Harold Benson
American Economic Institutions Professor of Information Systems and
Operations Management
Biography
Interests:
Global optimization, Multiple criteria decision making, Management science,
Operations management
Education:
Ph.D., Northwestern University, 1976; M.S., Northwestern University, 1973; B.S.,
University of Michigan, 1971.
Professor Benson currently teaches management science and operations
management. His recent research interests have been focused on global
optimization and multiple criteria decision making.
Author:
“Branch and Bound-Outer Approximation Algorithm for Sum-of-Ratios Fractional
Programs,” Journal of Optimization Theory and Applications, 2010; “Simplicial
Branch-and-Reduce Algorithm for Convex Programs with a Multiplicative
Constraint,” Journal of Optimization Theory and Applications, 2010;
“Branch-and-Reduce Algorithm for Convex Programs with
Additional Multiplicative Constraints,“ European Journal
of Operational Research, with E. J. Sun, 2009;
“Global Maximization of a Generalized Concave Multiplicative Function,”
Journal of Optimization Theory and Applications, 2008;
“Solving Sum-of-Ratios Fractional Programs via Concave Minimization,”
Journal of Optimization Theory and Applications, 2007;
“A Simplicial Branch and Bound Duality-Bounds Algorithm for the Linear Sumof-Ratios Problem,” European Journal of Operational Research, 2007;
“Continuous Modular Design Problem: Analysis and Solution Algorithms,”
Journal of Optimization Theory and Applications, 2006;
“Fractional Programming with Convex Quadratic Forms and Functions,”
European Journal of Operational Research, 2006; “Maximizing the Ratio
of Two Convex Functions Over a Convex Set,” Naval Research Logistics, 2006.
“A Global Optimization Approach for Generating Efficient Points for Multiobjective
Concave Fractional Programs,” Journal of Multi-Criteria Decision Analysis, 2005;
"Decomposition Branch-and-Bound Based Algorithm for Linear Programs with
Additional Multiplicative Constraints," Journal of Optimization Theory and
Applications, 2005; "On the Global Optimization of Sums of Linear Fractional
Functions over a Convex Set," Journal of Optimization Theory and Applications,
2004; "Concave Envelopes of Monomial Functions over Rectangles," Naval
Research Logistics, 2004; "On the Construction of Convex and Concave
Envelope Formulas for Bilinear and Fractional Functions on Quadrilaterals,"
Computational Optimization and Applications, 2004; "Generating Sum-of-Ratios
Test Problems in Global Optimization," Journal of Optimization Theory and
Applications, 2003; "A Weight Set Decomposition Algorithm for Finding All
Efficient Extreme Points in the Outcome Set of a Multiple Objective Linear
Program, " European Journal of Operational Research, with E. J. Sun, 2002;
"Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem," Journal
of Optimization Theory and Applications, 2002; Using Concave Envelopes to
Globally Solve the Nonlinear Sum of Ratios Problem," Journal of Global
Optimization, 2002; "Global Optimization of Nonlinear Sums of Ratios," Journal
of Mathematical Analysis and Applications, 2001; "Analysis of an Outcome Space
Formulation of the Multiplicative Programming Problem," New Frontiers of
Decision Making for the Information Technology Era, with G. Boger, 2000; "An
Outcome Space, Cutting Plane Algorithm for Linear Multiplicative Programming,
Journal of Optimization Theory and Applications, with G. Boger, 2000; "Outcome
Space Partition of the Weight Set in Multiobjective Linear Programming," Journal
of Optimization Theory and Applications, with E. Sun, 2000; "Pivoting in an
Outcome Polyhedron," Journal of Global Optimization, with E. Sun, 2000; "New
Closedness Results for Efficient Sets in Multiple Objective Mathematical
Programming," Journal of Mathematical Analysis and Applications, with E. Sun,
1999; "A Generalized Gamma-Valid Cut Procedure for Concave Minimization,"
Journal of Optimization Theory and Applications, 1999; "An Outcome Space
Branch and Bound-Outer Approximation Algorithm for Convex Multiplicative
Programming," Journal of Global Optimization, 1999; "An Outer Approximation
Algorithm for Generating All Efficient Extreme Points in the Outcome Set of a
Multiple Objective Linear Programming Problem," Journal of Global Optimization,
1998; "Global Optimization in Practice: An Application to Interactive
Multiple Objective Linear Programming," Journal of Global Optimization, with D.
Lee and J.P. McClure, 1998; "Hybrid Approach for Solving Multiple Objective
Linear Programs in Outcome Space," Journal of Optimization Theory and
Applications, 1998; "Further Analysis of an Outcome Set-Based Algorithm for
Multiple Objective Linear Programming, Journal of Optimization Theory and
Applications, 1998; "Generating the Efficient Outcome Set in Multiple Objective
Linear Programs: The Bicriteria Case," Acta Mathematica Vietnamica, 1997;
"A Multiple-Objective Linear Programming Model for the Citrus Rootstock
Selection Problem in Florida," Journal of Multi-Criteria Decision Analysis," with D.
Lee and J.P. McClure, 1997; "Multiplicative Programming Problems: Analysis and
Efficient Point Search Heuristic," Journal of Optimization Theory and
Applications, with G. Boger, 1997; "Dynamic Lot-Sizing with Setup Cost
Reduction," European Journal of Operational Research, with M. Denizel and S.
Erenguc, 1997;"Towards Finding Global Representations of Efficient Sets in
Multiple Objective Mathematical Programming," Naval Research Logistics, with
S. Sayin, 1997; "Deterministic Algorithms for Constrained Concave Minimization:
A Unified Critical Survey," Naval Research Logistics, 1996; "Outcome-Based
Algorithm for Optimizing Over the Efficient Set of a Bicriteria Linear Programming
Problem," Journal of Optimization Theory and Applications, with D. Lee, 1996;
"Scheduling Surgeries for Patients Requiring Post-Operative Intensive Care: A
Multiple Objective Integer Programming Approach," Advances in Multicriteria
Analysis, 1995; "A Geometrical Analysis of the Efficient Outcome Set in Multiple
Objective Convex Programs with Linear Criterion Functions," Journal of Global
Optimization, 1995; "Concave Minimization: Theory, Applications and
Algorithms," Handbook of Global Optimization, 1995; "A Finite Concave
Minimization Algorithm Using Branch and Bound and Neighbor Generation,"
Journal of Global Optimization, with S. Sayin, 1994; "Optimization Over the
Efficient Set: Four Special Cases," Journal of Optimization Theory and
Applications, with S. Sayin, 1994; "A Face Search Heuristic Algorithm for
Optimizing Over the Efficient Set," Naval Research Logistics, with S. Sayin,
1993; "A Bisection-Extreme Point Search Algorithm for Optimizing Over the
Efficient Set in the Linear Dependence Case," Journal of Global Optimization,
1993; "A Finite, Non-Adjacent Extreme Point Search Algorithm for Optimization
Over the Efficient Set," Journal of Optimization Theory and Applications, 1992;
"Complete Efficiency and the Initialization of Algorithms for Multiple Objective
Programming," Operations Research Letters, 1991; "Using Efficient Feasible
Directions in Interactive Multiple Objective Linear Programming," Operations
Research Letters, with Y. Aksoy, 1991; "Concave Minimization via Conical
Partitions and Polyhedral Outer Approximation," Mathematical Programming, with
R. Horst and N.V. Thoai, 1991; "An Optimization Approach for Scheduling
Internal Audits of Divisions," Decision Sciences, with W.R. Knechel, 1991; "An
All-Linear Programming Relaxation Algorithm for Optimizing Over the Efficient
Set," Journal of Global Optimization, 1991; "An Algorithm for Indefinite
Integer Quadratic Programming," Journal of Computers and Mathematics with
Applications, with S.S. Erenguc, 1991; "A Branch and Bound-Outer
Approximation Algorithm for Concave Minimization Over a Convex Set,"
Journal of Computers and Mathematics with Applications, with R. Horst, 1991; "A
Note on Adapting Methods for Continuous Global Optimization to the Discrete
Case," Annals of Operations Research, with S.S. Erenguc and R. Horst, 1990;
"Separable Concave Minimization via Partial Outer Approximation and Branch
and Bound," Operations Research Letters, 1990; An Algorithm for Concave
Integer Minimization Over a Polyhedron," Naval Research Logistics, with S.S.
Erenguc, 1990. “On the Structure and Properties of a Linear Multilevel
Programming Problem,” Journal of Optimization Theory and Applications, 1989;
“Using Convex Envelopes to Solve the Interactive Fixed Charge Linear
Programming Problem, “Journal of Optimization Theory and Applications, with S.
S. Erenguc, 1988;”A Bicriteria Mathematical Programming Model for Nutrition
Planning in Developing Nations,” Management Science, with T. L. Morin, 1987;
“On the Weighted Selection Algorithm for Certain Linear Programs with Nested
Constraint Coefficients,” Operations Research, with S.S. Erenguc, 1986; “An
Algorithm for Optimizing Over the Weakly-Efficient Set,” European Journal of
Operational Research, 1986; “The Interactive Fixed Charge Linear Programming
Problem,” Naval Research Logistics Quarterly, with S.S. Erenguc, 1986; “Finding
Certain Weakly-Efficient Vertices in Multiple Objective Linear Fractional
Programming, “ Management Science, l985; “Multiple Objective Linear
Programming with Parametric Criteria Coefficients,” Management Science, 1985;
“A Finite Algorithm for Concave Minimization Over a Polyhedron,” Naval
Research Logistics Quarterly, 1985; “On the Optimal Value Function for Certain
Linear Programs with Unbounded Optimal Solution Sets,” Journal of Optimization
Theory and Applications, 1985; “Optimization Over the Efficient Set,” Journal of
Mathematical Analysis and Applications, 1984; “Efficiency and Proper Efficiency
in Vector Maximization with Respect to Cones,” Journal of Mathematical
Analysis and Applications, 1983; “On a Domination Property for Vector
Maximization with Respect to Cones,” Journal of Optimization Theory and
Applications, 1983; “Errata Corrige,” 1984; “Admissible Points of a Convex
Polyhedron,” Journal of Optimization Theory and Applications,1982;”Algorithms
for Parametric Nonconvex Programming,” Journal of Optimization Theory and
Applications, 1982;”An Integrated Approach to the Analysis of Binary Choice
Data,” Applied Psychological Measurement, with G. W. Cermak and G. J.
Lieberman, 1982; “On the Convergence of Two Branch-and-Bound Algorithms for
Nonconvex Programming Problems,” Journal of Optimization Theory and
Applications, 1982; “Finding an Initial Efficient Extreme Point for a Linear Multiple
Objective Program,” The Journal of the Operational Research Society, 1981; “An
Improved Definition of Proper Efficiency for Vector Maximization with Respect to
Cones,” Journal of Mathematical Analysis and Applications, 1979; “Vector
Maximization with Two Objective Functions,” Journal of Optimization Theory and
Applications, 1979; “Existence of Efficient Solutions for Vector Maximization
Problems,” Journal of Optimization Theory and Applications, 1978; “The Vector
Maximization Problem: Proper Efficiency and Stability,” SIAM Journal on Applied
Mathematics, with T. L. Morin, 1977.
Current Associate Editorships:
•Journal of Optimization Theory and Applications
•Journal of Global Optimization.
Current Editorial Board Memberships:
• International Journal of Computational and Numerical Analysis and
Applications, 2000-present.
• International Journal for Rapid Publications in Mathematics, 2004-present.
• International Journal of Information Systems for Logistics and Management,
2004-present.
• International Journal of Productivity and Quality Management 2005-present.
Grants and Consulting:
Consultant for Registrar, University of Agriculture Malaysia, Selangor, Malaysia,
1996 - present; National Science Foundation Research Grant, 1986; College of
Business Administration Summer Research Grants, 1980, 1988, 1990, 19931997, 1999-2008, 2010; Consultant for American College Testing, Iowa City,
Iowa, 1983 – 84; Consultant for Shares Services, Inc., Gainesville, Florida, 1988;
Consultant for Pearson Education, Inc., Upper Saddle River, New Jersey, 2010.
Research Honors and Awards:
American Economic Institutions Professor of Information Systems and
Operations Management, Warrington College of Business
Administration, 2010-present.
American Economic Institutions Faculty Fellow, Warrington College of Business
Administration, 2005-2009.
Georg Cantor Lifetime Research Award from the International Society on Multiple
Criteria Decision Making, 2004. Description of Award: “As the highest form of
recognition that the International Society on Multiple Criteria Decision Making
bestows upon a researcher, who, over his distinguished career, has personified
the spirit of independent inquiry and whose many innovative ideas and
achievements are decidedly reflected in the theory, methodology, and practices
of MCDM.” (The International Society on Multiple Criteria Decision Making has
1470 members in 96 countries.)
American Economic Institutions Professor, Warrington College of Business
Administration, 1997-1998.
Knight-Ridder Professor, College of Business Administration, 1991-1992 and
1993-1994.
Member, Phi Beta Kappa (honorary society)
National Science Foundation Graduate Fellow in Operations Research, 19711974.
Teaching Honors and Awards:
Warrington College of Business Administration Undergraduate Faculty Member
of the Year, Decision and Information Sciences Department, 2006-2007.
(Recognized by Vote of the Warrington College of Business Administration
Student Body).
College of Business Administration, Teaching Improvement Program Award
Recipient, 1995-1996.
College of Business Administration, Highest Teacher Evaluation, First Year MBA
Core Courses, Fall, 1991.
College of Business Administration, Outstanding Teacher of the Year, Decision
and Information Sciences, 1990-1991.