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A survey of dynamic network flows
 Jay E. Aronson
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Dynamic network flow models describe networkstructured, decisionmaking problems over time. They are of interest because of their numerous applications and intriguing dynamic structure. The dynamic models are specially structured problems that can be solved with known general methods. However, specialized techniques have been developed to exploit the underlying dynamic structure. Here, we present a stateoftheart survey of the results, applications, algorithms and implementations for dynamic network flows.
Presented at the XII International Symposium on Mathematical Programming, Cambridge, Massachusetts, August 1985.
Prepared under National Science Foundation Grant ECS8307549. Reproduction in whole or in part is permitted for any purpose of the United States Government. This document has been approved for public release and sale; its distribution is unlimited.
 Aderohunmu, R.S. (1986) The solution of multiperiod network models with bundle constraints by aggregation. Department of Operations Research and Engineering Management, School of Engineering and Applied Sciences, Southern Methodist University, Dallas, TX
 Aderohunmu, R.S. and J.E. Aronson, Computational results of problems applying aggregation of multiperiod network models for production planning, presented at the Joint National TIMS/ORSA Meeting, Atlanta, GA (November 1985).
 Aderohunmu, R.S, Aronson, J.E. (1987) The solution of multiperiod network models with bundle constraints by aggregation. Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA
 Aderohunmu, R.S., Aronson, J.E. (1988) A forward networkbased implementation of an algorithm for solving multiperiod network problems (with bundle constraints by aggregation). College of Business Adminstration, The University of Georgia, Athens, GA
 Adolphson, D., Aronson, J.E. (1988) A forward generalized network algorithm. Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA
 Ali, A.I., D. Barnett, K. Farhangian, J.L. Kennington, B. McCarl, B. Patty, B. Shetty and P. Wong, Multicommodity network problems: Applications and computations, IIE Trans. 16(1984) 127–134.
 Ali, A.I., Helgason, R.V., Kennington, J.L., Lall, H. (1978) Primal simplex network codes: State of the art implementation technology. Networks 8: pp. 315339
 Ali, A.I., Helgason, R.V., Kennington, J.L., Lall, H. (1980) Computation comparison among three multicommodity network flow algorithms. Oper. Res. 28: pp. 9951000
 Ali, A.I., Kennington, J.L., Shetty, B. (1988) The equal flow problem. Eur. J. Oper. Res. 36: pp. 107115
 Ali, A.I., Padman, R., Thiagarajan, H. (1989) Dual algorithms for pure network problems. Oper. Res. 37: pp. 159171
 Allen, E.P. (1985) Using two sequences of pure network problems to solve the multicommodity network flow problem. Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX
 ARC: Analysis Research and Computation, Inc., PNET User's Guide, Austin, TX 78765 (1974).
 Anderson, E.J. (1979) Basic solutions and a ‘simplex’ method for a class of continuous linear programs. Optimization Techniques. SpringerVerlag, Berlin, pp. 2635
 Anderson, E.J., Nash, P., Philpott, A.B. (1982) A class of continuous network flow problems. Math. Oper. Res. 7: pp. 501514
 Anderson, E.J., Philpott, A.B. (1984) Duality and an algorithm for a class of continuous transportation problems. Math. Oper. Res. 9: pp. 222231
 Aronson, J.E. (1980) Forward linear programming. Graduate School of Industrial Administration, CarnegieMellon University, Pittsburgh, PA
 Aronson, J.E. (1980) The forward simplex method: Computational results. Graduate School of Industrial Administration, CarnegieMellon University, Pittsburg, PA
 Aronson, J.E. (1986) The multiperiod assignment problem: A multicommodity network flow model and specialized branch and bound algorithm. Eur. J. Oper. Res. 23: pp. 367381
 Aronson, J.E., Networks tutorial, in:Proc. 1988 Annual Meeting of the Decision Sciences Institute, Las Vegas, NV (November 1988).
 Aronson, J.E. and J.S. Aronofsky, Network generating models for equipment replacement with changing technology, Research in Progress, presented at the Joint National ORSA/TIMS Meeting, Dallas, TX (November 1984).
 Aronson, J.E. and J.S. Aronofsky, The integration of model generation and network optimization in a decision support environment, Technical Report 83OR5, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX (revised April 1987).
 Aronson, J.E., R.S. Barr , R.V. Helgason, J.L. Kennington, A. Loh and H. Zaki, The projective transformation algorithm by Karmarkar: A computational experiment with assignment problems, Technical Report 85OR3, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas TX (revised August 1985), presented at the TIMS XXVII International Meeting, Gold Coast City, Queensland, Australia (July 1986).
 Aronson, J.E., Chen, B.D. (1985) Decision horizon results for an infinite horizon, production planning network model. Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX
 Aronson, J.E., Chen, B.D. (1986) A forward network simplex algorithm for solving multiperiod network flow problems. Naval Research Logistics Quarterly 33: pp. 445467
 Aronson, J.E. and B.D. Chen, A primary/secondary memory implementation of a forward network simplex algorithm for multiperiod network flow problems, Computers and OR (1989a), forthcoming.
 Aronson, J.E. and B.D. Chen, A computational study of empirical decision horizons in infinite horizon, multiperiod network flow models, Working Paper No. 89275, Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA (revised January 1989b).
 Aronson, J.E., Morton, T.E., Thompson, G.L. (1984) A forward algorithm and planning horizon procedure for the production smoothing problem without inventory. Eur. J. Oper. Res. 15: pp. 348365
 Aronson, J.E., Morton, T.E., Thompson, G.L. (1985) A forward simplex method for staircase linear programs. Management Science 31: pp. 664679
 Aronson, J.E. and R.E. Steuer, An interactive procedure for solving multicriteria network flow problems, Working Paper in preparation, Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA, presented at the CORS/TIMS/ORSA Joint National Meeting, Vancouver, BC, Canada (May 1989).
 Aronson, J.E., Thompson, G.L. (1984) A survey on forward methods in mathematical programming. Large Scale Systems 7: pp. 116
 Aronson, J.E., Thompson, G.L. (1985) The solution of multiperiod personnel planning problems by the forward simplex method. Large Scale Systems 9: pp. 129139
 Assad, A.A. (1981) Analytical models in rail transportation: An annotated bibliography. INFOR 19: pp. 5980
 Assad, A.A. (1987) Multicommodity network flows: A survey. Networks 8: pp. 3792
 Baker, K.R. (1974) Scheduling a fulltime workforce to meet cyclic staffing requirements. Management Science 20: pp. 15611568
 Baker, K.R. (1976) Workforce allocation in cyclical scheduling problems. Oper. Res. Quart. 27: pp. 155155
 Baker, K.R. (1976) Workforce allocation in cyclical scheduling problems. Oper. Res. Quart. 27: pp. 155167
 Baker, L. (1977) Overview of computer based models applicable to freight container utilization. NITS, Springfield, VA
 Balas, E., Landweer, P. (1983) Traffic assignment in communication satellites. Oper. Res. Lett. 2: pp. 141147
 Balas, E., Saltzman, M.J. (1988) An algorithm for the threeindex assignment problem. Graduate School of Industrial Administration, CarnegieMellon University, Pittsburgh, PA
 Balas, E. and M.J. Saltzman, Facets of the threeindex assignment polytope, Discr. Appl. Math. (1989), forthcoming.
 Barnes, E.R. (1986) A variation on Karmarkar's algorithm for solving linear programming problems. Math. Progr. 36: pp. 174182
 Barr, R.S. (1985) Network optimization on microcomputers. Department of Operations Research and and Engineering Management, Southern Methodist University, Dallas TX
 Barr, R.S., Elam, J.J., Glover, F., Klingman, D. (1980) A network alternating path basis algorithm for transshipment problems. Extremal Methods and Systems Analysis. SpringerVerlag, NY
 Barr, R.S., Farhangian, K., Kennington, J.L. (1986) Networks with side constraints: An LU factorization update. Ann. Soc. Logistics Engineers 1: pp. 6885
 Barr, R.S., Glover, F., Klingman, D. (1974) An improved version of the outofkilter method and a comparative study of computer codes. Math. Progr. 7: pp. 6086
 Barr, R.S., Glover, F., Klingman, D. (1977) The alternating path basis algorithm for assignment problems. Math. Progr. 13: pp. 113
 Barr, R.S., Glover, F., Klingman, D. (1978) The generalized alternating path basis algorithm for transportation problems. Eur. J. Oper. Res. 2: pp. 137144
 Barr, R.S., Glover, F., Klingman, D. (1979) Enhancements to spanning tree labeling procedures for network optimization. INFOR 17: pp. 1633
 Bartholdi, J.J., Orlin, J.B., Ratliff, H.D. (1980) Cyclic scheduling via integer programs with circular ones. Oper. Res. 28: pp. 10741085
 Bartholdi, J.J., Ratliff, H.D. (1978) Unnetworks with applications to idle time scheduling. Management Science 24: pp. 850858
 Bartlett, T.E. (1957) An algorithm for the minimum number of transport units to maintain a fixed schedule. Naval Research Logistics Quarterly 4: pp. 207220
 Bean, J.C., Birge, J.R., Smith, R.L. (1987) Aggregation in dynamic programming. Oper. Res. 35: pp. 215220
 Bean, J.C., Lohmann, J.R., Smith, R.L. (1985) Dynamic infinite horizon replacement economy decision model. Engin. Econ. 30: pp. 99120
 Beck, P., Lasdon, L., Engquist, M. (1983) A reduced gradient algorithm for nonlinear network flow problems. ACM Trans. on Mathematical Software 9: pp. 5770
 Beckman, M.J. (1967) On the theory of traffic flows in networks. Traffic Quarterly 21: pp. 109116
 Bently, R.W., Lambe, T.A. (1980) Assignment of traffic to a network of signalized city streets. Transportation Research 14A: pp. 5765
 Berlin, G.N. (1979) The use of directed routes for assessing escape potential. National Fire Protection Association, Boston, MA
 Bertsekas, D.P. (1981) A new algorithm for the assignment problem. Math. Progr. 21: pp. 153171
 Bertsekas, D.P. (1985) A unified framework for primaldual methods in minimum cost network flow problems. Math. Progr. 32: pp. 125145
 Bertsekas, D.P., Distributed relaxation methods for linear network flow problems, in:Proc. 25th IEEE Conf. on Decision and Control, Athen, Greece (1986) pp. 2101–2106.
 Bertsekas, D.P. and J. Eckstein, Distributed asynchronous relaxation methods for linear network flow problems, in:Proc. IFAS87, Munich, West Germany (Pergamon Press, Oxford, UK, 1987).
 Bertsekas, D.P., Eckstein, J. (1988) Dual coordinate step methods for linear network flow problems. Math. Progr. 42: pp. 203243
 Bertsekas, D.P., Baz, D. (1987) Distributed asynchronous relaxation methods for convex network flow problems. SIAM Journal on Control and Optimization 25: pp. 7485
 Bertsekas, D.P., Hosein, P., Tseng, P. (1987) Relaxation methods for network flow problems with convex arc costs. SIAM Journal on Control and Optimization 25: pp. 12191243
 Bertsekas, D.P., Tseng, P. (1988) Relaxation methods for minimum cost ordinary and generalized network flow problems. Oper. Res. 36: pp. 93114
 Bertsekas, D.P., Tsitsiklis, J.N. (1988) Parallel and Distributed Algorithms. PrenticeHall, Englewood Cliffs NJ
 Bhaskaran, S., S. Chand and S.P. Sethi, Decision and forecast horizon procedures in operations management, Private Communication of Research in Progress (1986).
 Bhaskaran, S., Sethi, S.P. (1987) Decision and forecast horizons in a stochastic environment: A survey. Optimal Control Applications and Methods 8: pp. 201217
 Bhaumik, G. (1973) Optimum operating policies of a water distribution system with losses. The University of Texas at Austin, Austin, TX
 Bielli, M., Calicchio, G., Micoletti, B., Ricciardelli, S. (1982) The air traffic flow control problem as an application of network theory. Computers and Operations Research 9: pp. 265278
 Bixby, R., Cunningham, W. (1980) Converting linear programs to network programs. Math. Oper. Res. 5: pp. 321357
 Bixby, R.E., Fourer, R. (1988) Finding embedded network rows in linear programs. I: Extraction heuristics. Management Science 34: pp. 342376
 Bookbinder, J.H., Sethi, S.P. (1980) The dynamic transportation problem: A survey. Naval Research Logistics Quarterly 27: pp. 447452
 Bowman, E.H. (1956) Production scheduling by the transportation method of linear programming. Oper. Res. 4: pp. 100103
 Bradley, G.H. (1975) Survey of determinsitic networks. AIIE Trans. 7: pp. 222234
 Bradley, G.H., Brown, G.G., Graves, G.W. (1977) Design and implementation of largescale primal transshipment algorithms. Management Science 24: pp. 134
 Brown, G.G., McBride, R.D., Wood, R.K. (1985) Extracting embedded generalized networks from linear programming problems. Math. Progr. 32: pp. 1131
 Brown, G.G., Wright, W.G. (1984) Automatic identification of embedded network rows in largescale optimization models. Math. Progr. 29: pp. 4156
 Carey, M. (1980) A convex dynamic assignment model. School of Urban and Public Affairs, CarnegieMellon University, Pittsburth, PA
 Carey, M. (1986) A constraint qualification for a dynamic traffic assignment model. Transportation Science 20: pp. 5558
 Carey, M. (1987) Optimal timevarying flows on congested networks. Oper. Res. 35: pp. 5869
 Carey, M. (1988) An approach to modeling dynamic network flows on congested networks. School of Urban and Public Affairs, CarnegieMellon University, Pittsburgh, PA
 Carey, M., Srinivasan, A. (1982) Modeling network flows with timevarying demand. School of Urban and Public Affairs, CarnegieMellon University, Pittsburgh, PA
 Carey, M., Srinivasan, A. (1985) Externalities, optimal tolls and flow controls on congested networks with timevarying flows. School of Urban and Public Affairs, CarnegieMellon University, Pittsburgh, PA
 Carey, M. and A. Srinivasan, Congested network flows: Timevarying demands and starttime policies, Eur. J. Oper. Res. (1989), forthcoming.
 Chalmet, L.G., Francis, R.L., Saunders, P.B. (1982) Network models for building evacuation. Management Science 28: pp. 86105
 Chand, S., Morton, T.E. (1982) A perfect planning horizon procedure for a determinstic cash flow balance. Management Science 28: pp. 652669
 Chand, S., Morton, T.E. (1986) Minimal forecast horizon procedures for dynamic lot size models. Naval Research Logistics Quarterly 33: pp. 111122
 Chand, S., Sethi, S.P. (1982) Planning horizon procedures for machine replacement models with several possible replacement alternatives. Naval Research Logistics Quarterly 29: pp. 483493
 Charnes, A., Cooper, W.W. (1961) Management Models and Industrial Applications of Linear Programming. Wiley, New York
 Charnes, A., Cooper, W.W., Stedry, A. (1969) Multidimensional and dynamic assigment models with some remarks on organization design. Management Science 15: pp. B365B375
 Charnes, A., Karney, D., Klingman, D., Stutz, J., Glover, F. (1975) Past, present, and future of development, computational efficiency, and practical use of large scale transportation and transshipment computer codes. Computers and OR 2: pp. 7181
 Chen, B.D. (1985) Forward network programming. Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX
 Chen, C.J., Engquist, M. (1986) A primal simplex approach to pure processing networks. Management Science 32: pp. 15821598
 Chen, R.J., Meyer, R.R. (1988) Parallel optimization for traffic assignment. Math. Progr. 42: pp. 327345
 Choi, W., Francis, R.L., Hamacher, H.W., Tufekci, S. Network models of building evacuation problems with flowdependent exit capacities. In: Brans, J.P. eds. (1984) Operational Research. NorthHolland, Amsterdam, pp. 10471059
 Choi, W., Hamacher, H.W., Tufekci, S. (1988) Modeling of building evacuation problems by network flows with side constraints. Eur. J. Oper. Res. 35: pp. 98110
 Chvátal, V. (1983) Linear Programming. Freeman, New York
 Clark, R.H., Meyer, R.R. (1987) Multiprocessor algorithms for generalized network flows. Computer Sciences Department, University of Wisconsin, Madison, WI
 Cooke, K.L., Halsey, E. (1966) The shortest route through a network with timedependent internodal transit times. J. Math. Anal. and Appl. 14: pp. 493498
 Corban, A. (1964) A multidimensional transportation problem. Revue Roumaine des Mathematiques Pures et Appliquees 9: pp. 721735
 Corban, A. (1966) On a threedimensional transportation problem. Revue Roumaine des Mathematiques Pures et Appliquees 11: pp. 5775
 Crainic, T., Ferland, J.A., Rousseau, J.M. (1984) A tactical planning model for rail freight transportation. Transportation Science 18: pp. 165184
 Crum, R.L. (1976) Cash management in the multinational firm: A constrained generalized network approach. University of Florida, Gainesville, FL
 Crum, R.L., Dye, D.J. (1981) A network model of insurance company cash flow management. Math. Progr. Study 15: pp. 86101
 Crum, R.L., D. Klingman and L. Tavis, Implementation of largescale financial planning models: Solution, efficient transformations, J. Financial and Quantitative Analysis (1979)137–152.
 Crum, R.L., Klingman, D., Tavis, L. (1983) An operational approach to integrated working capital planning. J. Economics and Business 35: pp. 343378
 Crum, R.L., Klingman, D.D., Tavis, L.A. Strategic management of multinational companies: Networkbased planning systems. In: Shultz, R.L. eds. (1983) Applications of Management Science. JAI Press, Inc., Greenwich, CT, pp. 177201
 Cuimet, G.P. (1972) Empty freight car distribution. Queen's University, Kingston, Ontario, Canada
 Cunningham, W.H. (1976) A network simplex method. Math. Progr. 11: pp. 105116
 Cunningham, W.H. (1979) Theoretical properties of the network simplex method. Math. Oper. Res. 4: pp. 196208
 Dafermos, S. (1971) An extended traffic assignment model with application to twoway traffic. Transportation Science 5: pp. 366389
 Dafermos, S. (1972) The traffic assignment problem for multiclassuser transportation networks. Transportation Science 6: pp. 7387
 Dafermos, S. (1980) Traffic equilibrium and variational inequalities. Transportation Science 14: pp. 4254
 Dafermos, S. (1982) Relaxation algorithms for the general asymmetric traffic equilibrium problem. Transportation Science 14: pp. 231240
 Dafermos, S. (1982) The general multimodal network equilibrium problem with elastic demands. Networks 12: pp. 5772
 Dafermos, S., Nagurney, A. (1984) Sensitivity analysis for the general spatial economic equilibrium problem. Oper. Res. 32: pp. 10691086
 Dafermos, S., Nagurney, A. (1984) Sensitivity analysis for the asymmetric network equilibrium problem. Math. Progr. 28: pp. 174184
 Dafermos, S., Sparrow, F. (1969) The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards 75B: pp. 91117
 D'Ans, G.C., Gazis, D.C. (1976) Optimal control of oversaturated store and forward transportation networks. Transportation Science 10: pp. 119
 Dantzig, G.B.,Linear Programming and Extensions (Princeton, NJ, 1963).
 Dantzig, G.B., Blattner, W., Rao, M.R. Finding a cycle in a graph with minimum cost to times ratio with application to a ship routing problem. In: Rosenthiehl, P. eds. (1967) Theory of Graphs. DunodGordon and Breach, ParisNew York, pp. 7784
 Dantzig, G.B., Fulkerson, D.R. (1954) Minimizing the number of tankers to meet a fixed schedule. Naval Research Logistics Quarterly 1: pp. 217222
 Dantzig, G.B. and R.M. Van Slyke, Generalized upper bounded techniques for linear programming1, Proc. IBM Scientific Computing SymposiumCombination Problems (March 16–18, 1964) pp. 249–261; also see: Generalized upper bounded techniques, Journal of Computer System Science 1(1967)213–226.
 Decision Systems Associates, Inc., Implementation studies via simulation of the computerbased model for freight car distribution, Report prepared for U.S. Department of Transportation, FRA, DSAI, Rockville, MD (1978a).
 Computerbased model for optimal freight car distribution. U.S. Department of Transportation, DSAI, Rockville, MD
 Dejax, P.J., Crainic, T.G. (1987) A review of empty flows and fleet management models in freight transportation. Transportation Science 21: pp. 227247
 Dijkstra, E.W. (1959) A note on two problems in connexion with graphs. Numerische Mathematik 1: pp. 269271
 Drews, W.P. (1974) A simplexlike algorithm for continuoustime linear optimal control problems. Optimization Methods for Resource Allocation. English University Press, London, pp. 309322
 Dreyfus, S.E. (1969) An appraisal of some shortestpath algorithms. Oper. Res. 17: pp. 395412
 Dreyfus, S.E., Wagner, R.A. (1971) The Steiner problem in graphs. Networks 1: pp. 195207
 Elam, J.J., Glover, F., Klingman, D. (1979) A strongly convergent primal simplex algorithm for generalized networks. Math. Oper. Res. 4: pp. 3959
 Elam, J.J., Klingman, D. NETGENII: A system for generating networkbased mathematical programming test problems. In: Mulvey, J.M. eds. (1982) Evaluating Mathematical Programming Techniques. SpringerVerlag, New York
 Elnidani, M.A. (1986) The multicommodity, multiperiod assignment problem. Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX
 Elnidani, M.A., Aronson, J.E. (1989) The multicommodity, multiperiod assignment problem I: A specialized branch and bound algorithm. Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA
 Elnidani, M.A., Aronson, J.E. (1989) The multicommodity, multiperiod assignment problem II: Theoretical results. Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA
 Elnidani, M.A., Aronson, J.E. (1989) The multicommodity, multiperiod assignment problem III: Variations for facility location and personnel planning. Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA
 Erickson, R.E., Monma, C.L., Veinott, A.F. (1987) Sendandsplit method for minimumconcavecost network flows. Math. Oper. Res. 12: pp. 634664
 Ermol'ev, Y.M., Krivets, T.A., Petukhov, V.S. (1976) Planning of shipping empty seaborne containers. Cybernetics 12: pp. 664664
 Escudero, L.F. (1985) On nonlinear replicated networks. Questiio 9: pp. 5574
 Escudero, L.F. (1986) Performance evaluation of independent superbasic sets on nonlinear replicated networks. Eur. J. Oper. Res. 23: pp. 343355
 Evans, J.R. (1975) A singlecommodity transformation for certain multicommodity networks. Oper. Res. 26: pp. 673681
 Evans, J.R. (1981) The multicommodity assignment problem: A network aggregation heuristic. Computers and mathematics with Applications 7: pp. 187194
 Farina, R. and F. Glover, Optimal development and allocation of Colorado's energy resources over the coming decade, in:Energy Issues in Colorado's Future (Colorado Energy Research Institute, 1980) pp. 161–199.
 Farvolden, J.M. (1989) A primal partitioning solution for capacitated multicommodity network flow problems. Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ
 Federgruen, A., Groenevelt, H. (1986) Preemptive scheduling of uniform machines by ordinary network flow techniques. Management Science 32: pp. 341349
 Feeney, G., Controlling the distribution of empty freight cars, in:Proc. 10th National Meeting (Operations Research Society of America, 1957).
 Fernandes Grain, M.T. and M.C. Fogliatti de Sinay, Optimal distribution of empty railroad cars, in:Proc. 1st Int. Congress in France of Industrial Engineering and Management, Ecole Centrale de Paris, Paris, France (1986) pp. 21–26.
 Florez, H. (1986) Emptycontainer repositioning and leasing: An optimization model. Polytechnic Institute of New York, New York, NY
 Fong, C.O., Srinivasan, V. (1981) The multiregion dynamic capacity expansion problem, Parts I and II. Oper. Res. 29: pp. 787816
 Fong, C.O., Srinivasan, V. (1986) The multiregion dynamic capacity expansion problem: An improved heuristic. Management Science 32: pp. 11401152
 Ford, L.R., Fulkerson, D.R. (1956) Maximal flow through a network. Can. J. Math. 8: pp. 399399
 Ford, L.R., Fulkerson, D.R. (1956) Maximal flow through a network. Can. J. Math. 8: pp. 399404
 Ford, L.R., Fulkerson, D.R. (1958) Constructing maximal dynamic flows from static flows. Oper. Res. 6: pp. 419433
 Ford, L.R., Fulkerson, D.R. (1962) Flows in Networks. Princeton University Press, Princeton, NJ
 Fourer, R. (1985) A simplex algorithm for piecewiselinear programming I: Derivation and proof. Math. Progr. 33: pp. 204233
 Fourer, R. (1986) A simplex algorithm for piecewiselinear programming III: Computational analysis and applications. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL
 Fourer, R. (1988) A simplex algorithm for piecewiselinear programming II: Finiteness, feasibility and degeneracy. Math. Progr. 41: pp. 281316
 Frantzeskasis, L.F., Powell, W.B. (1988) Development and evaluation of a successive linear approximation procedure for stochastic dynamic networks. Deparment of Civil Engineering and Operations Research, Princeton University, Princeton, NJ
 Frieze, A.M. (1974) A bilinear programming formulation of the 3dimensional assignment problem. Math. Progr. 7: pp. 376379
 Frieze, A.M. (1983) Complexity of a 3dimensional assignment problem. Eur. J. Oper. Res. 13: pp. 161164
 Frieze, A.M., Yadegar, J. (1981) An algorithm for solving 3dimensional assignment problems with application to scheduling a teaching practice. J. Oper. Res. Soc. 32: pp. 989995
 Fulkerson, D.R. (1961) An outofkilter method for minimalcost flow problems. J. Society of Industrial and Applied Mathematics 9: pp. 1827
 Gaimon, C. (1986) Optimal inventory, backlogging and machine loading in a serial, multistage, multiperiod production environment. Int. J. Prod. Res. 24: pp. 647662
 Gale, D. (1957) A theorem on flows in network. Pacific J. Math. 7: pp. 10731086
 Gale, D. (1959) Transient flows in networks. Michigan Mathematical Journal 6: pp. 5963
 Garfinkel, R.S., Nemhauser, G.L. (1972) Integer Programming. Wiley, New York
 Gass, S.I. (1975) Linear Programming: Methods and Applications. McGrawHill, New York
 Gay, D.M. (1987) A variant of Karmarkar's linear programming algorithm for problems in the standard form. Math. Progr. 37: pp. 8190
 Gilbert, K.C., Hofstra, R.B. (1988) Multidimensional assignment problems. Decision Sciences 19: pp. 306321
 Gill, P.E., Murray, W., Saunders, M.A., Tomlin, J.A., Wright, M.H. (1986) On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method. Math. Progr. 36: pp. 183209
 Glickman, T.S., Sherali, H.D. (1985) Largescale network distribution of pooled empty freight cars over time, with limited substitution and equitable benefits. Transportation Research 19: pp. 8594
 Glover, F. Creating network structure in Lp's. In: Greenberg, , Maybee, eds. (1981) ComputerAssisted Analysis and Model Simplification. Academic Press, New York, pp. 361368
 Glover, F., Glover, R., Lorenzo, J., McMillan, C. (1982) The passengermix problem in the scheduled airlines. Interfaces 12: pp. 7380
 Glover, F., Glover, R., Martinson, F. (1984) A netform system for resource planning in the U.S. Bureau of Land Management. J. Oper. Res. Soc. 35: pp. 605616
 Glover, F., Hultz, J., Klingman, D. (1978) Improved computerbased planning techniques, Part I. Interfaces 8: pp. 1625
 Glover, F., Hultz, J., Klingman, D. (1979) Improved computerbased planning techniques, Part II. Interfaces 9: pp. 1220
 Glover, F., Hultz, J., Klingman, D., Stutz, J. (1978) Generalized networks: A fundamental computerbased planning tool. Management Science 24: pp. 12091220
 Glover, F., Jones, G., Karney, D., Klingman, D., Mote, J. (1979) An integrated production, distribution, and inventory planning system. Interfaces 9: pp. 2135
 Glover, F., Karney, D., Klingman, D. (1973) Doublepricing dual and feasible start algorithms for the capacitated transportation (distribution) problem. Center for Cybernetic Studies, The University of Texas at Austin, Austin, TX
 Glover, F., Karney, D., Klingman, D. (1974) Implementation and computational comparisons of primal, dual, and primaldual computer codes for minimum cost network flow problems. Networks 4: pp. 191212
 Glover, F., Karney, D., Klingman, D., Napier, A. (1974) A computational study on start procedures, basis change criteria, and solution algorithms for transportation problems. Management Science 20: pp. 793813
 Glover, F., Klingman, D. New advances in the solution of largescale network and networkrelated problems. In: Prekopa, A. eds. (1975) Colloquia Mathematica Societatis. NorthHolland, Amsterdam, pp. 210223
 Glover, F., Klingman, D. (1975) Improved labeling of L.P. bases in networks. Omega 23: pp. 220221
 Glover, F., Klingman, D. (1976) A practitioner's guide to the state of largescale network and networkrelated problems. AFIPSConference Proceedings 45: pp. 945950
 Glover, F., Klingman, D. (1977) Network applications in industry and government. AIIE Trans. 9: pp. 363376
 Glover, F., Klingman, D. Modeling and solving network problems. In: Greenberg, H. eds. (1978) Design and Implementation of Optimization Software. Sijthoff and Noordhoff, Alphen aan den Rijn
 Glover, F., Klingman, D. Mathematical optimization — a successful tool for logistics problems. In: Brans, J.P. eds. (1981) Operation Research '81. IFORS — NorthHolland, Amsterdam, pp. 453462
 Glover, F., Klingman, D. The simplex SON algorithm for LP/embedded network problems. In: Klingman, D., Mulvey, J. M. eds. (1981) Network Models and Associated Applications. NorthHolland, Amsterdam, pp. 148176
 Glover, F., Klingman, D. (1985) Basis exchange characterizations for the simplex SON algorithm for LP/embedded network problems. Mathematical Programming Study 24: pp. 141157
 Glover, F., Klingman, D. (1988) Layering strategies for creating exploitable structure in linear and integer programs. Math. Progr. 40: pp. 165182
 Glover, F., D. Klingman and C. McMillan, The netform concept: A more effective model form and solution procedure for largescale nonlinear problems,Proc. ACM '77 (Association for Computing Machinery Conference, October 1977).
 Glover, F., Klingman, D., Stutz, J. (1973) Extensions of the augmented predecessor method to generalized network problems. Transportation Science 7: pp. 377384
 Glover, F., Klingman, D., Stutz, J. (1974) Augmented threaded index method. INFOR 12: pp. 293298
 Glover, F., Martinson, F. (1982) Linear programming/netform model for vegetation allocation. Ecological Modeling. Elsevier, Amsterdam
 Glover, F., C. McMillan and P. Taylor, A computerbased decision support system for air terminal overload management,Proc. 10th Annual International Conference on Systems Sciences, Honolulu, HI (1977).
 Golden, B.L., Magnanti, T.L. (1977) Deterministic network optimization: A bibliography. Networks 7: pp. 149183
 Gorenstein, S., Poley, S., White, W. W. (1971) On the scheduling of the railroad freight operations. IBM, Philadelphia Scientific Center, Philadelphia, PA
 Gotlieb, C.C., The construction of classteacher timetables,Proc. IFIP Congress (1962) pp. 73–77.
 Gunawardane, G., A threedimensional assignment problem, presented at the ORSA/TIMS Joint National meeting, San Diego, CA (October 1982).
 Gurel, M. and D.M. Winbigler, Container provisioning for an airline network, presented at the 32nd National Meeting, ORSA, Chicago, IL (November 1967).
 Hajek, B., Ogier, R.G. (1984) Optimal dynamic routing in communciations networks with continuous traffic. Networks 14: pp. 457487
 Haghani, A.E. (1986) A combined model of train routing, makeup and empty distribution. Northwestern University, Evanston, IL
 Haghani, A.E., Daskin, M.S. (1986) A combined model of train routing, makeup and empty car distribution. Northwestern University, Evanston, IL
 Haley, K.B. (1962) The solid transportation problem. Oper. Res. 10: pp. 448463
 Haley, K.B. (1963) The multiindex problem. Oper. Res. 11: pp. 368379
 Haley, K.B. (1965) The existence of a solution to the multiindex problem. Oper. Res. Quart. 16: pp. 471474
 Halpern, J. (1979) A generalized dynamic network flows problem. Networks 9: pp. 133167
 Halpern, J., Outerbridge, R.A.M. (1977) PFLOW: A computer program for the generalized Pperiod maximal dynamic flows problem. Faculty of Business, University of Calgary, Alberta, Canada
 Halpern, J., Priess, I. (1974) Shortest path with time constraints on movement and parking. Networks 4: pp. 241253
 Hamacher, H. (1989) EJOR software exchange program. Eur. J. Oper. Res. 38: pp. 119119
 Hamacher, H.W., Tufekci, S. (1987) On the use of lexicographicminimum cost flows in evacuation modeling. Naval Research Logistics 34: pp. 487503
 Hartman, D. (1978) User's Manual: The interactive DYNAFLO program, Alevel. Manufacturing Flow Research Project, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI
 Hein, O. (1975) Naherungsverfahren für das ‘ÜberschussBedarf’ Problem. Angewandte Informatik 17: pp. 324326
 Hein, O. (1978) Naherungsverfahren für die Leerwagenverteilung. Eisenbahntechnische Rundschau 27: pp. 7377
 Helgason, R.V., Kennington, J.L. (1976) NETFLO program documentation. Department of Industrial Engineering and Operations Research, Southern Methodist University, Dallas, TX
 Helgason, R.V., Kennington, J.L. (1977) An efficient procedure for implementing a dualsimplex network flow algorithm. AIIE Trans. 9: pp. 6368
 Helgason, R.V., Kennington, J.L., Wong, P. (1982) An application of network programming for National Forest Planning. Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX
 Herren, H. (1973) The distribution of empty wagons by means of computer: Analytical model of the Swiss Federal Railways. Rail Int. 4: pp. 10051010
 Herren, H. (1977) Computercontrolled empty wagon distribution on the SBB. Rail Int. 8: pp. 2532
 Hillier, F.S., Lieberman, G.J. (1987) Introduction to Operations Research. HoldenDay, San Francisco, CA
 Ho, J.K., Loute, E. (1983) Computational experience with advanced implementation of decomposition algorithms. Math. Progr. 27: pp. 283290
 Hu, T.C., Prager, W. (1959) Network analysis of production systems. Naval Research Logistics Quarterly 6: pp. 1723
 Hughes, R.E., Powell, W.B. (1988) Mitigating and effects in the dynamic vehicle allocation model. Management Science 34: pp. 859879
 Hultz, J. (1976) Algorithms and applications for generalized networks. The University of Texas at Austin, Austin, TX
 IBM: International Business Machines Corporation, IBM Mathematical Programming System Extended/370, Mixed Integer Programming/370 (MIP/370) Program Reference Manual, White Plains, NY (November 1975).
 IBM: International Business Machines Corporation, IBM Mathematical Programming System Extended/370 Program Reference Manual, White Plains, NY (December 1979).
 Ikura, Y., Gross, G., Hall, G.S. (1986) PGandE's stateoftheart scheduling tool for hydro systems. Interfaces 16: pp. 6582
 Jarvis, J.J., Ratliff, H.D. (1982) Some equivalent objectives for dynamic network flow problems. Management Science 28: pp. 106109
 Jensen, P., Barnes, J.W. (1980) Network Flow Programming. Wiley, New York
 Johnson, E. Flows in networks. In: Moder, S. J., Elmaghraby, S.E. eds. (1979) Handbook of Operations Research. van Nostrand Rheinhold, New York, pp. 183206
 Jordan, W.C. (1982) The impact of uncertain demand and supply on empty rail car distribution. Cornell University, Ithaca, NY
 Jordan, W.C., Turnquist, M.A. (1983) A stochastic dynamic model for railroad car distribution. Transportation Science 17: pp. 123145
 Kang, M.K. (1978) Dynamic network flow models of conveyor systems. Manufacturing Flow Research Project, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI
 Karmarkar, N. (1984) A new polynomialtime algorithm for linear programming. Combinatorics 4: pp. 373395
 Karmarkar, N., A new polynomialtime algorithm for linear programming,Proc. 16th Annual ACM Symposium on the Theory of Computing (1984b) pp. 302–311.
 Karney, D., Klingman, D. (1976) Implementation and computational study on an incore outofcore primal network code. Oper. Res. 24: pp. 10561077
 Kennington, J.L. (1978) A survey of linear cost multicommodity network flows. Oper. Res. 26: pp. 209236
 Kennington, J.L., Helgason, R.V. (1980) Algorithms for Network Programming. Wiley, New York
 Kennington, J.L. and R. Muthukrishnan, An asynchronous algorithm to solve generalized network problems, presented at the ORSA/TIMS Joint National Meeting, Denver, CO (November 1988).
 Kibby, F.R., Potts, F.B. (1969) The minimum route problem with turn penalties and prohibitions. Transportation Research 3: pp. 397408
 Kim, Y., An optimal computational approach to the analysis of a generalized network of copper refining process, presented at the Joint National ORSA/TIMS/AIIE Conference, Atlantic City, NJ (1972).
 Klein, R.S., H. Luss and D.R. Smith, Multiperiod resource allocation: A lexicographic minimax approach, presented at the ORSA/TIMS Joint National Meeting, St. Louis, MO (1987).
 Klessig, R.W. (1974) An algorithm for nonlienar multicommodity flow problems. Networks 4: pp. 343355
 Klingman, D., Mote, J. (1982) A multiperiod production, distribution, and inventory planning model. Advances in Management Studies 1: pp. 5676
 Klingman, D., Mote, J., Phillips, N.V. (1988) A logistics planning system at W.R. Grace. Oper. Res. 36: pp. 811822
 Klingman, D., Napier, A., Stutz, J. (1974) NETGEN: A program for generating large scale capacitated assignment, transportation, and minimum cost flow network problems. Management Science 20: pp. 814821
 Klingman, D., Phillips, N.V., Steiger, D., Wirth, R., Padman, R., Krishnan, R. (1987) An optimizationbased integrated shortterm refined petroleum product planning system. Management Science 33: pp. 813830
 Klingman, D., Phillips, N.V., Steiger, D., Young, W. (1987) The successful deployment of management science throughout Citgo Petroleum Corporation. Interfaces 17: pp. 425
 Klingman, D., Randolph, P., Fuller, S. (1976) A cotton ginning problem. Oper. Res. 24: pp. 700718
 Konno, H. (1988) Minimum concave cost production systems: A further generalization of multiechelon model. Math. Progr. 41: pp. 185194
 Kornhauser, A.L., A very large transportation network interactive computer graphic information system and problem solver, Working Paper, Department of Civil Engineering, Transportation Program, Princeton University, Princeton, NJ, presented at the TIMS/ORSA Joint National Meeting, Boston, MA (May 1985).
 Kornhauser, A.L., Modeling for optimal real time railroad plant management, presented at the CORS/ORSA/TIMS Joint National Meeting, Vancouver, BC, Canada (May 1989).
 Kornhauser, A.L. and E.A. Adamidou, User and system optimal formulation and solution to the shared rail fleet management problem, presented at the TIMS/ORSA Joint National Meeting, Miami, FL (1986).
 Langley, R. (1973) Continuous and integer generalized flow problems. Georgia Institute of Technology, Atlanta, GA
 Lawler, E.L. (1976) Combinatorial Optimization, Networks and Matroids. Holt, Rinehart and Winston, New York
 Leue, O., Methoden zur Lösung dreidimensionaler Zuordnungsprobleme, Angewandte Informatik (April 1972) 154–162.
 Levin, A. (1969) Some fleet routing and scheduling problems for air transportation systems. Massachusetts Institute of Technology, Cambridge, MA
 Lundin, R.A., Morton, T.E. (1975) Planning horizons for the dynamic lot size model: Zabel vs. protective procedures and computational results. Oper. Res. 23: pp. 711734
 Luss, H., Smith, D.R. (1988) Multiperiod allocation of limited resources: A minimax approach. Naval Research Logistics Quarterly 35: pp. 493501
 Mangasarian, O.L. and R.R. Meyer, eds.,Parallel Methods in Mathematical Programming, Mathematical Programming 42, 2(1988), special issue.
 Marsten, R.E., The design of the XMP linear programming library, Transactions on Mathematical Software 7, 4(1981).
 Masson, G.M., Jordan, B.W. (1972) Generalized multistage connection networks. Networks 2: pp. 191209
 Maxwell, W.L., Wilson, R.C. (1981) Dynamic network flow modelling of fixed path material handling systems. AIIE Trans. 13: pp. 1221
 McBride, R.D., O'Leary, D.E., Widmeyer, G.R. (1988) A system for supporting cash management decisions. Graduate School of Business Administration, University of Southern California, Los Angeles, CA
 McCallum, C.J. (1977) A generalized upper bounding approach to a communications network planning problem. Networks 7: pp. 123
 Mendiratta, V.B. (1981) A dynamic optimization model of the empty car distribution process. Department of Civil Engineering, Northwestern University, Evanston, IL
 Mendiratta, V.B., Turnquist, M.A. (1982) A model for the management of empty freight cars. Transportation Research Rec. 838: pp. 5055
 Merchant, D.K. (1974) A study of dynamic traffic assignment and control. Cornell University, Ithaca, NY
 Merchant, D.K., Nemhauser, G.L. (1978) A model and an algorithm for the dynamic traffic assignment problem. Transportation Science 12: pp. 183199
 Merchant, D.K., Nemhauser, G.L. (1978) Optimality conditions for a dynamic traffic assignment model. Transportation Science 12: pp. 201207
 Meyer, R.R., Parallel algorithms for largescale nonlinear networks, presented at the SIAM Conference on Optimization, Houston, TX (May 1987).
 Meyer, R.R., Zenios, S.A. (1988) Parallel Optimization on Novel Computer Architectures. J.C. Baltzer, Basel
 Miller, D., J. Pekny and G.L. Thompson, Solution of large, dense transportation problems using a parallel primal algorithm, Oper. Res. Lett. (1989), forthcoming.
 Miller, L.W. (1979) Using linear programming to derive planning horizons for a production smoothing problem. Management Science 25: pp. 12321244
 Minieka, E. (1973) Maximal, lexicographic and dynamic network flows. Oper. Res. 12: pp. 517527
 Minieka, E. (1974) Dynamic network flows with are changes. Networks 4: pp. 255265
 Monma, C.L., Segal, M. (1982) A primal algorithm for finding minimumcost flows in capacitated networks with applications. The Bell System Technical Journal 61: pp. 949968
 Moravek, J., Vlach, M. (1967) On the necessary conditions for the existence of the solution of the multiindex transportation problem. Oper. Res. 15: pp. 542545
 Morton, T.E. (1978) Universal planning horizons for generalized convex production scheduling. Oper. Res. 26: pp. 10461057
 Morton, T.E., Forward algorithms for forward thinking managers, in:Applications of Management Science, ed. R.L. Schultz, Vol. 1 (JAI Press, Inc., 1981).
 Mulvey, J.M. A network portfolio approach for cash flow management, J. Cash Management (1984a) 46–48.
 Mulvey, J.M. (1984) A network planning model for the U.S. Air Traffic System. Department of Civil Engineering, Princeton University, Princeton, NJ
 Mulvey, J.M., Zenois, S.A. (1985) Solving large scale generalized networks. J. Information and Optimization Science 6: pp. 95112
 Mulvey, J.M., Zenios, S.A. (1987) Realtime operational planning for the U.S. air traffic system. Applied Numerical Mathematics 3: pp. 427441
 Murphy, F.H., Soyster, A.L. (1986) End effects in capacity expansion models with finite horizons. Naval Research Logistics Quarterly 33: pp. 373383
 Murtagh, B., Saunders, M. (1977) MINOS User's Guide. Stanford Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, CA
 Murtagh, B., Saunders, M. (1980) MINOS/Augmented User's Manual. Stanford Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, CA
 Nagurney, A. and D.S. Kim, Parallel vs. serial algorithms for largescale multicommodity spatial price equilibrium problems, International Journal of Supercomputer Applications (Spring 1989).
 Nagurney, A., Aronson, J.E. (1988) A general dynamic spatial price equilibrium model: Formulation, solution and computational results. J. Comput. Appl. Math. 22: pp. 339352
 Nagurney, A. and J.E. Aronson, A general dynamic spatial price network equilibrium model with gains and losses, Networks (1989), forthcoming.
 Nemhauser, G.L., Wolsey, L.A. (1988) Integer and Combinatorial Optimization. Wiley, New York
 Nguyen, Q.C. and R.E. Stone, A multiperiod resouree allocation problem with storable and substitutable resources, presented at the ORSA/TIMS Joint National Meeting, St. Louis, MO (1987).
 Oblak, M. and R.R. Vemuganti, The multiperiod assignment problem with changeover constraints, Working Paper, Merrick School of Business, University of Baltimore, Baltimore, MD, presented at the CORS/TIMS/ORSA Joint National Meeting, Vancouver, BC, Canada (May 1989).
 Olson, D.L., B. Shetty, M.A. Venkataramanan and I. Murthy, Network reoptimization procedures for multiobjective network problems, Ann. Oper. Res. 20(1989), this volume.
 Orlin, J.B. (1977) Quick optimal weekly scheduling with two consecutive days off. Department of Operations Research, Stanford University, Stanford, CA
 Orlin, J.B. (1983) Maximumthroughput dynamic network flows. Math. Progr. 27: pp. 214231
 Orlin, J.B. (1984) Minimum convex cost dynamic network flows. Math. Oper. Res. 9: pp. 190207
 Ouimet, G.P. (1972) Empty freight car distribution. Queen's University, Kingston, Ontario, Canada
 Perevezentsev, E.N. (1974) Scheduling of containers shipments. Proc. Central ScientificResearch Institute of the Maritime Fleet. Transport, Leningrad, USSR
 Perold, A.F. (1978) Continuous linear programming. Department of Operations Research, Stanford University, Stanford, CA
 Phillips, D., GarciaDiaz, A. (1981) Fundamentals of Network Analysis. PrenticeHall, New York
 Phillips, D.T., Ravindran, A., Solberg, J.J. (1976) Operations Research, Principles and Practice. Wiley, New York
 Philpott, A.B. (1985) Network programming in continuous time with node storage. Cambridge University, Cambridge, UK
 Pierskalla, W.P. (1967) The trisubstitution method for the threedimensional assignment problem. CORS Journal 5: pp. 7181
 Pierskalla, W.P. (1967) The multidimensional assignment and quadratic assignment problems. Case Western Reserve University, Operations Research Department, School of Management, Cleveland, OH
 Pierskalla, W.P. (1968) The multidimensional assignment problem. Oper. Res. 15: pp. 422431
 Posner, M.E., Szwarc, W. (1983) A transportation type aggregate production model with backordering. Management Science 29: pp. 188199
 Potts, R.B. Movement of empty containers within Australia, presented to the Operations Research Society of Victoria, Melbourne, Australia (September 1970).
 Powell, W.B. (1986) A stochastic model of the dynamic vehicle allocation problem. Transportation Science 20 2: pp. 117129
 Powell, W.B. (1987) An operational planning model for the dynamic vehicle allocation problem with uncertain demands. Transportation Research 21B: pp. 217232
 Powell, W.B. A comparative review of alternative algorithms for the dynamic vehicle allocation problem. In: Golden, B., Assad, A.A. eds. (1988) Vehicle Routing: Methods and Studies. NorthHolland, Amsterdam, pp. 249291
 Powell, W.B., Cape, D.J. (1988) Sensitivity analysis of dynamic networks: An application to pricing and load evaluation for truckload motor carriers. Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ
 Powell, W.B., Sheffi, Y. (1989) Design and implementation of an interactive optimization system for network design in the motor carrier industry. Oper. Res. 37: pp. 1229
 Powell, W.B., Sheffi, Y., Nickerson, K.S., Butterbaugh, K., Atherton, S. (1988) Maximizing profits for North American Van Lines' Truckload Division: A new framework for pricing and operations. Interfaces 18: pp. 2141
 Powell, W.B., Sheffi, Y., Thiriez, S. The dynamic vehicle allocation problem with uncertain demands. In: Volmuller, J., Hamerslag, R. eds. (1984) 9th Int. Symp. on Transportation and Traffic Theory. VNU Science Press, The Netherlands
 Premoli, A. (1986) Piecewiselinear programming: The compact (CPLP) algorithm. Math. Progr. 36: pp. 210227
 Propoi, A.I., Krivonozhko, V. (1977) The dynamic simplex method, RM7724. International Institute for Applied Systems Analysis, Laxenburg, Austria
 Ramsey, T.E., Rardin, R.R. (1983) Heuristics for multistage production planning problems. J. Oper. Res. Soc. 34: pp. 6170
 Rao, V.V., McGinnis, L.F. (1983) Optimal lot sizing in acyclic multiperiod production systems. IIE Trans. 15: pp. 5462
 Robillard, P. (1974) Multipath traffic assignment with dynamic input flows. Transportation Research 8: pp. 567583
 Rogers, D.F., Plante, R.D., Wong, R.T., Evans, J.R. (1988) Aggregation techniques and methodology in optimization. Department of Quantitative Analysis and Information Systems, College of Business Administration, University of Cincinnati, Cincinnati, OH
 Rosenthal, R.E. (1981) A nonlinear network flow algorithm for maximization of benefits in a hydroelectric power system. Oper. Res. 29: pp. 763786
 Rosenthal, R.E. (1986) Representing inverses in pure network flow optimization. Eur. J. Oper. Res. 23: pp. 356366
 Saksena, J.P., Kumar, S. (1966) The routing problem with ‘K’ specified nodes. Oper. Res. 14: pp. 909913
 Sandbothe, R.A. (1985) Solving the capacitated lot size model. Graduate School of Industrial Administration, CarnegieMellon University, Pittsburgh PA
 Sandbothe, R.A. and G.L. Thompson, A forward algorithm for the capacitated lot size model with stockouts, Oper. Res. (1989), forthcoming.
 Schell, E. Distribution of a product by several properties, Directorate of Management Analysis. In: Antosiewicz, H. eds. (1955) Proc. 2nd Symp. in Linear Programming. DCS/Comptroller H.Q., U.S. Air Force, Washington, DC, pp. 615642
 Sethi, A.P. (1983) Algorithmic enhancements of the simplex method. Graduate School of Industrial Administration, CarnegieMellon University, Pittsburgh, PA
 Sethi, A.P., Thompson, G.L. (1984) The pivot and probe algorithm for solving a linear program. Math. Progr. 29: pp. 219233
 Sethi, A.P., Thompson, G.L. (1986) Solution of constrained generalized transportation problems using the pivotandprobe algorithm. Computers and OR 13: pp. 19
 Sethi, A.P., G.L. Thompson and M.S. Hung, The pivotandprobe algorithm and XMP, presented at the TIMS/ORSA Joint National Meeting, Washington, DC (April 1988).
 Sethi, S.P., Chand, S. (1979) Planning horizon procedures for machine replacement models. Management Science 25: pp. 140151
 Shamma, M.M. (1971) A generalized assignment problem. Computer Science/Operations Research Center, Southern Methodist University, Dallas, TX
 Shan, Y. (1985) A dynamic multicommodity network flow model for real time optimal rail freight car management. Princeton University, Princeton, NJ
 Shanno, D.F. (1988) Computing Karmarkar projections quickly. Math. Progr. 41: pp. 6172
 Shetty, B. (1985) The equal flow problem. Department of Operations Research and Engineering Management, Southern Methodist University, Dallas TX
 Simmonard, M. (1966) Linear Programming. PrenticeHall, Englewood Cliffs, NJ
 Smith, R.L., Deferral strategies for a dynamic communications network, Networkds 9(1979)61–87.
 Srinivasan, V. (1974) A transshipment model for cash management decisions. Management Science 20: pp. 13501363
 Srinivasan, V., Thompson, G.L. (1972) Accelerated algorithms for labeling and relabeling of trees, with applications to distribution problems. Journal of the Association for Computing Machinery 19: pp. 712726
 Srinivasan, V., Thompson, G.L. (1973) Benefitcost analysis of coding techniques for the primal transportation algorithm. Journal of the Association for Computing Machinery 20: pp. 194213
 Stanley, J.D. (1984) A forward convexsimplex method with applications. School of Industrial administration, CarnegieMellon University, Pittsburgh, PA
 Stanley, J.D. (1987) A forward convexsimplex method. Eur. J. Oper. Res. 29: pp. 328335
 Steinberg, E., Napier, H.A. (1980) Optimal multilevel lot sizing for systems requirements planning. Management Science 26 12: pp. 12581271
 Stone, R.E. (1988) An algorithm for solving network problems with side variables. AT & T Bell Laboratories, Holmdel, NJ
 Szwarc, W., Posner, M.E. (1984) The tridiagonal transportation problem. Oper. Res. Lett. 3: pp. 2530
 Thompson, G.L. and R.A. Sandbothe, Bounds for the capacitated lot sized model: A transportation approach, presented at the Joint National ORSA/TIMS Meeting, Atlanta, GA (November 1985).
 Thompson, G.L., Zawack, D.J. (1985/1986) A problem expanding parametric programming method for solving the job shop scheduling problem. Ann. Oper. Res. 4: pp. 327342
 Tibrewala, R., Philippe, D., Browne, J. (1972) Optimal scheduling of two idle periods. Management Science 19: pp. 7175
 Todd, M.J. (1988) Exploiting special structure in Karmarkar's linear programming algorithm. Math. Progr. 41: pp. 97113
 Tomlin, J.A. (1988) Special ordered sets and an application to gas supply operations planning. Math. Progr. 42: pp. 6984
 Truemper, K., How to detect hidden networks and totallyunimodular subsections of linear programs, presented at the TIMS/ORSA Joint National Meeting, Chicago, IL (April 1983).
 Tseng, P. (1986) Relaxation methods for monotropic programming problems. Department of Electical Engineering and Computer Science, Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA
 Tseng, P., Bertsekas, D.P. (1987) Relaxation methods for linear programs. Math. Oper. Res. 12: pp. 569596
 Tseng, P., Bertsekas, D.P. (1987) Relaxation methods for problems with strictly convex separable costs and linear constraints. Math. Progr. 38: pp. 303321
 Tsui, L. (1978) DYNAFLO User's Manual. Manufacturing Flow Research Project, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI 48109
 Turnquist, M.A. (1986) MOVEM: A network optimization model for empty freight car distribution. School of Civil and Environmental Engineering, Cornell University, Ithaca, NY
 Turnquist, M.A. and W.C. Jordan, A computerbased method for railroad car distribution, Final Report, DTRS5680C00013, U.S. Department of Transportation, Office of University Research (1982).
 Vajda, S. (1961) Mathematical Programming. AddisonWesley, Reading, MA
 Veinott, A.F. (1969) Minimum concavecost solution of Leontief substitution models of multifacility inventory systems. Oper. Res. 17: pp. 262291
 Veinott, A.F., Wagner, H.M. (1962) Optimal capacity scheduling, I and II. Oper. Res. 10: pp. 518546
 Vemuganti, R.R., Oblak, M., Aggarwal, A. (1989) Network models for fleet management. Decision Sciences 20: pp. 182197
 Vlach, M. (1967) Branch and bound method for the three index assignment problem. EkonomickoMatematicky Obzor (Czechoslovakia) 3: pp. 181191
 Waddell, R. (1983) A model for equipment replacement decisions and policies. Interfaces 13: pp. 11
 Wagner, H.M. (1975) Principles of Operations Research. PrenticeHall, NJ
 Waddell, R. (1983) A model for equipment replacement decisions and policies. Interfaces 13: pp. 17
 Wagner, H.M. (1975) Principles of Operations Research. PrenticeHall, Englewood Cliffs, NJ
 Wagner, H.M., Whitin, T.M. (1958) Dynamic version of the economic lot size model. Management Science 5: pp. 8996
 White, W.W. (1972) Dynamic transshipment network: An algorithm and its application to the distribution of empty containers. Networks 2: pp. 211236
 White, W.W., Bomberault, A.M. (1969) A network algorithm for empty freight car allocations. IBM Systems Journal 8: pp. 147169
 Wilkinson, W.L. (1971) An algorithm for universal maximal dynamic flows in a network. Oper. Res. 19: pp. 16021612
 Wilkinson, W.L. (1973) Min/max bounds for dynamic network flows. Naval Research Logistics Quarterly 20: pp. 505516
 Williams, K.B., Haley, K.B. (1959) A practical application of linear programming in the mining industry. Oper. Res. Quart. 10: pp. 131138
 Yaged, B. (1971) Minimum cost routing for static network models. Networks 1: pp. 139172
 Yaged, B. (1973) Minimum cost routing for dynamic network models. Networks 3: pp. 193224
 Yaged, B. (1975) Economies of scale, networks, and network cost elasticity. IEEE Trans. on Systems, Man, and Cybernetics 5: pp. 3039
 Zadeh, N. (1973) On building minimum cost communications networks. Networks 3: pp. 315331
 Zadeh, N. (1974) On building minimum cost communications networks over time. Networks 4: pp. 1934
 Zahorik, A., Thomas, L.J., Trigeiro, W. (1984) Network programming models for production scheduling in multistage, multiitem, capacitated systems. Management Science 30: pp. 308325
 Zangwill, W.I. (1966) A deterministic multiperiod production scheduling model with backloggings. Management Science 13: pp. 105119
 Zangwill, W.I. (1968) Minimum concave cost flows in certain networks. Management Science 14: pp. 429450
 Zangwill, W.I. (1969) A backlogging model and a multiechelon model of a dynamic economic lot size production system — a network approach. Management Science 15: pp. 506527
 Zangwill, W.I. (1985) Setup cost reduction in series facility production. University of Chicago, Chicago, IL
 Zangwill, W.I. (1987) Eliminating inventory in a series facility production system. Management Science 33: pp. 11501164
 Zangwill, W.I. (1987) From EOQ toward ZI. Management Science 33: pp. 12091223
 Zawack, D.J., Thompson, G.L. (1987) A dynamic spacetime network flow model for city traffic congestion. Transportation Science 21: pp. 153161
 Zemanian, A.H. (1983) A dynamic marketing network with monopsonistic acquisition and perfectly competitive disposition. IEEE Trans. on Circuits and Systems 30: pp. 382387
 Zemanian, A.H. (1983) A dynamic marketing, storage and transportation system with perfect competition in each of its markets. IMA J. Appl. Math. 31: pp. 5178
 Zenios, S.A. (1986) Sequential and parallel algorithms for convex generalized network problems and related applications. Civil Engineering Department, Princeton University, Princeton, NJ
 Zenios, S.A., An annotated bibliography on parallel optimization, ORSA Journal on Computing (1989), forthcoming.
 Zenios, S.A., Lasken, R.A. (1988) Nonlinear network optimization on a massively parallel connection machine. Ann. Oper. Res. 14: pp. 147165
 Zenios, S.A., Mulvey, J.M. (1985) Simulating a distributed synchronous relaxation method for convex network problems. Department of Civil Engineering, Princeton University, Princeton, NJ
 Zenios, S.A., Mulvey, J.M. (1986) Nonlinear network programming on vector supercomputers: A study on the CRAYXMP. Oper. Res. 34: pp. 667682
 Zenios, S.A., Mulvey, J.M. (1988) A distributed algorithm for convex network optimization problems. Parallel Computing. NorthHolland, Amsterdam, pp. 4556
 Zenios, S.A., Mulvey, J.M. (1988) Vectorization and multitasking of nonlinear network programming algorithms. Math. Progr. 42: pp. 449470
 Zipkin, P. (1980) Bounds for aggregation nodes in network problems. Math. Prog. 19: pp. 155177
 Zipkin, P., Raimer, P. (1983) An improved disaggregation method for transportation problems. Math. Progr. 26: pp. 238242
 Title
 A survey of dynamic network flows
 Journal

Annals of Operations Research
Volume 20, Issue 1 , pp 166
 Cover Date
 19891201
 DOI
 10.1007/BF02216922
 Print ISSN
 02545330
 Online ISSN
 15729338
 Publisher
 Baltzer Science Publishers, Baarn/Kluwer Academic Publishers
 Additional Links
 Topics
 Industry Sectors
 Authors

 Jay E. Aronson ^{(1)}
 Author Affiliations

 1. Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Brooks Hall, 30602, Athens, Georgia, USA