Technical References and Mathematical Programming

This section offers mathematical programming citations which describe techniques useful in solving railroad resource scheduling problems. For a discussion of these citations from Kraft's (1998) dissertation, click here.

Networks, Multi Commodity Networks and Shortest Paths

Aashtiani, H. Z. and Magnanti, T. L. (1981) Equilibria on a Congested Transportation Network, SIAM Journal on Algebraic and Discrete Methods 2, (3) 213-226.

Andreatta, G. and Romeo, L. (1988) Stochastic Shortest Paths with Recourse, Networks 18, 193-204.

Ali, A.I., Kennington J.L. and Shetty, B. (1988) The Equal Flow Problem, European Journal of Operational Research 36,107-115.

Assad, A. A. (1978) Multicommodity Network Flows - A Survey, Networks 8, 37-91.

Barnhart, C. and Sheffi, Y. (1993) A Network-Based Primal-Dual Heuristic for the Solution of Multicommodity Network Flow Problems, Transportation Science 27 (2) 102-117.

Barr, R. S., Glover, F. and Klingman, D. (1974) An Improved Version of the Out-of-Kilter Method and a Comparative Study of Computer Codes, Mathematical Programming 7, 60-86.

Bradley, S. P., Hax, A.C. and Magnanti, T. L. (1977) Applied Mathematical Programming, Addison-Wesley Publishing Company.

Brown, G. G. and McBride, R. D. (1984) Solving Generalized Networks, Management Science 30 (12) 1497-1523.

Chen, S. and Saigal, R. (1977) A Primal Algorithm for Solving a Capacitated Network Flow Problem with Additional Linear Constraints, Networks 7, 59-79.

Chen, C. J. and Engquist, M. (1986) A Primal Simplex Approach to Pure Processing Networks, Management Science 32 (12) 1582-1598.

Dantzig, G. B., Orden, A. and Wolfe, P. (1955) The Generalized Simplex Method for Minimizing a Linear Form under Linear Inequality Restraints, Pacific Journal of Mathematics 5, 183-195.

Dial, R., Glover, F., Karney, D.and Klingman, D. (1979) A Computational Analysis of Alternative Algorithms and Labeling Techniques for Finding Shortest Path Trees, Networks 9, 251-248.

Dijkstra, E. W. (1959) A note on two problems in connexion (sic) with graphs, Numer. Math 1, 269-271.

Divoky, J. J. and Hung, M. S. (1990) Performance of Shortest Path Algorithms in Network Flow Problems, Management Science 36 (6).

Elam, J., Glover, F. and Klingman, D. (1979) A Strongly Convergent Primal Simplex Algorithm for Generalized Networks, Mathematics of Operations Research 4 (1) 39-59.

Farvolden, J.M., Powell W.B. and Lustig, I. J.(1993) A Primal Partitioning Solution for the Arc-Chain Formulation of a Multicommodity Network Flow Problem, Operations Research 41 (4) 669-693.

Florian, M., Nguyen, S. and Pallottino, S. (1981) A Dual Simplex Algorithm for Finding all Shortest Paths, Networks 11, 367-378.

Frederickson, G. N. (1987) Fast Algorithms for Shortest Paths in Planar Graphs, With Applications, SIAM Journal of Computing 16 (6) 1004-1022.

Fukushima, M. (1984) On the Dual Approach to the Traffic Assignment Problem, Transportation Research B 18 (3) 235-245.

Geoffrion, A. M. and Graves, G. W. (1974) Multicommodity Distribution System Design by Benders Decomposition, Management Science 20 (5) 822-844.

Glover, F. and Klingman, D. (1981) The Simplex SON Algorithm for LP/Embedded Network Problems, Mathematical Programming Study 15, 148-176.

Gopalan, R., Batta, R. and Karwan, M. H. (1990) The Equity Constrained Shortest Path Problem, Computers in Operations Research 17 (3) 297-307.

Grigoriadis, M. D. and White, W. W. (1972) A Partitioning Algorithm for the Multicommodity Network Flow Problem, Mathematical Programming 3, 157-177.

Hajek, B. and Ogier, R. G. (1984) Optimal Dynamic Routing in Communication Networks with Continuous Traffic, Networks 14, 457-487.

Halder, A.K. (1970) The Method of Competing Links, Transportation Science 4, 36-51.

Hartman, J. K. and Lasdon, L. S. (1972) A Generalized Upper Bounding Algorithm for Multicommodity Network Flow Problems, Networks 1, 333-354.

Hassin, R. (1984) On Multicommodity Flows in Planar Graphs, Networks 14, 225-235.

Hu, T. C. (1963) Multi-Commodity Network Flows, Operations Research 11, 344-360.

Jones, K.L., Lustig, I.J., Farvolden, J.M. and Powell, W.B. (1993) Multicommodity network flows: The Impact of formulation on decomposition, Mathematical Programming 62, 95-117.

Kennington, J. L. and Shalaby, M. (1977) An effective subgradient procedure for minimal cost multicommodity flow problems, Management Science 23, 994-1004.

Kennington, J. L. (1978) A Survey of Linear Cost Multicommodity Network Flows, Operations Research 26 (2) 209-236.

Marsten, R., Subramanian, R., Lustig, I. and Shanno, D. (1990) Interior Point Methods for Linear Programming: Just Call Newton, Lagrange, and Fiacco and McCormick!", Interfaces 20 ( 4) 105-116.

McBride, R. D. (1985) Solving Embedded Generalized Network Problems, European Journal of Operational Research 21, 82-92.

McBride, R. D. and Mamer, J. W. (1993) Solving Multicommodity Flow Problems with a Primal Embedded Network Simplex Algorithm, presented at Phoenix AZ ORSA/TIMS conference, November 1993.

Moss, F. H. and Segall, A. (1977) An Optimal control approach to dynamic routing in data communication networks, Part I: Principles, EE Publication 312, Technion- Israel Institute of Technology.

Moss, F. H. and Segall, A. (1978) An Optimal control approach to dynamic routing in data communication networks, Part II, Geometrical interpretation, EE Publication 319, Technion- Israel Institute of Technology.

Pape, U. (1974) Implementation and Efficiency of Moore-Algorithms for the Shortest Route Problem, Mathematical Programming 7, 212-222.

Pinar, M.C. and Zenios, S.A. (1993) Solving Nonlinear Programs with Embedded Network Structures, in Network Optimization Problems, edited by D.Z. Du and P. M. Pardalos, World Scientific Publishing Company, 177-202.

Powell, W.B. (1989) A Review of Sensitivity Results for Linear Networks and a New Approximation to Reduce the Effects of Degeneracy, Transportation Science 23 (4) 231-243.

Schrage, L. (1975) Implicit Representation of Variable Upper Bounds in Linear Programming, Mathematical Programming Study 4, 118-132.

Schultz, G.L. and Meyer, R.R. (1991) An Interior Point Method for Block Angular Optimization, SIAM Journal on Optimization 1.

Shapiro, J. F. (1977) A Note on the Primal-Dual and Out-of-Kilter Algorithms for Network Optimization Problems, Networks 7, 81-88.

Shier, D. R. (1979) On Algorithms for Finding the K Shortest Paths in a Network, Networks 9, 195-214.

Tobin, R. L. and Friesz, T. L. (1988) Sensitivity Analysis for Equilibrium Network Flow, Transportation Science 22 (4) 242-250.

Wardrop, J. G. (1952) Some Theoretical Aspects of Road Traffic Research, Proceedings, Institute of Civil Engineers Part II 1, 325-378.

Integer Programming

Balas, E. (1989) The Prize Collecting Traveling Salesman Problem, Networks 19, 621-636.

Bertsekas, D.P. and Tseng. P. (1988) Relaxation methods for minimum cost ordinary and generalized network flow problems, Operations Research 36 (1) 93-114.

Bryson, N. (1991) Parametric Programming and Lagrangian Relaxation: The Case of the Network Problem with a Single Side Constraint,"Computers and Operations Research 18 (2) 129-140.

Chajakis, E. D. (1993) Scheduling and Lagrangean Approximations, Ph.D. Dissertation, Department of Operations and Information Management, University of Pennsylvania, Philadelphia, PA.

Etcheberry, J. (1977) The Set Covering Problem: A New Implicit Enumeration Algorithm, Operations Research 25 (5) 760-772.

Fisher, M.L. and Hochbaum, D.S. (1980) Database Location in Computer Networks, Journal of the Association for Computing Machinery 27 (4) 718-735.

Fisher, M.L. (1981) The Lagrangian Relaxation Method for Solving Integer Programming Problems, Management Science 27 (1) 1-18.

Fisher, M.L (1985) An Applications Oriented Guide to Lagrangian Relaxation, Interfaces 15 (2) 10-21.

Geoffrion, A. M. (1974) Lagrangian Relaxation and its Uses in Integer Programming, Math. Programming Study (2) 82-114.

Golden, B. L., Levy, L. and Vohra, R. (1987) The Orienteering Problem, Naval Research Logistics 34, 307-318.

Guignard, M. and Rosenwein, M. B.(1989)An Improved Dual Based Algorithm for the Generalized Assignment Problem, Operations Research 37 (4) 658-663.

Guignard M. and Rosenwein, M. B. (1989) An application-oriented guide for designing Lagrangean dual ascent algorithms, European Journal of Operations Research 43, 197-205.

Held, M. and Karp, R. M. (1970) The Traveling Salesman Problem and Minimum Spanning Trees, Operations Research 18, 1138-1162.

Held, M. and Karp, R. M. (1971) The Traveling Salesman Problem and Minimum Spanning Trees: Part II, Mathematical Programming 1, 6-25.

Held, M. H., Wolfe, P. and Crowder, H. D. (1974) Validation of subgradient optimization, Mathematical Programming 6 (1) 62-88.

Kantor, M. G. and Rosenwein, M. B. (1992) The Orienteering Problem with Time Windows, Journal of the Operational Research Society 43 (6) 629-635.

Kedia, P. K. (1985) Multiplier Adjustment Method for Solving Certain Combinatorial Optimization Problems, Ph. D. Dissertation, the Department of Operations and Information Management, University of Pennsylvania, Philadelphia, PA.

Keller, C. P. (1989) Algorithms to solve the orienteering problem: A comparison. European Journal of Operational Research 41, 224-231.

Kleitman, D. J. (1971) An Algorithm for Certain Multi-Commodity Flow Problems. Networks 1, 75-90.

Leifer, A. C. and Rosenwein, M. B. (1994) Strong linear programming relaxations for the orienteering problem, European Journal of Operational Research 73, 517-523.

Miliotis, P. (1976) Integer Programming Approaches to the Traveling Salesman Problem, Mathematical Programming 10, 367-378.

Nagamochi, H. and Ibaraki, T. (1989) On max-flow min-cut and integral flow properties for multicommodity flows in directed networks, Information Processing Letters 31, 279-285.

Nagamochi, H. and Ibaraki, T. (1990) Multicommodity flows in certain planar directed networks, Discrete Applied Math. 27, 125-145.

Ramesh, R. and Brown, K. M. (1991) An efficient four-phase heuristic for the Generalized Orienteering Problem, Computers in Operations Research 18 (2) 151-161.

Rosenwein, M. B. (1986) Design and Application of Solution Methodologies to Optimize Problems in Transportation Logistics, Ph. D. Dissertation, the Department of Operations and Information Management, University of Pennsylvania, Philadelphia, PA.

Rosenwein, M. B. (1991) An Improved Bounding Procedure for the Constrained Assignment Problem, Computers and Operations Research 18 (6) 531-535.

Stochastic Programming and Chance Constraints

Bertsikas, D. P. and Tsitsiklis, J. N. (1991) An Analysis of Stochastic Shortest Path Problems, Mathematics of Operations Research 16 (3) 580-595.

Charnes, A. and Cooper, W. W. (1963) Deterministic Equivalents for Optimizing and Satisficing Under Chance Constraints, Operations Research 11, 18-39.

Cooper, L. and LeBlanc, L. J. (1977) Stochastic Transportation Problems and Other Network Related Convex Problems, Naval Research Logistics Quarterly 24, 327-337.

Malcolm, S. A. and Zenios, S. A. (1992) Robust Optimization for Power Systems Capacity Expansion under Uncertainty, Decision Sciences Department Working Paper 92-03-07, Wharton School, University of Pennsylvania, Philadelphia, PA.

Mulvey, J. M., Vanderbei, R. J., and Zenios, S. A. (1993) Robust Optimization of Large Scale Systems, Decision Sciences Department Working Paper 91-06-04 (Revised March 1993), Wharton School, University of Pennsylvania, Philadelphia, PA.

Soroush, H. and Mirchandani, P. B. (1990) The Stochastic Multicommodity Flow Problem, Networks 20, 121-155.

Scheduling Theory

Klein, R. S., Luss, H. and Smith, D. R. (1992) A Lexicographic Minimax Algorithm for Multiperiod Resource Allocation, Mathematical Programming 55 (2) Series A, 213-234.

Luss, H. and Smith, D. R. (1986) Resource Allocation among Competing Activities: A Lexicographic Minimax Approach, Operations Research Letters 5 (5) 227-231.

Luss, H. (1987) An Algorithm for Separable Non-Linear Minimax Problems, Operations Research Letters 6 (4) 159-162.

Ryu, C. (1993) Capacity-Oriented Planning and Scheduling in Production and Distribution Systems, Ph.D. Dissertation, the Department of Operations and Information Management, University of Pennsylvania, Philadelphia, PA.

Vehicle Routing

Bell, et al (1983) Improving the distribution of industrial gases with an online computerized routing and scheduling optimizer, Interfaces 13, 4-23

Christofides (1985) Vehicle Routing, in The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley.

Collins and Clavey (1986) The optimization of route scheduling: a case study, Pro 1986 International Transportation Conference.

Cornuejols and Harche (1989) Polyhedral study of the capacitated vehicle routing problem, Carnegie Mellon report.

Desrochers, Desrosiers and Solomon (1992) A new optimization algorithm for the vehicle routing problem with time windows, Research Report.

Desrochers, Lenstra, Savelsbergh and Soumis (1988) Vehicle routing with time windows: optimization and approximation, Chapter 4 in Vehicle Routing: Methods and Studies, North Holland.

Fisher, M. L. (1992) Vehicle Routing, a chapter in Handbook on Operations Research and Management Science: Volume on Networks and Distribution.

Fisher, M. L. (1991) A Polynomial Algorithm for the Degree Constrained Minimum K-Tree Problem, Working Paper 91-07-06, Department of Operations and Information Management, Wharton School, University of Pennsylvania, Philadelphia, Pa.

Fisher, M. L. (1990) Optimal solution of vehicle routing using K-trees, Working Paper, Department of Operations and Information Management, Wharton School, University of Pennsylvania, Philadelphia, Pa.

Fisher, Greenfield, Jaikumar and Lester (1982) A computerized vehicle routing application, Interfaces 12, 42-52.

Fisher, Greenfield, Jaikumar and Kedia (1982) Real-time scheduling of a bulk delivery fleet: practical application of Lagrangean relaxation,Working Paper, Department of Operations and Information Management, Wharton School, University of Pennsylvania, Philadelphia, Pa.

Fisher and Jaikumar (1981) A generalized assignment heuristic for vehicle routing, Networks 11, 109-124.

Fisher, M. L., Jaikumar, R. and Van Wassenhove, L. N. (1986) A Multiplier Adjustment Method for the Generalized Assignment Problem, Management Science 32 (9) 1095-1103.

Glover and Klingman (1984) A note on admissible exchanges in spanning trees, Adv in Management Studies 3, 101-104.

Glover and Klingman (1983) Finding minimum spanning trees with a fixed number of links at a node, Colloquia Mathematica Societatis, 425-439.

Golden and Assad (1986) Perspectives on vehicle routing: exciting new developments, Operations Research 34, 803-810.

Kolen, Rinnooy Kan and Trienekens (1987) Vehicle routing with time windows, Operations Research 35, 266-273.

Koskosidias, Powell and Solomon, M. (1992) An Optimization Based Heuristic for Vehicle Routing and Scheduling with Time Window Constraints, Transportation Science 26 (2) 69-85.

Laporte and Nobert (1987) Exact algorithms for the vehicle routing problem, Annals of Discrete Math 31, 147-184.

Madsen (1990) Lagrangean relaxation and vehicle routing, IMSOR Research report.

Nygard, Greenberg, Bolkan and Swanson (1988) Generalized assignment methods for the deadline vehicle routing problem, in Vehicle Routing: Methods and Studies, North-Holland.

Zielinski (1985) Implementing a computerized vehicle routing system: a case study, Auerbach Reports 1, 1-14.

Logit Models and Consumer Choice

Anderson, S. P., DePalma, A. and Thisse, J.F. (1988) A Representative Consumer Theory of the Logit Model, International Economic Review 29 (3) 461-466.

Borsch-Supan, A. (1990) On the Compatibility of Nested Logit Models with Utility Maximization, Journal of Econometrics 43 (3) 373-388.

Green, P. E. and Krieger, A. M. (1988) Choice Rules and Sensitivity Analysis in Conjoint Simulators, Journal of the Academy of Marketing Science 16 (1) 114-127.

Koning, R. H and Ridder, G. (1994) On the compatibility of nested logit models with Utility Maximization, Journal of Econometrics 63 (2) 389-396.

Manrai, A. K. (1995) Mathematical models of Brand Choice Behavior, European Journal of Operational Research 82 (1) 1-17.

Simulation Theory

Ho, Y. C., ed. (1992) Discrete Event Dynamic Systems: Analyzing Complexity and Performance in the Modern World, IEEE Press.

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Last Updated: March 23, 2002