and testing of new variants

(author(s): Egon Balas, P. Bonami) Mathematical Programming Computation 1 , 2009; 165-199

• On the cycle polytope of a directed graph and its relaxations

(author(s): Egon Balas, Ruediger Stephan) Networks 54(1), 2009; 47-55

• Can pure cutting plane algorithms work?
  Integer Programming and Combinatorial Optimization (IPCO 13)

(author(s): Egon Balas, M. Fischetti, A. Zanette) Springer 5035, 2008; 416-434

• Job shop scheduling with setup times, deadlines and precedence constraints

(author(s): Egon Balas, Neil Simonetti, Alkis Vazacopoulos) Journal Of Scheduling 11(4), 2008; 253-262

• Optimizing over the split closure

(author(s): Egon Balas, Anureet Saxena) Mathematical Programming A 113(2), 2008; 219-240

• A Special Issue in Memory of George B. Dantzig

(author(s): Egon Balas, Alan Hoffman, S. McCormick) Discrete Optimization 5(2), 2008; 145-150

• Will to Freedom: A Perilous Journey through Fascism and Communism

Syracuse University Press, paperback edition, 2008

• New variants of lift-and-project cut generation from the LP simplex tableau: open source implementation and testing
  Integer Programming and Combinatorial Optimization (IPCO 12)

(author(s): Egon Balas, P. Bonami) Springer, 2007; 89-103

• Polyhedral theory for the Asymmetric Traveling Salesman Problem
  The Traveling Salesman Problem and its Variations

Springer 12, 2007; 117-168

• The prize collecting traveling salesman problem and its applications
  The Traveling Salesman Problem and Its Variations

Kluwer, 2007; 663-695

• Some thoughts on the development of integer programming during my research career

Annals Of Operations Research 149(1), 2007; 19-26

• In Memoriam: Peter Hammer (1936-2006)

OR/MS Today 34, 2007

• New facets of the STS polytope generated from known facets of the ATS polytope

(author(s): Egon Balas, Robert Carr, Matteo Fischetti, Neil Simonetti) Discrete Optimization 3(1), 2006

• Projection, lifting and extended formulation in integer and combinatorial optimization

Annals Of Operations Research 140(1), 2005; 125-161

• The vertex separator problem: A polyhedral investigation

(author(s): Egon Balas, C de Souza) Mathematical Programming 103(3), 2005; 583-608

• The vertex separator problem: Algorithms and computations

(author(s): C de Souza, Egon Balas) Mathematical Programming 103(3), 2005; 609-631

• Pivot and Shift--a mixed integer programming heuristic

(author(s): Egon Balas, S. Schmieta, C. Wallace) Discrete Optimization 1(1), 2004; 3-12

• Logical constraints as cardinality rules: Tight representation

Combinatorial Optimization 8(2), 2004; 115-128

• On unions and dominants of polytopes

(author(s): Egon Balas, A Bockmayr, N Pisaruk, L Wolsey) Mathematical Programming 99(2), 2004; 223-239

• A precise correspondence between lift-and-project cuts, simple disjunctive cuts, and mixed integer Gomory cuts for 0-1 programming

(author(s): Egon Balas, M Perregaard) Mathematical Programming B 94(3-Feb), 2003; 221-245

• Some thoughts on the development of integer programming During My Research Career - Lecture delivered upon receiving the Euro Gold Medal, July 9, 2001, Rotterdam (Vol 141, Pg 1, 2002)00589-1)

European Journal Of Operational Research 143(3), 2002; 644-644

• Lift-and-project for mixed 0-1 programming: Recent progress00340-7)

(author(s): Egon Balas, M Perregaard) Discrete Applied Mathematics 123(1-3), 2002; 129-154

• Octane: A new heuristic for pure 0-1 programs

(author(s): Egon Balas, S Ceria, M Dawande, François Margot, G Pataki) Operations Research 49(2), 2001; 207-225

• Linear time dynamic-programming algorithms for new classes of restricted TSPs: A computational study

(author(s): Egon Balas, N Simonetti) Informs Journal On Computing 13(1), 2001; 56-75

• On the cycle polytope of a directed graph36:134::AID-NET43.0.CO;2-2)

(author(s): Egon Balas, M Oosten) Networks 36(1), 2000; 34-46

• New classes of efficiently solvable generalized Traveling Salesman Problems

Annals of Operations Research 86, 1999; 529-558

• Lifted cycle inequalities for the Asymmetric Traveling Salesman Problem

(author(s): Egon Balas, M Fischetti) Mathematics Of Operations Research 24(2), 1999; 273-292

• Job shop scheduling with deadlines

(author(s): Egon Balas, G Lancia, P Serafini, A Vazacopoulos) Journal Of Combinatorial Optimization 1(4), 1998; 329-353

• Disjunctive programming: Properties of the convex hull of feasible points00136-X)

Discrete Applied Mathematics 89(3-Jan), 1998

• On the dimension of projected polyhedra00096-1)

(author(s): Egon Balas, M Oosten) Discrete Applied Mathematics 87(1-3), 1998; 1-9

• Optimized crossover-based genetic algorithms for the maximum cardinality and maximum weight clique problems

(author(s): Egon Balas, W Niehaus) Journal of Heuristics 4(2), 1998; 107-122

• Projection with a minimal system of inequalities

Computational Optimization and Applications 10(2), 1998; 189-193

• Guided local search with shifting bottleneck for job shop scheduling

(author(s): Egon Balas, A Vazacopoulos) Management Science 44(2), 1998; 262-275

• A Modified Lift-And-Project Procedure

Mathematical Programming 79(3-Jan), 1997; 19-31

• On The Monotonization Of Polyhedra

(author(s): Egon Balas, M Fischetti) Mathematical Programming 78(1), 1997; 59-84

• A Dynamic Subgradient-Based Branch-And-Bound Procedure For Set Covering

(author(s): Egon Balas, MC Carrera) Operations Research 44(6), 1996; 875-890

• Gomory Cuts Revisited

(author(s): Egon Balas, S Ceria, Gerard Cornuejols, N Natraj) Operations Research Letters 19(1), 1996

• Weighted And Unweighted Maximum Clique Algorithms With Upper Bounds From Fractional Coloring

(author(s): Egon Balas, J Xue) Algorithmica 15(5), 1996; 397-412

• The Prize Collecting Traveling Salesman Problem 2. Polyhedral Results

Networks 25(4), 1995; 199-216

• The Precedence-Constrained Asymmetric Traveling Salesman Polytope

(author(s): Egon Balas, M FISCHETTI, WR PULLEYBLANK) Mathematical Programming 68(3), 1995; 241-265

• The One-Machine Problem With Delayed Precedence Constraints And Its Use In Job-Shop Scheduling

(author(s): Egon Balas, JK LENSTRA, A VAZACOPOULOS) Management Science 41(1), 1995; 94-109

• Linear-Time Separation Algorithms For The 3-Index Assignment Polytope

(author(s): Egon Balas, LQ QI) Discrete Applied Mathematics 43(1), 1993

• A Lift-And-Project Cutting Plane Algorithm For Mixed 0-1 Programs

(author(s): Egon Balas, S CERIA, G CORNUEJOLS) Mathematical Programming 58(3), 1993; 295-324

• A Lifting Procedure For The Asymmetric Traveling Salesman Polytope And A Large New Class Of Facets

(author(s): Egon Balas, M FISCHETTI) Mathematical Programming 58(3), 1993; 325-352

• The Fixed-Outdegree 1-Arborescence Polytope

(author(s): Egon Balas, M FISCHETTI) Mathematics Of Operations Research 17(4), 1992; 1001-1018

• A Parallel Shortest Augmenting Path Algorithm For The Assignment Problem

(author(s): Egon Balas, D MILLER, J PEKNY, P TOTH) Journal Of The Acm 38(4), 1991; 985-1004

• Minimum Weighted Coloring Of Triangulated Graphs, With Application To Maximum Weight Vertex Packing And Clique Finding In Arbitrary Graphs

(author(s): Egon Balas, X JUE) Siam Journal On Computing 20(2), 1991; 209-221

• An Algorithm For The 3-Index Assignment Problem

(author(s): Egon Balas, MJ SALTZMAN) Operations Research 39(1), 1991; 150-161

• The Perfectly Matchable Subgraph Polytope Of An Arbitrary Graph

(author(s): Egon Balas, WR PULLEYBLANK) Combinatorica 9(4), 1989; 321-337

• Sequential Convexification In Reverse Convex And Disjunctive Programming

(author(s): Egon Balas, JM TAMA, J TIND) Mathematical Programming 44(3), 1989; 337-350

• The Prize Collecting Traveling Salesman Problem

Networks 19(6), 1989; 621-636

• On The Set Covering Polytope .2. Lifting The Facets With Coefficients In (0,1,2)

(author(s): Egon Balas, SM NG) Mathematical Programming 45(1), 1989

• Facets Of The 3-Index Assignment Polytope

(author(s): Egon Balas, MJ SALTZMAN) Discrete Applied Mathematics 23(3), 1989; 201-229

• On Graphs With Polynomially Solvable Maximum-Weight Clique Problem

(author(s): Egon Balas, CS YU) Networks 19(2), 1989; 247-253

• On The Set Covering Polytope .1. All The Facets With Coefficients In (0, 1, 2)

(author(s): Egon Balas, SM NG) Mathematical Programming 43(1), 1989; 57-69

• On The Convex-Hull Of The Union Of Certain Polyhedra

Operations Research Letters 7(6), 1988; 279-283

• The Shifting Bottleneck Procedure For Job Shop Scheduling

(author(s): J ADAMS, Egon Balas, D ZAWACK) Management Science 34(3), 1988; 391-401

• On The Maximum Weight Clique Problem

(author(s): Egon Balas, V CHVATAL, J NESETRIL) Mathematics Of Operations Research 12(3), 1987; 522-535

• Some Computational Results On Real 0-1 Knapsack-Problems - Comment

(author(s): Egon Balas, R NAUSS, E ZEMEL) Operations Research Letters 6(3), 1987; 139-140

• A Fast Algorithm For Finding An Edge-Maximal Subgraph With A Tr-Formative Coloring

Discrete Applied Mathematics 15(3-Feb), 1986; 123-134

• Finding A Maximum Clique In An Arbitrary Graph

(author(s): Egon Balas, CS YU) Siam Journal On Computing 15(4), 1986; 1054-1068

• Disjunctive Programming And A Hierarchy Of Relaxations For Discrete Optimization Problems

Siam Journal On Algebraic And Discrete Methods 6(3), 1985; 466-486

• On The Facial Structure Of Scheduling Polyhedra

Mathematical Programming Study 24(OCT), 1985; 179-218

• A Sharp Bound On The Ratio Between Optimal Integer And Fractional Covers

Mathematics Of Operations Research 9(1), 1984

• Nonlinear 0-1 Programming .1. Linearization Techniques

(author(s): Egon Balas, JB MAZZOLA) Mathematical Programming 30(1), 1984

• Nonlinear 0-1 Programming .2. Dominance Relations And Algorithms

(author(s): Egon Balas, JB MAZZOLA) Mathematical Programming 30(1), 1984; 22-45

• Benders Method Revisited

(author(s): Egon Balas, C BERGTHALLER) Journal Of Computational And Applied Mathematics 9(1), 1983

• The Perfectly Matchable Subgraph Polytope Of A Bipartite Graph

(author(s): Egon Balas, W PULLEYBLANK) Networks 13(4), 1983; 495-516

• Traffic Assignment In Communication Satellites

(author(s): Egon Balas, PR LANDWEER) Operations Research Letters 2(4), 1983; 141-147

• Citation Classic - An Additive Algorithm For Solving Linear-Programs With Zero-One Variables

Current Contents/Engineering Technology & Applied Sciences, 1982; 18-18

• A Restricted Lagrangean Approach To The Traveling Salesman Problem

(author(s): Egon Balas, N CHRISTOFIDES) Mathematical Programming 21(1), 1981; 19-46

• An Algorithm For Large Zero-One Knapsack-Problems

(author(s): Egon Balas, E ZEMEL) Operations Research 28(5), 1980; 1130-1154

• Cutting Planes From Conditional Bounds - A New Approach To Set Covering

Mathematical Programming Study 12(APR), 1980; 19-36

• Pivot And Complement - A Heuristic For 0-1 Programming

(author(s): Egon Balas, CH MARTIN) Management Science 26(1), 1980; 86-96

• Set Covering Algorithms Using Cutting Planes, Heuristics, And Subgradient Optimization - A Computational Study

(author(s): Egon Balas, A HO) Mathematical Programming Study 12(APR), 1980; 37-60

• Strengthening Cuts For Mixed Integer Programs

(author(s): Egon Balas, RG JEROSLOW) European Journal Of Operational Research 4(4), 1980; 224-234

• Adjacent Vertices Of The All 0-1 Programming Polytope

(author(s): Egon Balas, MW PADBERG) Rairo-Recherche Operationnelle-Operations Research 13(1), 1979

• Facets Of Knapsack Polytope From Minimal Covers

(author(s): Egon Balas, E ZEMEL) Siam Journal On Applied Mathematics 34(1), 1978; 119-148

• Node Covering Algorithm

(author(s): Egon Balas, H SAMUELSSON) Naval Research Logistics 24(2), 1977; 213-233

• Note On Duality In Disjunctive Programming

Journal Of Optimization Theory And Applications 21(4), 1977; 523-528

• Critical cutsets of graphs and canonical facets of set packing polytopes

(author(s): Egon Balas, E Zemel) Mathematics of Operations Research 2(1), 1977; 15-19

• Set partitioning: A survey

(author(s): Egon Balas, MW Padberg) Siam Review 18(4), 1976; 710-760

• All facets of the knapsack polytope

(author(s): Egon Balas, E ZEMEL) Operations Research 23, 1975; B389-B389

• Facets Of Knapsack Polytope From Minimal Covers

(author(s): Egon Balas, E ZEMEL) Notices Of The American Mathematical Society 22(2), 1975; A322-A322

• Facets of the knapsack polytope

Mathematical Programming 8(2), 1975; 146-164

• Intersection cuts from outer polars of truncated cubes

(author(s): Egon Balas, A Zoltners) Naval Research Logistics 22(3), 1975; 477-496

• Linear characterization of permutation vectors

Notices of the American Mathematical Society 22(5), 1975; A521-A522

• Nonconvex quadratic programming via generalized polars

Siam Journal on Applied Mathematics 28(2), 1975; 335-349

• On the set-covering problem II. An algorithm for set partitioning

(author(s): Egon Balas, M PADBERG) Operations Research 23(1), 1975; 74-90

• Strengthening cuts for mixed integer programs

(author(s): Egon Balas, RG JEROSLOW) Notices of the American Mathematical Society 22(2), 1975; A321-A321

• Facets of the knapsack polytope

Notices Of The American Mathematical Society 21(1), 1974; A11-A11

• Group theoretic approach to integer programming and the 0-1 case

Operations Research 21(1), 1973; 321-322

• On the set-covering problem

(author(s): Egon Balas, MW Padberg) Operations Research 20(6), 1972; 1152-1161

• Duality in discrete programming II. The quadratic case

Management Science Series A-Theory 16(1), 1969; 14-32

WORKING PAPERS

• Final point cuts

(author(s): Egon Balas, Aleksandr Kazachkov, François Margot) 2015

• Orthant cuts as GICs and L&P cuts

(author(s): Egon Balas, Thiago Serra) 2014

• Generalized intersection cuts from certain nonconvex lattice-free sets

2014

• Partial hyperplane activation for generalized intersection cuts (revision of earlier paper)

(author(s): Egon Balas, Aleksandr Kazachkov, François Margot, Selvaprabu Nadarajah) 2014

• Final intersection points for generalized intersection cuts

(author(s): Egon Balas, Aleksandr Kazachkov) 2014

• Partial hyperplane activation for GICs with vertices of rank 1 and rank 2

2013

• Orthant cuts: generalized intersection cuts from certain nonconvex lattice-free sets

2013

• On lift-and-project cuts from four-term disjunctions for solving MIPs

(author(s): Egon Balas, Tamas Kis) 2013

• Mixed integer cuts from disjunctions with redundant terms

(author(s): Egon Balas, Andrea Qualizza) 2010

• Stronger cuts from weaker disjunctions

(author(s): Egon Balas, A. Qualizza) 2010

AWARDS AND HONORS

• Mathematical Optimization Society - Appointed to 3-member committee for selecting the winner of the Khachiyan Prize for lifetime accomplishment (2012)
• Mathematical Optimization Society - Member of Selection Committee for the Khachiyan Prize for lifetime accomplishment of the Mathematical Optimization Society (2012)
• Academy of Sciences, Bologna, Italy - corresponding member (2011)
• Profiles in Operations Research: Pioneers and Innovators, Springer, 2011, 447-462 - Honored by an essay by Graham K. Rand, Lancaster University, "Egon Balas", in A. Assad and S. Gass (editors) (2011)
• University of Liege, Belgium - Honarary Doctorate (2008)
• IFORS Hall of Fame (International Federation of Operational Research Society) - (2006)
• National Academy of Engineering - (2006)
• University of Waterloo - Honorary doctorate in Mathematics (2005)
• Hungarian Academy of Sciences - External member (2004)
• INFORMS - Fellow (2002)
• Miguel Hernandez University, Spain - Honarary Doctorate (2002)
• Special issue of Mathematical Programming for 80th Birthday (2002)
• EURO Gold Medal (2001)
• Thomas Lord Foundation - The Thomas Lord Professorship in Operations Research, a chair endowed by the Thomas Lord Foundation (1996)
• Jon von Neumann Theory Prize (1995)
• Carnegie Mellon University - University Professorship (1990)
• NSF and ONR - awardee since the early 1970''s (1970)

UNIVERSITY SERVICE

• Balas Award, occasional member of the selection committee for best summer paper (2011 - )
• University Professors’ Ad hoc committees, Committee Member (1990 - )
• Review Committee of Tepper School''s Dean, Chairperson (2006 - 2007)
• GSIA Dean''s Advisory Council, Committee Member (1990 - 2000)
• GSIA Dean Search Committee, Committee Member (1995 - 1996)
• GSIA Doctoral Committee, Committee Member (1995 - 1996)
• GSIA Dean Search Committee, Committee Member (1990 - 1991)
• Carnegie Mellon University Research Council, Committee Member (1986 - 1991)
• GSIA Doctoral Committee, Committee Member (1972 - 1987)

CONSULTING

• CombineNet, Inc. (2003 - 2010)
• Algorithmica, Inc. Developed rolling mill scheduling system used by the Cleveland Works of LTV Steel for 10 years. (1993 - 1999)
• Sumitomo Steel (January 1988 - 1991)
• LTV Steel (January 1985 - 1988)
• American Airlines (January 1984 - 1986)
• Federal Energy Administration. Developed game-theoretic model for selecting the optimal size of the Strategic Petroleum Reserve (1976)

PROFESSIONAL ACTIVITIES

• Editorial

Member of the Editorial Board, Discrete Optimization (2003-)
Member of the Editorial Board, Naval Research Logistics (2003-)
Advisory Editor, Journal of Combinatorial Optimization (1996-)
Member of the Editorial Board, Computational Optimization and Applications (1991-)
Associate Editor, Annals of Operations Research (1983-)
Member of the Editorial Board, Zeitschrift fur Operations Research (1980-)
Advisory Editor, Discrete Applied Mathematics (1976-)
Editorial Associate,European Journal of Operational Research (1976-)
Member of the Editorial Board, Revue d''Automatique, Informatique et Recherche Operationnelle (R.A.I.R.O.) (1976-2004)
Associate Editor, Operations Research (1967-1996)
Member of the Editorial Board, Ricerca Operativa (1981-1995)
Member of the Editorial Board, Cahiers du Centre d''Etudes de Recherche Operationnelle (1986-1995)
Associate Editor, Naval Research Logistics Quarterly (1979-1989) (1976 -)

• Conference Organizer, International Symposium on Mathematical Programming, Organizing Committee and the Program Committee (2015 - July 2015)
• Other professional activities

Member of the Selection Committee for the Leonid Khachyan Prize, 2012-2015.
Member of the Selection Committee for the John von Neumann Theory Prize, 1998-2001
Member of the Program Committee for the 2015 International Symposium on Mathematical Programming
Member of Program Committee, Tenth Conference on Integer Programming and Combinatorial Optimization (IPCO 10), 2004
Chairman of the Program Committee, Fourth Conference on Integer Programming and Combinatorial Optimization, (IPCO 4) 1995
Member of the Program Committee, Second Conference on Integer Programming and Combinatorial Optimization, (IPCO 2) 1992
Member of the Program Committee for the 7th, 8th, 9th, 10th, 11th, 12th, 13th, 14th, 15th and 16th International Symposium on Mathematical Programming
Council Member, Mathematical Programming Society (1988-1991)
Council Member, TIMS (1972-1975)
Chairman, TIMS Publications Committee (1974-1975) (2001)

COURSES TAUGHT

• Graph Theory (47835) 2015 Mini 1 Section: A
  2011 Mini 1 Section: A
  2009 Mini 1 Section: A
  2007 Mini 1 Section: A
  2005 Mini 1 Section: A

• Networks and Matchings (47836) 2015 Mini 2 Section: A
  2013 Mini 2 Section: A
  2011 Mini 2 Section: A
  2009 Mini 2 Section: A
  2007 Mini 2 Section: A
  2005 Mini 2 Section: A

• Integer Programming (47830) 2015 Mini 3 Section: A
  2013 Mini 3 Section: A
  2009 Mini 3 Section: A
  2007 Mini 3 Section: A
  2006 Mini 3 Section: A

• Advanced Integer Programming (47831) 2015 Mini 4 Section: A
  2013 Mini 4 Section: A
  2009 Mini 4 Section: A
  2007 Mini 4 Section: A
  2006 Mini 4 Section: A

• Convex Polytopes (47861) 2013 Mini 1 Section: A
  2012 Mini 3 Section: A
  2010 Mini 3 Section: A
  2008 Mini 2 Section: A
  2008 Mini 3 Section: A
  2006 Mini 2 Section: A

• Topics in Combinatorial Optimization (21366) 2012 Section: B

• Advanced Linear Programming (47838) 2012 Mini 4 Section: A
  2010 Mini 4 Section: A

• Linear Programming (47834) 2008 Mini 1 Section: A
  2006 Mini 1 Section: A

• Sequencing and Scheduling (45866) 2008 Mini 4 Section: A