Current and Recent Funded Research

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• National Science Foundation, "GOALI: Planning Horizons for Optimal Decision Making Over Time with Applications to Production Systems Optimization," DMI-0322114, Program in Manufacturing Enterprise Systems, $256,931, 2003-2006, Project Director, Robert L. Smith, Co-Principal Investigator, Dr. Danial Reaume, General Motors R & D Center. Additional support: $75,000 (direct cost) Matching Funds General Motors R & D.

Within the context of today's rapidly changing world, firms are confronted daily with the challenge of making decisions that not only make economic sense now but also position the firm for grappling with a future often characterized by rapidly evolving technology and markets. Key to making these decisions are the planning horizons employed. Historically, selection of planning horizons has been based upon tradition or engineering judgment. If that horizon is myopic, the resulting decision can be short-sighted and fail to anticipate events that can render today's decision unwise. If the horizon is too long, considerable resources may be expended to collect irrelevant data and the resulting problem can present formidable computational demands. The overall goal of this research is to provide a rational framework that leads to a planning horizon choice that is efficient and yet far-sighted, leading to decisions which are undistorted by unanticipated end-of-study effects. Examples of such decision-making problems include the sizing and timing of capacity expansions, planning for production scheduling and maintenance tasking, and the replacement and acquisition of new equipment.

We propose to validate the models and methods developed on the problem of jointly optimizing manufacture and maintenance schedules in the context of vehicle production along a collection of production lines at General Motors. The research will be collaboratively pursued with faculty and students at the University of Michigan and research engineering staff at General Motors R & D Laboratories. The intellectual merit of this work includes establishing methods and conditions under which one may finitely compute an optimal first policy to a problem with infinite data, thereby extending solution procedures to cover nonhomogeneous Markov decision processes. The broad impact of this work lies in the potential of the models, algorithms, and rules-of-thumb developed to assist decision makers in deciding how far into the future they need to look to make a wise decision today. This research will be grounded in a real application arena at General Motors with the intent of increasing the productivity and reliability of national manufacturing systems. Students will serve as interns at GM thus directly assisting in the transfer of technology both in the research and educational domains.

• National Science Foundation, "Collaborative Research: Adaptive Search for Global Optimization," (collaborative research with Professor Zelda Zabinsky, University of Washington ), DMI-0244291, Program in Operations Research, $186,596, June 1, 2003-2006, Project Director, Robert L. Smith. Additional support: $20,000 (direct cost) Matching Funds University of Michigan.

Mathematical models of complex systems, in particular those arising in engineering applications, offer an opportunity to optimize their design and operation. This can be accomplished through the selection of an objective function and decision variables that mathematically optimize system performance. Many local search algorithms exist which can find a local optimum for such models, but effective global search algorithms that promise to find a global optimum are just beginning to become available. These global optimization algorithms are compromised however by an inability to be scaled up to solve practical large scale optimization problems. It is particularly important therefore that new algorithms be developed with a rigorous theoretical foundation that makes reliable predictions about their performance as a function of the size or scale of the problems to be solved. The overall objective of this proposed research is to improve the effectiveness of global optimization methods by establishing a theoretical foundation for a class of stochastic search methods. The conceptual framework proposed is that of solving global optimization problems by stochastic emulation of distributions that concentrate around the global optimum. Development of rapid sampling algorithms can thereby lead to efficient global optimization algorithms. These algorithms will be tested on three application areas: structural optimization, shape optimization and equipment replacement under technological change. The approach promises to lead to an efficient algorithm that will render tractable problems like our three application areas.

• General Motors, "Joint Optimization of Investment, Production, and Maintenance in Production Systems," GM Collaborative Research Laboratory in Advanced Vehicle Manufacturing, $614,000 (equivalent with indirect costs), 12/2002-12/2007. Co-Project Leader, Robert L. Smith (with Daniel Reaume, General Motors).

Automotive manufacturing requires decision-making at the strategic, tactical, and operational level. These decisions include include investments, production targets, production schedules, and maintenance schedules. While optimizing any one of these decisions is beneficial, a significantly greater benefit is potentially available from the integrated optimization of the entire system of decisions. With steadily dropping vehicle prices and rising incentives, automobile manufacturers are under intense pressure to cut costs by increasing the efficiency of manufacturing operations. Simultaneously, however, flexibility is a priority since customers are demanding a more rapid introduction of new vehicle models and expecting their custom orders to be filled ever more quickly. Unfortunately, increasing flexibility generally decreases efficiency due to added investment and system complexity.

Such tradeoffs are often exacerbated by local optimization of a single aspect of a production system. For example, flexibility at a line could be increased through investment in newly flexible manufacturing equipment, but such equipment is far more expensive and less reliable than traditional dedicated equipment. Considering several lines together as a coordinated system, on the other hand, one could achieve significant flexibility with only minimal investments in moderately flexible equipment. Similarly, at a more micro-level, efficiency may be increased by closely coordinating maintenance and production activities. For example, shutting down production briefly to allow preventive maintenance to be performed leads to increased reliability and throughput that may far outweigh the production time foregone.

The objectives of this research are to:
i) Develop an integrated model of plant investment, production planning, production scheduling, and maintenance.
ii) Develop optimization techniques to optimize this model.
iii) Synthesize the results of optimization experiments into a set of key principles underlying the design and operation of production systems.

• National Science Foundation, "Complex Networks Optimization" DMI-0217283, Program in Operations Research and Production Systems, $106,841, 2002-8/31/2004, Project Director, Robert L. Smith, Co-Principal Investigator, Marina Epelman.

This research project will study optimization algorithms rooted in the ideas of game theory in the context of complex network optimization, and particularly decentralized network optimization. Probably the central issue in managing such decentralized networks has been how to set prices so as to motivate the competing users to evolve to an overall system optimal configuration. The research will investigate the powerful paradigm of economic competition in the framework of artificial dynamic games that are played off-line, resulting in an algorithm that is potentially practical for large-scale systems optimization. The basic paradigm that will be investigated derives from Fictitious Play which is an adaptive procedure wherein each player assumes that other players will play according to the empirical distribution of their previous plays. The Fictitious Play method is a novel paradigm for optimization that draws from several distinct disciplines and application areas, including classical optimization, game theory, transportation science, and queueing network protocols. The robust nature of the algorithm allows for the ill-structured black box models of real systems which seldom exhibit the kind of smoothness properties that classical optimization methods demand. Its applicability in the context of two important real-world systems: a) internet traffic routing protocols and b) dynamic route guidance will be tested.

Complex networks optimization is an important capability in a society increasingly dominated by ever more complex networks of people and machines. Examples include intelligent transportation systems, computer networks, and supply chains of customers and suppliers. The success of the research will lead to the development of a theoretical basis for the optimization of such complex-structured systems. The applicability of the proposed algorithmic paradigm of game theory through its application to realistic problems arising in the design and operation of the communications and transportation networks will be tested and refined. This research will not only lead to potential improvements in these application arenas but will also necessitate significant interactions with industry and government to insure realism for the models and data developed.

• National Science Foundation GOALI, "Large Scale Dynamic Programming for Optimizing the Design and Operation of Complex Systems with Applications to Production Line Design," DMI-9900267, Program in Operations Research and Production Systems, $205,000, 1999-2004. Project Director, Robert L. Smith, Co-Principal Investigator, Dr. Jeffrey Alden, General Motors R & D Center. Additional support: $75,000 (direct cost) Matching Funds General Motors R & D.

Dynamic programming is an extremely general framework for the formulation and solution of nonlinear discrete optimization problems. It allows for the explicit incorporation of either-or decisions as well as the effects of underlying uncertainty that may be present in the system being modeled. Its principal drawback is the tendency for the underlying state space of the formulation to grow explosively with respect to the size of the system. This grant provides funding for the development of procedures to limit to manageable proportions the growth of the state space that needs to be considered. This will be accomplished in two ways: a) Model Simlification though hierarchical state aggregation, and b) Solution Acceleration through state pruning. The former approach can introduce errors which will be controlled through the ability to compute bounds on the resulting error of the approximation. The models and algorithms developed will be implemented and validated on a large scale problem in production line design in cooperation with research staff at the General Motors R&D Center at Warren, Michigan. If this research effort is successful, the resulting ability to approximately model and optimize large scale complex systems with easily implemented dynamic progamming techniques will greatly expand the class of design and operational problems in manufacturing and service sectors that are amenable to analysis.

• National Science Foundation, "Adaptive Search for Global Optimization," (collaborative research with Professor Zelda Zabinsky, University of Washington ), DMI-9820744, Program in Operations Research and Production Systems, $204,000, 1999-2004, Project Director, Robert L. Smith.

Mathematical models of complex systems, in particular those arising in engineering applications, offer an opportunity to optimize their design and operation. This can be accomplished through the selection of an objective function and decision variables that mathematically optimize system performance. Many local search algorithms exist which can find a local optimum for such models, but effective global search algorithms that promise to find a global optimum are just beginning to become available. These global optimization algorithms are compromised however by an inability to be scaled up to solve practical large scale optimization problems. It is particularly important therefore that new algorithms be developed with a rigorous theoretical foundation that makes reliable predictions about their performance as a function of the size or scale of the problems to be solved. The overall objective of this proposed research is to improve the effectiveness of global optimization methods by establishing a theoretical foundation for a class of stochastic search methods. The conceptual framework proposed is that of solving global optimization problems by stochastic emulation of distributions that concentrate around the global optimum. Development of rapid sampling algorithms can thereby lead to efficient global optimization algorithms. These algorithms will be tested on three application areas: structural optimization, shape optimization and equipment replacement under technological change. The approach promises to lead to an efficient algorithm that will render tractable problems like our three application areas.

• National Science Foundation, "Infinite Horizon Optimization," DMI-9713723, Program in Operations Research and Production Systems, $181,000, 1997-8/31/2002, Project Director, Robert L. Smith

Most of the decision problems facing planners today are sequential in nature, requiring a series of decisions made over time, usually in the context of a changing environment. Examples include the sizing and timing of capacity expansions, planning for production scheduling, and the replacement and acquisition of new equipment. In spite of the fact that tomorrow will likely result in a very different world than the one we face today, stationary models for sequential decision making continue to be the predominant model of choice for practitioners for two fundamental reasons: a) (methodology driven) stationary models lead to finite algorithms for finding optimal policies, and b) (data driven) stationary models eliminate the need to forecast the future. We seek to develop finite algorithms and forecasting procedures for the determination of optimal decisions in the context of non-stationary models that accurately reflect a future characterized by technological change. Selection of a planning horizon for non-stationary models has been in the past based upon tradition or engineering judgment. When that horizon is myopic, the resulting decisions taken can be short-sighted and fail to properly position the firm for a future characterized by rapidly changing technology. The overall goal of this research is to provide a rational framework that leads to a planning horizon choice that is far-sighted, leading to decisions undistorted by potential end-of-study effects.

• Federal Highway Administration, "Traffic Modeling in Dynamic Route Guidance and Coordinated Signal Control,'' FHWA Grant DTFH61-94-C-00017-003, $450,000, 1993-2000, Project Director, Robert L. Smith, Co-Principal Investigator, Stephane Lafortune.

1) Dynamic Route Guidance : To develop models and algorithms for dynamic route guidance using real-time traffic information, 2) Coordinated Signal Control: To develop models and algorithms for adaptive signal control and its coordination with route guidance, and 3) Benefits of Advanced Traveler Information Systems: To quantify the potential benefits of ATIS (Advanced Traveler Information Systems).

• Army Research Office ASSERT Grant, "Optimization Algorithms for Low Energy Mobile Digital Communications Systems," ARO DAAG55-98-1-0155, $120,000, 1998-3/31/2002, Co-Principal Investigator, Robert L. Smith, Project Director, Wayne Stark.

We investigate the application of global optimization algorithms for low power communication networks.

• Army Research Office MURI Grant, "Low Energy Electronics Design for Mobile Platforms," ARO DAAH04-96-1-0377, 1997-2002, Co-Principal Investigators Sean Coffey, Jack East, Alfred Hero, Linda Katehi, Stephane Lafortune, Pinaki Mazumdar, David Neuhoff, Kamal Sarabandi, Robert L. Smith, Demosthenis Teneketzis, Kimberly Wasserman, Project Director, Wayne Stark.

In order to address the need for low-energy electronics design for mobile platforms in future Army communication systems a multidisciplinary effort is needed to investigate system and component design, simulation and optimization techniques. The emphasis in this research is on the optimization, from a systems perspective, of energy requirements for a given performance level incorporating realistic models of device and circuit characteristics and energy consumption. The objectives of our proposed program are to carry out detailed investigations to determine the best possible approaches and design methodologies to achieve significant energy reduction in a mobile platform performing various functions including communications, surveillance, detection, diagnostics, and GPS direction finding.

PhD Students

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• Stephen Baumert, "Stochastic Search Methods for Large-Scale Optimization," 2004, Chairman, Assistant Professor, Air Force Institute of Technology, Daton, Ohio.
• Theodore Lambert, "Fictitious Play for Optimizing Large Scale Complex Systems," 2002, Co-Chairman (with Marina Epelman). Assistant Professor, Truckee Meadows Community College, Reno, Nevada
• Bailey, Matthew, "State Aggregation for Large Scale Acyclic Deterministic Dynamic Programming Problems," 2001, Co-Chairman (with Jeffrey Alden) Assistant Professor, University of Pittsburgh.
• Torpong Cheevaprawatdomrong, "Monotonicity in Infinite Horizon Optimization," 2001. Staff Member, Jong Stit Co.,Ltd.,Bangkok, Thailand.
• Seksan Kiatsupaibul, "Markov Chain Monte Carlo Methods for Global Optimization," graduated 2000. VP Business Development,
  Far East Cold Storage Co., Ltd., Thailand.
• Allise Wachs, "Average Cost Optimality in Stochastic Infinite Horizon Optimization,'' graduated 1998, Co-Chairman (with Irwin Schochetman). Managing Scientist, Exponent Failure Analysis Associates, Farmington Hills, Michigan.
• Dan Reaume, "Efficient Random Search for Constrained Global and Convex Optimization,'' graduated 1997, Co-Chairman (with Edwin Romeijn). Research Engineer, General Motors Research Laboratories, Warren, Michigan.
• Alfredo Garcia, "Approximating Equilibria in Infinite Horizon Games,'' graduated 1997. Assistant Professor, University of Virginia, Charlottesville.
• Julie Chou, "Accelerating the Solution of Dynamic Programs through State Aggregation,'' graduated 1995, Co-Chairman (with Edwin Romeijn). Director of Research and Solution Development, Saltare, San Mateo California.
• William Cross, "Approximating Solutions in Infinite Horizon Optimization,'' graduated 1995, Chairman. Senior Actuarial Assistant, The St. Paul Companies, St. Paul, Minnesota.
• Karl Wunderlich, "Dynamic Link Time Prediction in Vehicular Traffic Networks,'' graduated 1994, Chairman. Member of the Technical Staff, MITRE Corp.
• David Kaufman,"Optimal Direction Choice for Hit-and-Run Acceleration,'' graduated 1992, Chairman. Consultant, AT&T Laboratories, Holmdel, NJ.
• Edwin Romeijn, "Global Optimization by Random Walk Sampling Methods,'' graduated 1992, Co-Chairman (with Alexander Rinnooy Kan). Asssociate Professor, University of Florida, Gainesville.
• Yunsun Park, "Average Optimality in Infinite Horizon Optimization,'' graduated 1990, Co-Chairman (with James C. Bean). Professor, Myong-Ji University, Korea.
• Peter Benson, "A Calculus for Infinite Horizon Optimization,'' graduated 1990, Co-Chairman (with James C. Bean). Vice President, JP Morgan, NY.
• David Kim, "Aggregation in Large Scale Markov Chains,'' graduated 1990, Chairman. Associate Professor, Department of Industrial and Manufacturing Engineering, Oregon State University, Corvallis, Oregon.
• Sarah McAllister Ryan, "Degeneracy in Discrete Infinite Horizon Optimization,'' graduated 1988, Co-Chairman (with James C. Bean). Assocaite Professor, Iowa State University, Ames, Iowa.
• Jeffrey M. Alden, "Error Bounds for Rolling Horizon Procedures,'' graduated 1987, Co-Chairman (with Stephen M. Pollock). Senior Research Engineer, General Motors Research Laboratories, Warren, Michigan.
• Zelda Zabinsky, "Computational Complexity of Adaptive Algorithms in Monte Carlo Optimization,'' graduated 1985, Chairman. Professor, University of Washington, Seattle.
• Julia L. Higle, "Deterministic Equivalence in Stochastic Infinite Horizon Problems,'' graduated 1985, Co-Chairman (with James C. Bean). Professor, University of Arizona, Tucson.
• Donald E. Brown, "A Bayesian Justification for Cross-Entropy Minimization in Decision Analysis,'' graduated 1985, Chairman. Professor, University of Virginia, Charlottesville.
• Wallace J. Hopp, "Non-homogeneous Markov Decision Processes with Applications to R & D Planning,'' graduated 1984, Co-Chairman (with James C. Bean). Professor, Northwestern University.

Publications

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1. "Existence of Efficient Solutions in Infinite Horizon Optimization under Continuous and Discrete Controls," with I.E. Schochetman, Operations Research Letters, Forthcoming, 2005.
2. "A Fictitious Play Approach to Large-Scale Optimization" with Theodore J. Lambert III and Marina A. Epelman, Operations Research, forthcoming, 2004.
3. "Infinite Horizon Production Scheduling in Time-varying Systems under Stochastic Demand," with T. Cheevaprawatdomrong, Operations Research, Volume 52, Number 1, January-February 2004.
4. "Optimal Estimation of Univariate Black Box Lipschitz Functions with Upper and Lower Error Bounds" with Zelda Zabinsky and Birna P. Kristinsdottir, Computers & Operations Research, Volume 30, Issue 10, Pages 1539-1553, September 2003.
5. "A Paradox in Equipment Replacement under Technological Improvement" with Torpong Cheevaprawatdomrong, Operations Research Letters, 31, pages 77 ­ 82, 2003.
6. "Implementing Pure Adaptive Search for Global Optimization," with Daniel Reaume and Edwin R. Romeijn, Journal of Global Optimization, Vol. 20, No. 1, pages 33-47, 2001.
7. "On the Closure of the Sum of Closed Subspaces," with I.E. Schochetman and S-K. Tsui, International Journal of Mathematics and Mathematical Sciences, v. 26, no. 5, 1-11, 2001.
8. "Solving Nonstationary Infinite Horizon Stochastic Production Planning Problems," with Alfredo Garcia, Operations Research Letters, Vol. 27, No. 3, pp. 135-141, 2000.
9. "Link Travel Time Prediction for Decentralized Route Guidance Architectures," with Karl Wunderlich and David Kaufman, IEEE Transactions on Intelligent Transportation Systems, Vol. 1, No. 1, pp. 4-14, March 2000.
10. "Markov Perfect Equilibrium Existence for a Class of Undiscounted Infinite Horizon Dynamic Games," with Alfredo Garcia, Journal of Optimization Theory and Applications, Vol. 106, No. 2, pp. 433-441, August 2000,
11. "A Finite Algorithm for Solving Infinite Dimensional Optimization Problems,'" with I.E. Schochetman, Annals of Operations Research, Special volume dedicated to A. V. Fiacco's 70th birthday, v. 101, 119-142, 2001.
12. "Solving Nonstationary Infinite Horizon Dynamic Optimization Problems," with Alfredo Garcia, Journal of Mathematical Analysis and Applications, Vol. 244, No. 2, pp 304-317, 2000.
13. "Fictitious Play for Finding System Optimal Routings in Dynamic Traffic Networks " with Alfredo Garcia and Dan Reaume, Transportation Research B, Vol. 34, pp 147-156, 2000.
14. "Parallel Algorithms for Solving Aggregated Shortest Path Problems,'' with Edwin Romeijn, Computers and Operations Research, Special Issue on Aggregation, Volume 26, Issue 10-11, pp 941-953, 1999.
15. "A Mixed Integer Linear Programming Model for Dynamic Route Guidance,'' with David Kaufman and Jason Nonis, Transportation Research Part B: Methodological, vol. 32, no. 6, pp. 431-440, 1998.
16. "Approximating Shortest Paths in Large Scale Networks with Application to Intelligent Transportation Systems,'' with Julie Chou and Edwin Romeijn, INFORMS Journal on Computing, 10 , no. 2, 163--179, 1998.
17. "Infinite Horizon Production Planning in Time Varying Systems with Convex Production and Inventory Costs,'' with Rachel Zhang, Management Science, Vol. 44, no 9:1313-20, 1998.
18. "Shadow Prices in Infinite Dimensional Linear Programming,'' with Edwin Romeijn, Mathematics of Operations Research, Vol. 23, No. 1, 239-256, Feb 1998.
19. "Existence and Discovery of Average Cost Optimal Solutions in Deterministic Infinite Horizon Optimization,'' with I.E. Schochetman, Mathematics of Operations Research, 23 , no. 2, 416--432, 1998.
20. "Approximating Extreme Points in Infinite Dimensional Convex Sets,'' with William Cross and Edwin Romeijn,
    Mathematics of Operations Research, , Vol. 23, No. 1, May, 1998.
21. "User Equilibrium Properties of Fixed Points in Iterative Dynamic Routing/Assignment Models'' with David Kaufman and Karl Wunderlich, Transportation Research C, Vol. 6, Issue 1, 1998.
22. "Direction Choice For Accelerated Convergence In Hit-and-Run Sampling,'' with David Kaufman, Operations Research, Jan-Feb, 1998.
23. "Solution Existence for Infinite Quadratic Programming,'' with I.E. Schochetman and S-K. Tsui,
    Mathematical Programming with Data Perturbations, A. Fiacco, Editor, Marcel Dekker, NY, 363-385, 1997.
24. "The Hit-and-Run Sampler: A Globally Reaching Markov Chain Sampler for Generating Arbitrary Probability Distributions," Proceedings of the Winter Simulation Conference, San Diego, 1996.
25. "An Exact Aggregation/Disaggregation Algorithm for Large Scale Markov Chains,'' with David S. Kim,
    Naval Research Logistics, Vol. 42, pp. 1115-1128, 1995.
26. "Solution Existence for Time-Varying Infinite Horizon Optimal Control,'' with I.E. Schochetman, and S.-K. Tsui,
    Journal of Mathematical Analysis and Applications, 195, 135-147, 1995.
27. "Optimal Solution Approximation for Infinite Positive-definite Quadratic Programming,'' with Peter Benson, I.E. Schochetman, and James C. Bean, Journal of Optimization Theory and Applications, 85, 235-248, 1995.
28. "Simulated Annealing and Adaptive Search in Global Optimization,'' with Edwin Romeijn, Probability in the Engineering and Informational Sciences, Vol. 8, pp. 571-590, 1994.
29. "Optimal Solution Characterization for Infinite Positive Semi-definite Quadratic Programming,'' with Peter Benson, I.E. Schochetman, and James C. Bean, Applied Mathematics Letters , Vol. 7, pp. 65-67, 1994.
30. "Simulated Annealing for Constrained Global Optimization,'' with Edwin Romeijn, Journal of Global Optimization , Vol. 5, pp. 101-126, 1994.
31. "Equipment Replacement Under Technological Change,'' with James C. Bean and Jack R. Lohmann, Naval Research Logistics , Vol. 41, pp. 117-128, 1994.
32. "Solution Approximation in Infinite Horizon Linear Quadratic Control,'' with I.E Schochetman, IEEE Transactions on Automatic Control , Vol. 39, No. 3, 596-601, 1994.
33. "Dynamic System-Optimal Traffic Assignment using a State Space Model,'' with Stephane Lafortune, Raja Sengupta, and David Kaufman, Transportation Research. Part B , Vol. 27B, No. 6, 451-472, 1993.
34. "Optimal Average Value Convergence in Nonhomogeneous Markov Decision Processes,'' with Yun Sun Park and James C. Bean, Journal of Mathematical Analysis and Applications , Vol. 179, No. 2, 525-536, 1993.
35. "Improving Hit-and-Run for Global Optimization,'' with Z. Zabinsky, J. F. McDonald, H. E. Romeijn, and D. E. Kaufman, Journal of Global Optimization , Vol. 3, 171-192, 1993.
36. "Hit-and-Run Algorithms for Generating Multivariate Distributions,'' with Claude Belisle and Edwin Romeijn, Mathematics of Operations Research , Vol 18, No. 2, 255-266, May 1993.
37. "Conditions for the Discovery of Solution Horizons,'' with James C. Bean, Mathematical Programming , Vol 59, No. 2, 215-229, 1993.
38. "Fastest Paths in Time-Dependent Networks for IVHS Applications,'' with David E. Kaufman, ITS Journal , Vol. 1, No. 1, 1993.
39. "Posterior Convergence under Incomplete Information,'' with Aharon Ben-Tal and Donald E. Brown, Systems and Management Science by Extremal Methods , Editors: F. Y. Phillips and J. J. Rousseau, Kluwer Academic Publishers, 1992, pp 245-254.
40. "Convergence of Best Approximations from Unbounded Sets,'' with I.E. Schochetman, Journal of Mathematical Analysis and Applications , Vol. 166, No. 1, pp. 112-128, 1992.
41. "Capacity Expansion Under Stochastic Demands," with James C. Bean and Julia Higle, Operations Research , Vol 40, Suppl 2, May-June 1992.
42. "Rolling Horizon Procedures in Nonhomogeneous Markov Decision Processes,'' with Jeffrey M. Alden, Operations Research , Vol. 40, Suppl. 2, S183-194, May-June 1992.
43. "Finite Dimensional Approximation in Infinite Dimensional Mathematical Programming,'' with I.E. Schochetman, Mathematical Programming , Vol. 54, No. 3, pp. 307-333, 1992.
44. "A Tie-breaking Algorithm for Discrete Infinite Horizon Optimization,'' with Sarah M. Ryan and James C. Bean, Operations Research , Vol. 40, pp. S117-S126, Jan-Feb 1992.
45. "Duality in Infinite Dimensional Linear Programming,'' with H. Edwin Romeijn and James C. Bean, Mathematical Programming , Vol. 53, pp. 79-97, 1992.
46. `Pure Adaptive Search in Global Optimization'' with Zelda Zabinsky, Mathematical Programming , Vol. 53, pp. 323-338, 1992.
47. "Shake-and-Bake Algorithms for Generating Uniform Points on the Boundary of Bounded Polyhedra,'' with C.G.E. Boender, R.J. Caron, A.H.G. Rinnooy Kan, J.F. McDonald, H. Edwin Romeijn, J. Telgen, and A.C.F. Vorst, Operations Research , Vol. 39, No. 6, pp. 935-953, November-December
    1991.
48. "An Iterative Routing/Assignment Method for Anticipatory Real-time Route Guidance,'' with D. Kaufman and K. Wunderlich, IEEE VNIS Conference Proceedings , Dearborn, MI, Oct. 20-23, pp. 693-700, 1991.
49. "Convergence of Selections with Applications in Optimization,'' with I.E. Schochetman, Journal of Mathematical Analysis and Applications , Vol. 155, pp. 278-292, 1991.
50. "Denumerable State Nonhomogeneous Markov Decision Processes'' with James C. Bean and Jean B. Lasserre, Journal of Mathematical Analysis and Applications , Vol. 153, pp. 64-77, 1990.
51. "Deterministic Equivalence in Stochastic Infinite Horizon Problems'' with Julia L. Higle and James C. Bean, Mathematics of Operations Research , Vol. 15, pp. 396-407, 1990.
52. "An Exact Aggregation/Disaggregation Algorithm for Mandatory Set Decomposable Markov Chains," with David S. Kim, In Numerical Solution of Markov Chains, W.J.Stewart (eds.), Marcel Dekker Inc., New York 1990.
53. "A Correspondance Principle for Relative Entropy Minimization'' with Donald E. Brown, Naval Research Logistics , Vol. 37, pp. 191-202, 1990.
54. "Infinite Horizon Optimization,'' with I.E. Schochetman, Mathematics of Operations Research , Vol. 14, pp. 559-574, 1989.
55. "Pure Adaptive Search in Monte Carlo Optimization,'' with Nitin R. Patel and Zelda Zabinsky, Mathematical Programming , Vol. 43, pp. 317-328, 1988.
56. "A New Optimality Criterion for Non-homogeneous Markov Decision Processes,'' with Wallace J Hopp and James C. Bean, Operations Research, Vol. 35, pp. 875-883, 1987.
57. "Forecast Horizons for the Discounted Dynamic Lot Size Problem Allowing Speculative Motive,'' with James C. Bean and Candace Y. Yano, Naval Research Logistics, Vol. 34, pp. 761-774, 1987.
58. "Aggregation in Dynamic Programming,'' with James C. Bean and John R. Birge, Operations Research , Vol. 35, pp. 215-220, 1987.
59. "Hit-and-Run Algorithms for the Identification of Nonredundant Constraints,'' with H.C.P. Berbee, C.G.E. Boender, A.H.G. Rinnooy Kan, C.L. Scheffer, and J. Telgen, Mathematical Programming Vol. 37, pp.184-207, 1987.
60. "The Expected Number of Extreme Points of a Random Linear Program,'' with Sancho E. Berenguer, Mathematical Programming 35, pp. 129-134, 1986.
61. "Optimal Capacity Expansion Over an Infinite Horizon,'' with James C. Bean, Management Science , Vol. 31, No. 12, pp. 1523-1532, 1985.
62. "A Dynamic Infinite Horizon Replacement Economy Decision Model,'' with James C. Bean and Jack R. Lohmann, The Engineering Economist , Vol. 30, No. 2, pp. 99-120, 1985.
63. "An Information Theory Model for the Evaluation of Circumstantial Evidence,'' with Allan R. Sampson, IEEE Transactions on Systems, Man, and Cybernetics , Vol. SMC-15, No. 1, pp. 9-16, 1985.
64. "Random Procedures for Nonredundant Constraint Identification in Stochastic Linear Programs,'' with John R. Birge, American Journal of Mathematics and Management Sciences , (Special Issue on Statistics in Optimization), Vol. 4, Nos. 1 and 2, pp. 41-70, 1984.
65. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed Over Bounded Regions,'' Operations Research , Vol. 32, pp. 1296-1308, 1984.
66. "Conditions for the Existence of Planning Horizons,'' with James C. Bean, Mathematics of Operations Research , Vol. 9, No. 3, pp. 391-401, August, 1984.
67. "The Asymptotic Extreme Value Distribution of the Sample Minimum of a Concave Function Under Linear 54. Constraints,'' with Nitin R. Patel, Operations Research , Vol. 3, No. 4, pp. 789-794, 1983.
68. "Assessing Risks Through the Determination of Rare Event Probabilities,'' with Allan R. Sampson, Operations Research , Vol. 8, No. 5, pp. 839-866, 1982.
69. "Random Polytopes: Their Definition, Generation, and Aggregate Properties,'' with Jerrold H. May, Mathematical Programming , Vol. 24, pp. 39-54, September, 1982.
70. "The Definition and Generation of Geometrically Random Linear Constraint Sets,'' with Jerrold H. May, in Mulvey, J. M., Ed., Evaluating Mathematical Programming Techniques , Springer- Verlag, 1982.
71. "Planning Horizons for the Deterministic Capacity Problem,'' Computers and Operations Research , (Special Issue on Recent Developments in Inventory Theory), Vol. 8, No. 3, pp. 209-220, 1981.
72. "Optimal Expansion Policies for the Deterministic Capacity Problem,'' The Engineering Economist , Vol. 24, Spring, 1980.
73. "Turnpike Results for Single Location Capacity Expansion,'' Management Science , Vol. 25, May 1979.
74. "Deferral Strategies for a Dynamic Communications Network,'' Networks , Vol. 9, No. 1, 1979.
75. "Comment on 'Probabilities Based on Circumstantial Evidence','' with Robert P. Charrow, Journal of the American Statistical Association Vol. 72, June, 1977.
76. "General Horizon Results for the Deterministic Capacity Problem,'' IEEE International Conference on Communications: Conference Record , June 1976.
77. "A Conversation on Collins,'' with Robert P. Charrow, Georgetown Law Journal , Vol. 64, No. 3, February, 1976.
78. "Upper and Lower Bounds for Probability of Guilt Based on Circumstantial Evidence,'' with Robert P. Charrow, Journal of the American Statistical Association , Vol. 70, pp. 555-560, 1975.
79. "A Review of 'Systems Analysis and Design','' Operations Research , Vol. 22, July-August, 1974.
80. "An Elementary Proof of the Duality Theorem of Linear Programming,'' Journal of Optimization Theory and Applications , Vol. 12, pp. 129-135, 1973.
81. "Accommodating Student Demand for Courses by Varying the Classroom-size Mix,'' Operations Research , Vol. 19, pp. 862-874, 1971.

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