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A survey of dynamic network flows

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Abstract

Dynamic network flow models describe network-structured, decision-making 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 state-of-the-art survey of the results, applications, algorithms and implementations for dynamic network flows.

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References

  • Aderohunmu, R.S., The solution of multiperiod network models with bundle constraints by aggregation, Doctoral Dissertation, Department of Operations Research and Engineering Management, School of Engineering and Applied Sciences, Southern Methodist University, Dallas, TX (August, 1986).

    Google Scholar 

  • 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 and J.E. Aronson, The solution of multiperiod network models with bundle constraints by aggregation, Working Paper No. 87-244, Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA (December 1987).

    Google Scholar 

  • Aderohunmu, R.S. and J.E. Aronson, A forward network-based implementation of an algorithm for solving multiperiod network problems (with bundle constraints by aggregation), Working Paper (forthcoming), College of Business Adminstration, The University of Georgia, Athens, GA, presented at TIMS/ORSA Washington, DC (April 1988).

    Google Scholar 

  • Adolphson, D. and J.E. Aronson, A forward generalized network algorithm, Private Communication of Research in Progress, Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA (1988).

    Google Scholar 

  • 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., R.V. Helgason, J.L. Kennington and H. Lall, Primal simplex network codes: State of the art implementation technology, Networks 8(1978)315–339.

    Google Scholar 

  • Ali, A.I., R.V. Helgason, J.L. Kennington and H. Lall, Computation comparison among three multicommodity network flow algorithms, Oper. Res. 28(1980)995–1000.

    Google Scholar 

  • Ali, A.I., J.L. Kennington and B. Shetty, The equal flow problem, Eur. J. Oper. Res. 36(1988) 107–115.

    Google Scholar 

  • Ali, A.I., R. Padman and H. Thiagarajan, Dual algorithms for pure network problems, Oper. Res. 37, 1(1989)159–171.

    Google Scholar 

  • Allen, E.P., Using two sequences of pure network problems to solve the multicommodity network flow problem, Doctoral Dissertation, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX (May 1985).

    Google Scholar 

  • ARC: Analysis Research and Computation, Inc., PNET User's Guide, Austin, TX 78765 (1974).

  • Anderson, E.J., Basic solutions and a ‘simplex’ method for a class of continuous linear programs, in:Optimization Techniques, Proc. 9th IFIP Conf. on Optimization Techniques, Warsaw, Poland (Springer-Verlag, Berlin, 1979), pp. 26–35.

    Google Scholar 

  • Anderson, E.J., P. Nash and A.B. Philpott, A class of continuous network flow problems, Math. Oper. Res. 7,4(1982)501–514.

    Google Scholar 

  • Anderson, E.J., and A.B. Philpott, Duality and an algorithm for a class of continuous transportation problems, Math. Oper. Res. 9, 2(1984)222–231.

    Google Scholar 

  • Aronson, J.E., Forward linear programming, Doctoral Dissertation, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA (April 1980a).

    Google Scholar 

  • Aronson, J.E., The forward simplex method: Computational results, Working Paper No. 62-79-80, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburg, PA (April 1980b).

    Google Scholar 

  • Aronson, J.E., The multiperiod assignment problem: A multicommodity network flow model and specialized branch and bound algorithm, Eur. J. Oper. Res. 23(1986)367–381.

    Google Scholar 

  • 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 83-OR-5, 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 85-OR-3, 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. and B.D. Chen, Decision horizon results for an infinite horizon, production planning network model, Technical Report 85-OR-11, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX (September 1985).

    Google Scholar 

  • Aronson, J.E. and B.D. Chen, A forward network simplex algorithm for solving multiperiod network flow problems, Naval Research Logistics Quarterly, 33, 3(1986)445–467.

    Google Scholar 

  • 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. 89-275, Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA (revised January 1989b).

  • Aronson, J.E., T.E. Morton and G.L. Thompson, A forward algorithm and planning horizon procedure for the production smoothing problem without inventory, Eur. J. Oper. Res. 15, 3(1984)348–365.

    Google Scholar 

  • Aronson, J.E., T.E. Morton and G.L. Thompson, A forward simplex method for staircase linear programs, Management Science 31, 6(1985)664–679.

    Google Scholar 

  • 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. and G.L. Thompson, A survey on forward methods in mathematical programming, Large Scale Systems 7(1984)1–16.

    Google Scholar 

  • Aronson, J.E. and G.L. Thompson, The solution of multiperiod personnel planning problems by the forward simplex method, Large Scale Systems 9(1985)129–139.

    Google Scholar 

  • Assad, A.A., Analytical models in rail transportation: An annotated bibliography, INFOR 19, 1(1981)59–80.

    Google Scholar 

  • Assad, A.A., Multicommodity network flows: A survey, Networks 8, 1(1987)37–92.

    Google Scholar 

  • Baker, K.R., Scheduling a full-time workforce to meet cyclic staffing requirements, Management Science 20(1974)1561–1568.

    Google Scholar 

  • Baker, K.R., Workforce allocation in cyclical scheduling problems, Oper. Res. Quart. 27(1976)155.

    Google Scholar 

  • Baker, K.R. Workforce allocation in cyclical scheduling problems, Oper. Res. Quart. 27(1976) 155–167.

    Google Scholar 

  • Baker, L., Overview of computer based models applicable to freight container utilization, Report prepared for U.S. Department of Transportation, NITS, Springfield, VA (1977).

    Google Scholar 

  • Balas, E. and P. Landweer, Traffic assignment in communication satellites Oper. Res. Lett. 2(1983) 141–147.

    Google Scholar 

  • Balas, E. and M.J. Saltzman, An algorithm for the three-index assignment problem, Management Science Research Report 550, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA (September 1988).

    Google Scholar 

  • Balas, E. and M.J. Saltzman, Facets of the three-index assignment polytope, Discr. Appl. Math. (1989), forthcoming.

  • Barnes, E.R., A variation on Karmarkar's algorithm for solving linear programming problems, Math. Progr. 36, 2(1986)174–182.

    Google Scholar 

  • Barr, R.S., Network optimization on microcomputers, Department of Operations Research and and Engineering Management, Southern Methodist University, Dallas TX. Presented at the ORSA/TIMS Joint National Meeting, Boston, MA (April 1985).

    Google Scholar 

  • Barr, R.S., J.J. Elam, F. Glover and D. Klingman, A network alternating path basis algorithm for transshipment problems, in:Extremal Methods and Systems Analysis (Springer-Verlag, NY, 1980).

    Google Scholar 

  • Barr, R.S., K. Farhangian and J.L. Kennington, Networks with side constraints: An LU factorization update. Ann. Soc. Logistics Engineers 1, 1(1986)68–85.

    Google Scholar 

  • Barr, R.S., F. Glover and D. Klingman, An improved version of the out-of-kilter method and a comparative study of computer codes, Math. Progr. 7, 1(1974)60–86.

    Google Scholar 

  • Barr, R.S., F. Glover and D. Klingman, The alternating path basis algorithm for assignment problems, Math. Progr. 13, 1(1977)1–13.

    Google Scholar 

  • Barr, R.S., F. Glover and D. Klingman, The generalized alternating path basis algorithm for transportation problems, Eur. J. Oper. Res. 2(1978)137–144.

    Google Scholar 

  • Barr, R.S., F. Glover and D. Klingman, Enhancements to spanning tree labeling procedures for network optimization, INFOR 17, 1(1979)16–33.

    Google Scholar 

  • Bartholdi III, J.J., J.B. Orlin and H.D. Ratliff, Cyclic scheduling via integer programs with circular ones, Oper. Res. 28, 5(1980)1074–1085.

    Google Scholar 

  • Bartholdi, J.J. and H.D. Ratliff, Unnetworks with applications to idle time scheduling, Management Science 24(1978)850–858.

    Google Scholar 

  • Bartlett, T.E., An algorithm for the minimum number of transport units to maintain a fixed schedule, Naval Research Logistics Quarterly 4(1957)207–220.

    Google Scholar 

  • Bean, J.C., J.R. Birge and R.L. Smith, Aggregation in dynamic programming, Oper. Res. 35, 2(1987)215–220.

    Google Scholar 

  • Bean, J.C., J.R. Lohmann and R.L. Smith, Dynamic infinite horizon replacement economy decision model, Engin. Econ. 30, 2(1985)99–120.

    Google Scholar 

  • Beck, P., L. Lasdon and M. Engquist, A reduced gradient algorithm for nonlinear network flow problems, ACM Trans. on Mathematical Software 9(1983)57–70.

    Google Scholar 

  • Beckman, M.J., On the theory of traffic flows in networks, Traffic Quarterly 21(1967)109–116.

    Google Scholar 

  • Bently, R.W. and T.A. Lambe, Assignment of traffic to a network of signalized city streets. Transportation Research 14A(1980)57–65.

    Google Scholar 

  • Berlin, G.N., The use of directed routes for assessing escape potential, National Fire Protection Association, Boston, MA (1979).

    Google Scholar 

  • Bertsekas, D.P., A new algorithm for the assignment problem, Math. Progr. 21(1981)153–171.

    Google Scholar 

  • Bertsekas, D.P., A unified framework for primal-dual methods in minimum cost network flow problems, Math. Progr. 32, 2(1985)125–145.

    Google Scholar 

  • 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. IFAS-87, Munich, West Germany (Pergamon Press, Oxford, UK, 1987).

  • Bertsekas, D.P. and J. Eckstein, Dual coordinate step methods for linear network flow problems, Math. Progr. 42, 2(1988)203–243.

    Google Scholar 

  • Bertsekas, D.P. and D. El Baz, Distributed asynchronous relaxation methods for convex network flow problems, SIAM Journal on Control and Optimization 25(1987)74–85.

    Google Scholar 

  • Bertsekas, D.P., P. Hosein and P. Tseng, Relaxation methods for network flow problems with convex arc costs, SIAM Journal on Control and Optimization 25(1987)1219–1243.

    Google Scholar 

  • Bertsekas, D.P. and P. Tseng, Relaxation methods for minimum cost ordinary and generalized network flow problems, Oper. Res. 36, 1(1988)93–114.

    Google Scholar 

  • Bertsekas, D.P. and J.N. Tsitsiklis,Parallel and Distributed Algorithms (Prentice-Hall, Englewood Cliffs NJ, 1988).

    Google Scholar 

  • 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. and S.P. Sethi, Decision and forecast horizons in a stochastic environment: A survey, Optimal Control Applications and Methods 8, 3(1987)201–217.

    Google Scholar 

  • Bhaumik, G., Optimum operating policies of a water distribution system with losses Unpublished Dissertation, The University of Texas at Austin, Austin, TX (August 1973).

    Google Scholar 

  • Bielli, M., G. Calicchio, B. Micoletti and S. Ricciardelli, The air traffic flow control problem as an application of network theory, Computers and Operations Research 9, 4(1982)265–278.

    Google Scholar 

  • Bixby, R. and W. Cunningham, Converting linear programs to network programs, Math. Oper. Res. 5(1980)321–357.

    Google Scholar 

  • Bixby, R.E. and R. Fourer, Finding embedded network rows in linear programs. I: Extraction heuristics, Management Science 34, 3(1988)342–376.

    Google Scholar 

  • Bookbinder, J.H. and S.P. Sethi, The dynamic transportation problem: A survey, Naval Research Logistics Quarterly 27, 3(1980)447–452.

    Google Scholar 

  • Bowman, E.H., Production scheduling by the transportation method of linear programming, Oper. Res. 4(1956)100–103.

    Google Scholar 

  • Bradley, G.H., Survey of determinsitic networks, AIIE Trans. 7, 3(1975)222–234.

    Google Scholar 

  • Bradley, G.H., G.G. Brown and G.W. Graves, Design and implementation of large-scale primal transshipment algorithms, Management Science 24(1977)1–34.

    Google Scholar 

  • Brown, G.G., R.D. McBride and R.K. Wood, Extracting embedded generalized networks from linear programming problems, Math. Progr. 32, 1(1985)11–31.

    Google Scholar 

  • Brown, G.G. and W.G. Wright, Automatic identification of embedded network rows in large-scale optimization models, Math. Progr. 29, 1(1984)41–56.

    Google Scholar 

  • Carey, M., A convex dynamic assignment model, Working Paper, School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburth, PA (1980).

    Google Scholar 

  • Carey, M., A constraint qualification for a dynamic traffic assignment model, Transportation Science 20, 1(1986)55–58.

    Google Scholar 

  • Carey, M., Optimal time-varying flows on congested networks, Oper. Res. 35, 1(1987)58–69.

    Google Scholar 

  • Carey, M., An approach to modeling dynamic network flows on congested networks, Working Paper, School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburgh, PA (1988).

    Google Scholar 

  • Carey, M. and A. Srinivasan, Modeling network flows with time-varying demand, Report to the Urban Mass Transportation Administration under Contract No. PA-06-0063, School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburgh, PA (1982).

    Google Scholar 

  • Carey, M. and A. Srinivasan, Externalities, optimal tolls and flow controls on congested networks with time-varying flows, School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburgh, PA (July 1985).

    Google Scholar 

  • Carey, M. and A. Srinivasan, Congested network flows: Time-varying demands and start-time policies, Eur. J. Oper. Res. (1989), forthcoming.

  • Chalmet, L.G., R.L. Francis and P.B. Saunders, Network models for building evacuation, Management Science 28, 1(1982)86–105.

    Google Scholar 

  • Chand, S. and T.E. Morton, A perfect planning horizon procedure for a determinstic cash flow balance, Management Science 28, 6(1982)652–669.

    Google Scholar 

  • Chand, S. and T.E. Morton, Minimal forecast horizon procedures for dynamic lot size models, Naval Research Logistics Quarterly 33, 1(1986)111–122.

    Google Scholar 

  • Chand, S. and S.P. Sethi, Planning horizon procedures for machine replacement models with several possible replacement alternatives, Naval Research Logistics Quarterly 29, 3(1982) 483–493.

    Google Scholar 

  • Charnes, A. and W.W. Cooper,Management Models and Industrial Applications of Linear Programming, Vol. I and II (Wiley, New York, 1961).

    Google Scholar 

  • Charnes, A., W.W. Cooper and A. Stedry, Multi-dimensional and dynamic assigment models with some remarks on organization design, Management Science 15, 8(1969)B-365–B-375.

    Google Scholar 

  • Charnes, A., D. Karney, D. Klingman, J. Stutz and F. Glover, Past, present, and future of development, computational efficiency, and practical use of large scale transportation and transshipment computer codes, Computers and OR 2(1975)71–81.

    Google Scholar 

  • Chen, B.D., Forward network programming, Doctoral Dissertation, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX (May 1985).

    Google Scholar 

  • Chen, C.J. and M. Engquist, A primal simplex approach to pure processing networks, Management Science 32, 12(1986)1582–1598.

    Google Scholar 

  • Chen, R.J. and R.R. Meyer, Parallel optimization for traffic assignment, Math. Progr. 42, 2(1988) 327–345.

    Google Scholar 

  • Choi, W., R.L. Francis, H.W. Hamacher and S. Tufekci, Network models of building evacuation problems with flow-dependent exit capacities, Operational Research (Proc. 10th Int. Conf. on Operations Research, Washington, DC, August 1984), ed. J.P. Brans (North-Holland, Amsterdam, 1984) pp. 1047–1059.

    Google Scholar 

  • Choi, W., H.W. Hamacher and S. Tufekci, Modeling of building evacuation problems by network flows with side constraints, Eur. J. Oper. Res. 35(1988)98–110.

    Google Scholar 

  • Chvátal, V.,Linear Programming (Freeman, New York, 1983).

    Google Scholar 

  • Clark, R.H. and R.R. Meyer, Multiprocessor algorithms for generalized network flows, Computer Sciences Technical Report, No. 739, Computer Sciences Department, University of Wisconsin, Madison, WI (1987).

    Google Scholar 

  • Cooke, K.L. and E. Halsey, The shortest route through a network with time-dependent internodal transit times, J. Math. Anal. and Appl. 14(1966)493–498.

    Google Scholar 

  • Corban, A., A multidimensional transportation problem, Revue Roumaine des Mathematiques Pures et Appliquees 9(1964)721–735.

    Google Scholar 

  • Corban, A., On a three-dimensional transportation problem, Revue Roumaine des Mathematiques Pures et Appliquees 11(1966)57–75.

    Google Scholar 

  • Crainic, T., J.A. Ferland and J.M. Rousseau, A tactical planning model for rail freight transportation, Transportation Science 18, 2(1984)165–184.

    Google Scholar 

  • Crum, R.L., Cash management in the multinational firm: A constrained generalized network approach, Working Paper, University of Florida, Gainesville, FL (1976).

    Google Scholar 

  • Crum, R.L. and D.J. Dye, A network model of insurance company cash flow management, Math. Progr. Study, Vol. 15 (1981) 86–101.

    Google Scholar 

  • Crum, R.L., D. Klingman and L. Tavis, Implementation of large-scale financial planning models: Solution, efficient transformations, J. Financial and Quantitative Analysis (1979)137–152.

  • Crum, R.L., D. Klingman and L. Tavis, An operational approach to integrated working capital planning, J. Economics and Business 35(1983a)343–378.

    Google Scholar 

  • Crum, R.L., D.D. Klingman and L.A. Tavis, Strategic management of multinational companies: Network-based planning systems, in:Applications of Management Science, ed. R.L. Shultz, Vol. 3 (JAI Press, Inc., Greenwich, CT, 1983b) pp. 177–201.

    Google Scholar 

  • Cuimet, G.P., Empty freight car distribution, Master's Thesis, Queen's University, Kingston, Ontario, Canada (April 1972).

    Google Scholar 

  • Cunningham, W.H., A network simplex method, Math. Progr. 11(1976)105–116.

    Google Scholar 

  • Cunningham, W.H., Theoretical properties of the network simplex method, Math. Oper. Res. 4, 2(1979)196–208.

    Google Scholar 

  • Dafermos, S., An extended traffic assignment model with application to two-way traffic, Transportation Science 5(1971)366–389.

    Google Scholar 

  • Dafermos, S., The traffic assignment problem for multiclass-user transportation networks, Transportation Science 6(1972)73–87.

    Google Scholar 

  • Dafermos, S., Traffic equilibrium and variational inequalities, Transportation Science 14(1980) 42–54.

    Google Scholar 

  • Dafermos, S., Relaxation algorithms for the general asymmetric traffic equilibrium problem, Transportation Science 14(1982a)231–240.

    Google Scholar 

  • Dafermos, S., The general multimodal network equilibrium problem with elastic demands, Networks 12(1982b)57–72.

    Google Scholar 

  • Dafermos, S. and A. Nagurney, Sensitivity analysis for the general spatial economic equilibrium problem, Oper. Res. 32, 5(1984a)1069–1086.

    Google Scholar 

  • Dafermos, S. and A. Nagurney, Sensitivity analysis for the asymmetric network equilibrium problem, Math. Progr. 28, 2(1984b)174–184.

    Google Scholar 

  • Dafermos, S. and F. Sparrow, The traffic assignment problem for a general network, Journal of Research of the National Bureau of Standards 75B(1969)91–117.

    Google Scholar 

  • D'Ans, G.C. and D.C. Gazis, Optimal control of oversaturated store and forward transportation networks, Transportation Science 10(1976)1–19.

    Google Scholar 

  • Dantzig, G.B.,Linear Programming and Extensions (Princeton, NJ, 1963).

  • Dantzig, G.B., W. Blattner and M.R. Rao, Finding a cycle in a graph with minimum cost to times ratio with application to a ship routing problem, in:Theory of Graphs, ed. P. Rosenthiehl (Dunod, Paris; Gordon and Breach, New York, 1967) pp. 77–84.

    Google Scholar 

  • Dantzig, G.B. and D.R. Fulkerson, Minimizing the number of tankers to meet a fixed schedule, Naval Research Logistics Quarterly 1(1954)217–222.

    Google Scholar 

  • Dantzig, G.B. and R.M. Van Slyke, Generalized upper bounded techniques for linear programming-1, 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 computer-based model for freight car distribution, Report prepared for U.S. Department of Transportation, FRA, DSAI, Rockville, MD (1978a).

  • Decision Systems Associates, Inc., Computer-based model for optimal freight car distribution, FRA Contract DPT-FR-65140, U.S. Department of Transportation, DSAI, Rockville, MD (1978b).

    Google Scholar 

  • Dejax, P.J. and T.G. Crainic, A review of empty flows and fleet management models in freight transportation, Transportation Science 21, 4(1987)227–247.

    Google Scholar 

  • Dijkstra, E.W., A note on two problems in connexion with graphs, Numerische Mathematik 1 (1959)269–271.

    Google Scholar 

  • Drews, W.P., A simplex-like algorithm for continuous-time linear optimal control problems, in:Optimization Methods for Resource Allocation (Proc. NATO Conf., Elsinore, Denmark) (English University Press, London, 1974), pp. 309–322.

    Google Scholar 

  • Dreyfus, S.E., An appraisal of some shortest-path algorithms, Oper. Res. 17(1969)395–412.

    Google Scholar 

  • Dreyfus, S.E. and R.A. Wagner, The Steiner problem in graphs, Networks 1(1971)195–207.

    Google Scholar 

  • Elam, J.J., F. Glover and D. Klingman, A strongly convergent primal simplex algorithm for generalized networks, Math. Oper. Res. 4, 1(1979)39–59.

    Google Scholar 

  • Elam, J.J. and D. Klingman, NETGEN-II: A system for generating network-based mathematical programming test problems, in:Evaluating Mathematical Programming Techniques, Lecture Notes in Economics and Mathematical Systems 199, ed. J.M. Mulvey (Springer-Verlag, New York, 1982).

    Google Scholar 

  • Elnidani, M.A., The multicommodity, multiperiod assignment problem, Doctoral Dissertation, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX (May 1986).

    Google Scholar 

  • Elnidani, M.A. and J.E. Aronson, The multicommodity, multiperiod assignment problem I: A specialized branch and bound algorithm, Working Paper 89-276, Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA (presented at the TIMS XXVII International Meeting, Gold Coast City, Queensland, Australia, July 1986) (1989a).

    Google Scholar 

  • Elnidani, M.A. and J.E. Aronson, The multicommodity, multiperiod assignment problem II: Theoretical results, Working Paper 89-277, Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA (presented at the ORSA/TIMS Joint National Meeting, Denver, CO, October 1988) (1989b).

    Google Scholar 

  • Elnidani, M.A. and J.E. Aronson, The multicommodity, multiperiod assignment problem III: Variations for facility location and personnel planning, Working Paper 89-278, Department of Management Sciences and Information Technology, College of Business Administration, The University of Georgia, Athens, GA (presented at the Joint National ORSA/TIMS Meeting, Los Angeles, CA, April 1986) (1989c).

    Google Scholar 

  • Erickson, R.E., C.L. Monma and A.F. Veinott, Jr., Send-and-split method for minimum-concavecost network flows, Math. Oper. Res. 12, 4(1987)634–664.

    Google Scholar 

  • Ermol'ev, Y.M., T.A. Krivets and V.S. Petukhov, Planning of shipping empty seaborne containers, Cybernetics 12(1976)664.

    Google Scholar 

  • Escudero, L.F., On nonlinear replicated networks, Questiio 9(1985)55–74.

    Google Scholar 

  • Escudero, L.F., Performance evaluation of independent superbasic sets on nonlinear replicated networks, Eur. J. Oper. Res. 23, 3(1986)343–355.

    Google Scholar 

  • Evans, J.R., A single-commodity transformation for certain multicommodity networks, Oper. Res. 26, 4(1975)673–681.

    Google Scholar 

  • Evans, J.R., The multicommodity assignment problem: A network aggregation heuristic, Computers and mathematics with Applications, 7, 2(1981)187–194.

    Google Scholar 

  • 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., A primal partitioning solution for capacitated multicommodity network flow problems. Doctoral Dissertation, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ (1989).

    Google Scholar 

  • Federgruen, A. and H. Groenevelt, Preemptive scheduling of uniform machines by ordinary network flow techniques, Management Science 32, 3(1986)341–349.

    Google Scholar 

  • 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., Empty-container repositioning and leasing: An optimization model, Doctoral Dissertation, Polytechnic Institute of New York, New York, NY (1986).

    Google Scholar 

  • Fong, C.O. and V. Srinivasan, The multiregion dynamic capacity expansion problem, Parts I and II, Oper. Res. 29, 4(1981)787–816.

    Google Scholar 

  • Fong, C.O. and V. Srinivasan, The multiregion dynamic capacity expansion problem: An improved heuristic, Management Science 32, 9(1986)1140–1152.

    Google Scholar 

  • Ford, Jr., L.R. and D.R. Fulkerson, Maximal flow through a network, Can. J. Math. 8(1956)399.

    Google Scholar 

  • Ford, Jr., L.R. and D.R. Fulkerson, Maximal flow through a network, Can. J. Math. 8(1956)399–404.

    Google Scholar 

  • Ford, Jr., L.R. and D.R. Fulkerson, Constructing maximal dynamic flows from static flows, Oper. Res. 6(1958)419–433.

    Google Scholar 

  • Ford, Jr., L.R. and D.R. Fulkerson,Flows in Networks (Princeton University Press, Princeton, NJ, 1962).

    Google Scholar 

  • Fourer, R., A simplex algorithm for piecewise-linear programming I: Derivation and proof, Math. Progr. 33, 2(1985)204–233.

    Google Scholar 

  • Fourer, R., A simplex algorithm for piecewise-linear programming III: Computational analysis and applications, Technical Report 86-03, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL (1986).

    Google Scholar 

  • Fourer, R., A simplex algorithm for piecewise-linear programming II: Finiteness, feasibility and degeneracy, Math. Progr. 41, 3(1988)281–316.

    Google Scholar 

  • Frantzeskasis, L.F. and W.B. Powell, Development and evaluation of a successive linear approximation procedure for stochastic dynamic networks, Report SOR-88-13, Deparment of Civil Engineering and Operations Research, Princeton University, Princeton, NJ (1988).

    Google Scholar 

  • Frieze, A.M., A bilinear programming formulation of the 3-dimensional assignment problem, Math. Progr. 7, 3(1974)376–379.

    Google Scholar 

  • Frieze, A.M., Complexity of a 3-dimensional assignment problem, Eur. J. Oper. Res. 13(1983) 161–164.

    Google Scholar 

  • Frieze, A.M. and J. Yadegar, An algorithm for solving 3-dimensional assignment problems with application to scheduling a teaching practice, J. Oper. Res. Soc. 32(1981)989–995.

    Google Scholar 

  • Fulkerson, D.R., An out-of-kilter method for minimal-cost flow problems, J. Society of Industrial and Applied Mathematics 9, 1(1961)18–27.

    Google Scholar 

  • Gaimon, C., Optimal inventory, backlogging and machine loading in a serial, multi-stage, multiperiod production environment, Int. J. Prod. Res. 24, 3(1986)647–662.

    Google Scholar 

  • Gale, D., A theorem on flows in network, Pacific J. Math. 7(1957)1073–1086.

    Google Scholar 

  • Gale, D., Transient flows in networks, Michigan Mathematical Journal 6(1959)59–63.

    Google Scholar 

  • Garfinkel, R.S. and G.L. Nemhauser,Integer Programming (Wiley, New York, 1972).

    Google Scholar 

  • Gass, S.I.,Linear Programming: Methods and Applications, 4th ed. (McGraw-Hill, New York, 1975).

    Google Scholar 

  • Gay, D.M., A variant of Karmarkar's linear programming algorithm for problems in the standard form, Math. Progr. 37, 1(1987)81–90.

    Google Scholar 

  • Gilbert, K.C. and R.B. Hofstra, Multidimensional assignment problems, Decision Sciences 19, 2(1988)306–321.

    Google Scholar 

  • Gill, P.E., W. Murray, M.A. Saunders, J.A. Tomlin and M.H. Wright, On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method, Math. Progr. 36, 2(1986)183–209.

    Google Scholar 

  • Glickman, T.S. and H.D. Sherali, Large-scale network distribution of pooled empty freight cars over time, with limited substitution and equitable benefits, Transportation Research 19(1985)85–94.

    Google Scholar 

  • Glover, F., Creating network structure in Lp's, in:Computer-Assisted Analysis and Model Simplification, ed. Greenberg and Maybee (Academic Press, New York, 1981) pp. 361–368.

    Google Scholar 

  • Glover, F., R. Glover, J. Lorenzo and C. McMillan, The passenger-mix problem in the scheduled airlines, Interfaces 12, 3(1982)73–80.

    Google Scholar 

  • Glover, F., R. Glover, and F. Martinson, A netform system for resource planning in the U.S. Bureau of Land Management, J. Oper. Res. Soc. 35(1984)605–616.

    Google Scholar 

  • Glover, F., J. Hultz and D. Klingman, Improved computer-based planning techniques, Part I, Interfaces 8, 4(1978a)16–25.

    Google Scholar 

  • Glover, F., J. Hultz and D. Klingman, Improved computer-based planning techniques, Part II, Interfaces 9, 4(1979)12–20.

    Google Scholar 

  • Glover, F., J. Hultz, D. Klingman and J. Stutz, Generalized networks: A fundamental computerbased planning tool, Management Science 24. 12(1978b)1209–1220.

    Google Scholar 

  • Glover, F., G. Jones, D. Karney, D. Klingman and J. Mote, An integrated production, distribution, and inventory planning system, Interfaces 9, 5(1979)21–35.

    Google Scholar 

  • Glover, F., D. Karney and D. Klingman, Double-pricing dual and feasible start algorithms for the capacitated transportation (distribution) problem, CCS Research Report 105, Center for Cybernetic Studies, The University of Texas at Austin, Austin, TX (1973).

    Google Scholar 

  • Glover, F., D. Karney and D. Klingman, Implementation and computational comparisons of primal, dual, and primal-dual computer codes for minimum cost network flow problems, Networks 4, 3(1974)191–212.

    Google Scholar 

  • Glover, F., D. Karney, D. Klingman, and A. Napier, A computational study on start procedures, basis change criteria, and solution algorithms for transportation problems, Management Science 20, 5(1974)793–813.

    Google Scholar 

  • Glover, F. and D. Klingman, New advances in the solution of large-scale network and network-related problems, in:Colloquia Mathematica Societatis, ed. A. Prekopa, (North-Holland, Amsterdam, 1975a) pp. 210–223.

    Google Scholar 

  • Glover, F., and D. Klingman, Improved labeling of L.P. bases in networks, Omega, 23, 2(1975b)220–221.

    Google Scholar 

  • Glover, F. and D. Klingman, A practitioner's guide to the state of large-scale network and network-related problems,AFIPS-Conference Proceedings, Vol. 45, Montvale, NJ (1976), pp. 945–950.

    Google Scholar 

  • Glover, F. and D. Klingman, Network applications in industry and government, AIIE Trans. 9, 4(1977)363–376.

    Google Scholar 

  • Glover, F. and D. Klingman, Modeling and solving network problems, in:Design and Implementation of Optimization Software, ed. H. Greenberg (Sijthoff and Noordhoff, Alphen aan den Rijn, 1978).

    Google Scholar 

  • Glover, F. and D. Klingman, Mathematical optimization — a successful tool for logistics problems, in:Operation Research '81, ed. J.P. Brans (IFORS — North-Holland, Amsterdam, 1981a) pp. 453–462.

    Google Scholar 

  • Glover, F., and D. Klingman, The simplex SON algorithm for LP/embedded network problems, in:Network Models and Associated Applications, ed. D. Klingman and J. M. Mulvey, Mathematical Programming Study, 15 (North-Holland, Amsterdam, 1981b) pp. 148–176.

    Google Scholar 

  • Glover, F. and D. Klingman, Basis exchange characterizations for the simplex SON algorithm for LP/embedded network problems, Mathematical Programming Study 24(1985)141–157.

    Google Scholar 

  • Glover, F. and D. Klingman, Layering strategies for creating exploitable structure in linear and integer programs, Math. Progr. 40, 2(1988)165–182.

    Google Scholar 

  • Glover, F., D. Klingman and C. McMillan, The netform concept: A more effective model form and solution procedure for large-scale nonlinear problems,Proc. ACM '77 (Association for Computing Machinery Conference, October 1977).

  • Glover, F., D. Klingman and J. Stutz, Extensions of the augmented predecessor method to generalized network problems, Transportation Science 7(1973)377–384.

    Google Scholar 

  • Glover, F., D. Klingman and J. Stutz, Augmented threaded index method, INFOR 12, 3(1974) 293–298.

    Google Scholar 

  • Glover, F. and F. Martinson, Linear programming/netform model for vegetation allocation, in:Ecological Modeling (Elsevier, Amsterdam, 1982).

    Google Scholar 

  • Glover, F., C. McMillan and P. Taylor, A computer-based decision support system for air terminal overload management,Proc. 10th Annual International Conference on Systems Sciences, Honolulu, HI (1977).

  • Golden, B.L., and T.L. Magnanti, Deterministic network optimization: A bibliography, Networks 7(1977)149–183.

    Google Scholar 

  • Gorenstein, S., S. Poley and W. W. White, On the scheduling of the railroad freight operations, IBM Data Processing Report, Technical Report 320-2999, IBM, Philadelphia Scientific Center, Philadelphia, PA (1971).

    Google Scholar 

  • Gotlieb, C.C., The construction of class-teacher timetables,Proc. IFIP Congress (1962) pp. 73–77.

  • Gunawardane, G., A three-dimensional 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. and R.G. Ogier, Optimal dynamic routing in communciations networks with continuous traffic, Networks 14(1984)457–487.

    Google Scholar 

  • Haghani, A.E., A combined model of train routing, makeup and empty distribution, Doctoral Dissertation, Northwestern University, Evanston, IL (1986).

    Google Scholar 

  • Haghani, A.E., and M.S. Daskin, A combined model of train routing, makeup and empty car distribution. Technical Report, Northwestern University, Evanston, IL (1986).

    Google Scholar 

  • Haley, K.B., The solid transportation problem, Oper. Res. 10(1962)448–463.

    Google Scholar 

  • Haley, K.B., The multi-index problem, Oper. Res. 11(1963)368–379.

    Google Scholar 

  • Haley, K.B., The existence of a solution to the multi-index problem, Oper. Res. Quart. 16(1965) 471–474.

    Google Scholar 

  • Halpern, J., A generalized dynamic network flows problem,. Networks 9, 2(1979)133–167.

    Google Scholar 

  • Halpern, J. and R.A.M. Outerbridge, PFLOW: A computer program for the generalized P-period maximal dynamic flows problem, Working paper WP-11-77, Faculty of Business, University of Calgary, Alberta, Canada (August 1977).

    Google Scholar 

  • Halpern, J. and I. Priess, Shortest path with time constraints on movement and parking. Networks 4(1974)241–253.

    Google Scholar 

  • Hamacher, H., EJOR software exchange program, Eur. J. Oper. Res. 38(1989)119.

    Google Scholar 

  • Hamacher, H.W., and S. Tufekci, On the use of lexicographic-minimum cost flows in evacuation modeling, Naval Research Logistics 34(1987)487–503.

    Google Scholar 

  • Hartman, D., User's Manual: The interactive DYNAFLO program, A-level, Working Paper No. 6, Manufacturing Flow Research Project, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI (December 1978).

    Google Scholar 

  • Hein, O., Naherungsverfahren für das ‘Überschuss-Bedarf’ Problem, Angewandte Informatik 17 (1975)324–326.

    Google Scholar 

  • Hein, O., Naherungsverfahren für die Leerwagenverteilung, Eisenbahntechnische Rundschau 27 (1978)73–77.

    Google Scholar 

  • Helgason, R.V. and J.L. Kennington, NETFLO program documentation, Technical Report IEOR 76011, Department of Industrial Engineering and Operations Research, Southern Methodist University, Dallas, TX (September 1976).

    Google Scholar 

  • Helgason, R.V., and J.L. Kennington, An efficient procedure for implementing a dual-simplex network flow algorithm, AIIE Trans. 9, 1(1977)63–68.

    Google Scholar 

  • Helgason, R.V., J.L. Kennington and P. Wong, An application of network programming for National Forest Planning, Technical Report, 81006, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX, (February, 1982).

    Google Scholar 

  • Herren, H., The distribution of empty wagons by means of computer: Analytical model of the Swiss Federal Railways, Rail Int. 4(1973)1005–1010.

    Google Scholar 

  • Herren, H., Computer-controlled empty wagon distribution on the SBB, Rail Int. 8(1977)25–32.

    Google Scholar 

  • Hillier, F.S. and G.J. Lieberman,Introduction to Operations Research, 4th ed. (Holden-Day, San Francisco, CA, 1987).

    Google Scholar 

  • Ho, J.K., and E. Loute, Computational experience with advanced implementation of decomposition algorithms. Math. Progr. 27, 3(1983)283–290.

    Google Scholar 

  • Hu, T.C. and W. Prager, Network analysis of production systems, Naval Research Logistics Quarterly 6(1959)17–23.

    Google Scholar 

  • Hughes, R.E., and W.B. Powell, Mitigating and effects in the dynamic vehicle allocation model, Management Science 34, 7(1988)859–879.

    Google Scholar 

  • Hultz, J., Algorithms and applications for generalized networks, Unpublished Dissertation The University of Texas at Austin, Austin, TX (1976).

    Google Scholar 

  • 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., G. Gross and G.S. Hall, PGandE's state-of-the-art scheduling tool for hydro systems, Interfaces 16, 1(1986)65–82.

    Google Scholar 

  • Jarvis, J.J., and H.D. Ratliff, Some equivalent objectives for dynamic network flow problems, Management Science 28, 1(1982)106–109.

    Google Scholar 

  • Jensen, P. and J.W. Barnes,Network Flow Programming (Wiley, New York, 1980).

    Google Scholar 

  • Johnson, E., Flows in networks, in:Handbook of Operations Research, ed. S. J. Moder and S.E. Elmaghraby, (van Nostrand Rheinhold, New York, 1979) pp 183–206.

    Google Scholar 

  • Jordan, W.C., The impact of uncertain demand and supply on empty rail car distribution, Doctoral Dissertation, Cornell University, Ithaca, NY (1982).

    Google Scholar 

  • Jordan, W.C. and M.A. Turnquist, A stochastic dynamic model for railroad car distribution, Transportation Science 17(1983)123–145.

    Google Scholar 

  • Kang, M.K., Dynamic network flow models of conveyor systems, Working Paper, No. 5, Manufacturing Flow Research Project, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI (March 1978).

    Google Scholar 

  • Karmarkar, N., A new polynomial-time algorithm for linear programming, Combinatorics 4(1984a) 373–395.

    Google Scholar 

  • Karmarkar, N., A new polynomial-time algorithm for linear programming,Proc. 16th Annual ACM Symposium on the Theory of Computing (1984b) pp. 302–311.

  • Karney, D. and D. Klingman, Implementation and computational study on an in-core out-of-core primal network code, Oper. Res. 24, 6(1976)1056–1077.

    Google Scholar 

  • Kennington, J.L., A survey of linear cost multicommodity network flows, Oper. Res. 26, 2(1978) 209–236.

    Google Scholar 

  • Kennington, J.L. and R.V. Helgason,Algorithms for Network Programming (Wiley, New York, 1980).

    Google Scholar 

  • 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. and F.B. Potts, The minimum route problem with turn penalties and prohibitions, Transportation Research 3(1969)397–408.

    Google Scholar 

  • 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., An algorithm for nonlienar multicommodity flow problems, Networks 4(1974) 343–355.

    Google Scholar 

  • Klingman, D. and J. Mote, A multi-period production, distribution, and inventory planning model, Advances in Management Studies 1, 2(1982)56–76.

    Google Scholar 

  • Klingman, D., J. Mote and N.V. Phillips, A logistics planning system at W.R. Grace, Oper. Res. 36, 6(1988)811–822.

    Google Scholar 

  • Klingman, D., A. Napier and J. Stutz, NETGEN: A program for generating large scale capacitated assignment, transportation, and minimum cost flow network problems, Management Science 20, 5(1974)814–821.

    Google Scholar 

  • Klingman, D., N.V. Phillips, D. Steiger, R. Wirth, R. Padman and R. Krishnan, An optimization-based integrated short-term refined petroleum product planning system, Management Science 33, 7(1987a)813–830.

    Google Scholar 

  • Klingman, D., N.V. Phillips, D. Steiger and W. Young, The successful deployment of management science throughout Citgo Petroleum Corporation, Interfaces 17, 1(1987b)4–25.

    Google Scholar 

  • Klingman, D., P. Randolph and S. Fuller, A cotton ginning problem, Oper. Res. 24, 4(1976) 700–718.

    Google Scholar 

  • Konno, H., Minimum concave cost production systems: A further generalization of multi-echelon model. Math. Progr. 41, 2(1988)185–194.

    Google Scholar 

  • 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., Continuous and integer generalized flow problems, Unpublished Dissertation, Georgia Institute of Technology, Atlanta, GA (1973).

    Google Scholar 

  • Lawler, E.L.,Combinatorial Optimization, Networks and Matroids, (Holt, Rinehart and Winston, New York, 1976).

    Google Scholar 

  • Leue, O., Methoden zur Lösung dreidimensionaler Zuordnungsprobleme, Angewandte Informatik (April 1972) 154–162.

  • Levin, A., Some fleet routing and scheduling problems for air transportation systems, Report FTL-R68-5, Massachusetts Institute of Technology, Cambridge, MA (1969).

    Google Scholar 

  • Lundin, R.A. and T.E. Morton, Planning horizons for the dynamic lot size model: Zabel vs. protective procedures and computational results, Oper. Res. 23, 4(1975)711–734.

    Google Scholar 

  • Luss, H. and D.R. Smith, Multiperiod allocation of limited resources: A minimax approach, Naval Research Logistics Quarterly 35(1988)493–501.

    Google Scholar 

  • 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., and B.W. Jordan, Jr., Generalized multi-stage connection networks, Networks 2(1972)191–209.

    Google Scholar 

  • Maxwell, W.L. and R.C. Wilson, Dynamic network flow modelling of fixed path material handling systems, AIIE Trans. 13, 1(1981)12–21.

    Google Scholar 

  • McBride, R.D., D.E. O'Leary and G.R. Widmeyer, A system for supporting cash management decisions, Working Paper, Graduate School of Business Administration, University of Southern California, Los Angeles, CA (1988).

    Google Scholar 

  • McCallum, C.J., A generalized upper bounding approach to a communications network planning problem, Networks 7(1977)1–23.

    Google Scholar 

  • Mendiratta, V.B., A dynamic optimization model of the empty car distribution process, Doctoral Dissertation, Department of Civil Engineering, Northwestern University, Evanston, IL (1981).

    Google Scholar 

  • Mendiratta, V.B. and M.A. Turnquist, A model for the management of empty freight cars, Transportation Research Rec. 838(1982)50–55.

    Google Scholar 

  • Merchant, D.K., A study of dynamic traffic assignment and control, Doctoral Dissertation, Cornell University, Ithaca, NY (1974).

    Google Scholar 

  • Merchant, D.K. and G.L. Nemhauser, A model and an algorithm for the dynamic traffic assignment problem, Transportation Science 12, 3(1978a)183–199.

    Google Scholar 

  • Merchant, D.K. and G.L. Nemhauser, Optimality conditions for a dynamic traffic assignment model, Transportation Science 12, 3(1978b)201–207.

    Google Scholar 

  • Meyer, R.R., Parallel algorithms for large-scale nonlinear networks, presented at the SIAM Conference on Optimization, Houston, TX (May 1987).

  • Meyer, R.R. and S.A. Zenios, eds.,Parallel Optimization on Novel Computer Architectures, Ann. Oper. Res. 14 (1988) (J.C. Baltzer, Basel, 1988).

    Google Scholar 

  • 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. Using linear programming to derive planning horizons for a production smoothing problem, Management Science 25, 12(1979)1232–1244.

    Google Scholar 

  • Minieka, E., Maximal, lexicographic and dynamic network flows, Oper. Res. 12, 2(1973)517–527.

    Google Scholar 

  • Minieka, E., Dynamic network flows with are changes, Networks 4(1974)255–265.

    Google Scholar 

  • Monma, C.L. and M. Segal, A primal algorithm for finding minimum-cost flows in capacitated networks with applications, The Bell System Technical Journal 61, 6(1982)949–968.

    Google Scholar 

  • Moravek, J. and M. Vlach, On the necessary conditions for the existence of the solution of the multi-index transportation problem, Oper. Res. 15(1967)542–545.

    Google Scholar 

  • Morton, T.E., Universal planning horizons for generalized convex production scheduling, Oper. Res. 26, 6(1978)1046–1057.

    Google Scholar 

  • 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., A network planning model for the U.S. Air Traffic System, Working Paper EES-83-8, Department of Civil Engineering, Princeton University, Princeton, NJ (1984b).

    Google Scholar 

  • Mulvey, J.M. and S.A. Zenois, Solving large scale generalized networks, J. Information and Optimization Science 6(1985)95–112.

    Google Scholar 

  • Mulvey, J.M. and S.A. Zenios, Real-time operational planning for the U.S. air traffic system, Applied Numerical Mathematics, 3(1987)427–441.

    Google Scholar 

  • Murphy, F.H. and A.L. Soyster, End effects in capacity expansion models with finite horizons, Naval Research Logistics Quarterly 33, 3(1986)373–383.

    Google Scholar 

  • Murtagh, B. and M. Saunders, MINOS User's Guide, Technical Report 77-9, Stanford Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, CA (February 1977).

    Google Scholar 

  • Murtagh, B. and M. Saunders, MINOS/Augmented User's Manual, Technical Report SOL 80-14, Stanford Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, CA (June 1980).

    Google Scholar 

  • Nagurney, A. and D.S. Kim, Parallel vs. serial algorithms for large-scale multicommodity spatial price equilibrium problems, International Journal of Supercomputer Applications (Spring 1989).

  • Nagurney, A. and J.E. Aronson, A general dynamic spatial price equilibrium model: Formulation, solution and computational results, J. Comput. Appl. Math. 22(1988)339–352.

    Google Scholar 

  • Nagurney, A. and J.E. Aronson, A general dynamic spatial price network equilibrium model with gains and losses, Networks (1989), forthcoming.

  • Nemhauser, G.L. and L.A. Wolsey,Integer and Combinatorial Optimization (Wiley, New York, 1988).

    Google Scholar 

  • 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., Quick optimal weekly scheduling with two consecutive days off, Technical Report 77-1 Department of Operations Research, Stanford University, Stanford, CA (1977).

    Google Scholar 

  • Orlin, J.B., Maximum-throughput dynamic network flows, Math. Progr. 27, 2(1983)214–231.

    Google Scholar 

  • Orlin, J.B., Minimum convex cost dynamic network flows, Math. Oper. Res. 9, 2(1984)190–207.

    Google Scholar 

  • Ouimet, G.P., Empty freight car distribution, Masters Thesis, Queen's University, Kingston, Ontario, Canada (1972).

    Google Scholar 

  • Perevezentsev, E.N., Scheduling of containers shipments, in:Proc. Central Scientific-Research Institute of the Maritime Fleet, No. 195 (Transport, Leningrad, USSR, 1974), in Russian.

    Google Scholar 

  • Perold, A.F., Continuous linear programming, Doctoral Dissertation, Department of Operations Research, Stanford University, Stanford, CA (1978).

    Google Scholar 

  • Phillips, D. and A. Garcia-Diaz,Fundamentals of Network Analysis (Prentice-Hall, New York, 1981).

    Google Scholar 

  • Phillips, D.T., A. Ravindran and J.J. Solberg,Operations Research, Principles and Practice (Wiley, New York, 1976).

    Google Scholar 

  • Philpott, A.B., Network programming in continuous time with node storage, Engineering Department, Cambridge University, Cambridge, UK (1985),Infinite Programming, Proc. of a Symposium on Infinite Dimensional Linear Programming, ed. E. Anderson and A. Philpott (1984).

    Google Scholar 

  • Pierskalla, W.P., The tri-substitution method for the three-dimensional assignment problem, CORS Journal 5(1967a)71–81.

    Google Scholar 

  • Pierskalla, W.P., The multi-dimensional assignment and quadratic assignment problems, Technical Memorandum No. 93, Case Western Reserve University, Operations Research Department, School of Management, Cleveland, OH (September 1967b).

    Google Scholar 

  • Pierskalla, W.P., The multi-dimensional assignment problem, Oper. Res. 15, 2(1968)422–431.

    Google Scholar 

  • Posner, M.E. and W. Szwarc, A transportation type aggregate production model with backordering, Management Science 29, 2(1983)188–199.

    Google Scholar 

  • Potts, R.B. Movement of empty containers within Australia, presented to the Operations Research Society of Victoria, Melbourne, Australia (September 1970).

  • Powell, W.B., A stochastic model of the dynamic vehicle allocation problem, Transportation Science 20, 2(1986)117–129.

    Google Scholar 

  • Powell, W.B., An operational planning model for the dynamic vehicle allocation problem with uncertain demands, Transportation Research 21B, 3(1987)217–232.

    Google Scholar 

  • Powell, W.B. A comparative review of alternative algorithms for the dynamic vehicle allocation problem, in:Vehicle Routing: Methods and Studies, ed. B. Golden and A.A. Assad (North-Holland, Amsterdam, 1988), pp. 249–291.

    Google Scholar 

  • Powell, W.B. and D.J. Cape, Sensitivity analysis of dynamic networks: An application to pricing and load evaluation for truckload motor carriers, Report SOR-88-8, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ (1988).

    Google Scholar 

  • Powell, W.B. and Y. Sheffi, Design and implementation of an interactive optimization system for network design in the motor carrier industry, Oper. Res. 37, 1(1989)12–29.

    Google Scholar 

  • Powell, W.B., Y. Sheffi, K.S. Nickerson, K. Butterbaugh and S. Atherton, Maximizing profits for North American Van Lines' Truckload Division: A new framework for pricing and operations, Interfaces 18, 1(1988)21–41.

    Google Scholar 

  • Powell, W.B., Y. Sheffi and S. Thiriez, The dynamic vehicle allocation problem with uncertain demands, in:9th Int. Symp. on Transportation and Traffic Theory, ed. J. Volmuller and R. Hamerslag (VNU Science Press, The Netherlands, 1984).

    Google Scholar 

  • Premoli, A. Piecewise-linear programming: The compact (CPLP) algorithm, Math. Progr. 36, 2(1986)210–227.

    Google Scholar 

  • Propoi, A.I. and V. Krivonozhko, The dynamic simplex method, RM-77-24, International Institute for Applied Systems Analysis, Laxenburg, Austria (1977).

    Google Scholar 

  • Ramsey, Jr., T.E. and R.R. Rardin, Heuristics for multistage production planning problems, J. Oper. Res. Soc. 34, 1(1983)61–70.

    Google Scholar 

  • Rao, V.V. and L.F. McGinnis, Optimal lot sizing in acyclic multiperiod production systems, IIE Trans. 15(1983)54–62.

    Google Scholar 

  • Robillard, P., Multipath traffic assignment with dynamic input flows, Transportation Research 8(1974)567–583.

    Google Scholar 

  • Rogers, D.F., R.D. Plante, R.T. Wong and J.R. Evans, Aggregation techniques and methodology in optimization, Working Paper QA-1988-10, Department of Quantitative Analysis and Information Systems, College of Business Administration, University of Cincinnati, Cincinnati, OH (1988).

    Google Scholar 

  • Rosenthal, R.E., A nonlinear network flow algorithm for maximization of benefits in a hydroelectric power system, Oper. Res. 29, 4(1981)763–786.

    Google Scholar 

  • Rosenthal, R.E., Representing inverses in pure network flow optimization, Eur. J. Oper. Res. 23, 3(1986)356–366.

    Google Scholar 

  • Saksena, J.P. and S. Kumar, The routing problem with ‘K’ specified nodes, Oper. Res. 14(1966) 909–913.

    Google Scholar 

  • Sandbothe, R.A., Solving the capacitated lot size model, Doctoral Dissertation, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh PA (November 1985).

    Google Scholar 

  • 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,Proc. 2nd Symp. in Linear Programming ed. H. Antosiewicz, 2, DCS/Comptroller H.Q., U.S. Air Force, Washington, DC, 615–642 (January 1955).

    Google Scholar 

  • Sethi, A.P., Algorithmic enhancements of the simplex method, Doctoral Dissertation, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA (1983).

    Google Scholar 

  • Sethi, A.P. and G.L. Thompson, The pivot and probe algorithm for solving a linear program, Math. Progr. 29, 2(1984)219–233.

    Google Scholar 

  • Sethi, A.P. and G.L. Thompson, Solution of constrained generalized transportation problems using the pivot-and-probe algorithm, Computers and OR 13(1986)1–9.

    Google Scholar 

  • Sethi, A.P., G.L. Thompson and M.S. Hung, The pivot-and-probe algorithm and XMP, presented at the TIMS/ORSA Joint National Meeting, Washington, DC (April 1988).

  • Sethi, S.P. and S. Chand, Planning horizon procedures for machine replacement models, Management Science 25, 2(1979)140–151

    Google Scholar 

  • Shamma, M.M. A generalized assignment problem, Doctoral Dissertation, Computer Science/Operations Research Center, Southern Methodist University, Dallas, TX (March, 1971).

    Google Scholar 

  • Shan, Y., A dynamic multicommodity network flow model for real time optimal rail freight car management, Doctoral Dissertation, Princeton University, Princeton, NJ (1985).

    Google Scholar 

  • Shanno, D.F., Computing Karmarkar projections quickly, Math. Progr. 41, 1(1988)61–72.

    Google Scholar 

  • Shetty, B., The equal flow problem, Doctoral Dissertation, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas TX (May 1985).

    Google Scholar 

  • Simmonard, M.,Linear Programming (Prentice-Hall, Englewood Cliffs, NJ, 1966).

    Google Scholar 

  • Smith, R.L., Deferral strategies for a dynamic communications network, Networkds 9(1979)61–87.

    Google Scholar 

  • Srinivasan, V., A transshipment model for cash management decisions, Management Science 20, 10(1974)1350–1363.

    Google Scholar 

  • Srinivasan, V. and G.L. Thompson, Accelerated algorithms for labeling and relabeling of trees, with applications to distribution problems, Journal of the Association for Computing Machinery 19, 4(1972)712–726.

    Google Scholar 

  • Srinivasan, V. and G.L. Thompson, Benefit-cost analysis of coding techniques for the primal transportation algorithm, Journal of the Association for Computing Machinery 20(1973) 194–213.

    Google Scholar 

  • Stanley, J.D., A forward convex-simplex method with applications, Doctoral Dissertation, Graduate School of Industrial administration, Carnegie-Mellon University, Pittsburgh, PA (April 1984).

    Google Scholar 

  • Stanley, J.D., A forward convex-simplex method, Eur. J. Oper. Res. 29(1987)328–335.

    Google Scholar 

  • Steinberg, E. and H.A. Napier, Optimal multi-level lot sizing for systems requirements planning, Management Science 26, 12(1980)1258–1271.

    Google Scholar 

  • Stone, R.E., An algorithm for solving network problems with side variables, Working paper, AT & T Bell Laboratories, Holmdel, NJ (Nov. 1988).

    Google Scholar 

  • Szwarc, W. and M.E. Posner, The tridiagonal transportation problem, Oper. Res. Lett. 3, 1(1984) 25–30.

    Google Scholar 

  • 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. and D.J. Zawack, A problem expanding parametric programming method for solving the job shop scheduling problem, Ann. Oper. Res. 4(1985/1986)327–342.

    Google Scholar 

  • Tibrewala, R., D. Philippe and J. Browne, Optimal scheduling of two idle periods, Management Science 19(1972)71–75.

    Google Scholar 

  • Todd, M.J., Exploiting special structure in Karmarkar's linear programming algorithm, Math. Progr. 41, 1(1988)97–113.

    Google Scholar 

  • Tomlin, J.A., Special ordered sets and an application to gas supply operations planning, Math. Progr. 42, 1(1988)69–84.

    Google Scholar 

  • Truemper, K., How to detect hidden networks and totally-unimodular subsections of linear programs, presented at the TIMS/ORSA Joint National Meeting, Chicago, IL (April 1983).

  • Tseng, P., Relaxation methods for monotropic programming problems, Doctoral Dissertation, Department of Electical Engineering and Computer Science, Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA (1986).

    Google Scholar 

  • Tseng, P. and D.P. Bertsekas, Relaxation methods for linear programs, Math. Oper. Res. 12, 4 (1987a)569–596.

    Google Scholar 

  • Tseng, P. and D.P. Bertsekas, Relaxation methods for problems with strictly convex separable costs and linear constraints, Math. Progr. 38,3(1987b)303–321.

    Google Scholar 

  • Tsui, L., DYNAFLO User's Manual, Working paper No. 7, Manufacturing Flow Research Project, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI 48109 (October 1978).

    Google Scholar 

  • Turnquist, M.A., MOV-EM: A network optimization model for empty freight car distribution, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY (1986).

    Google Scholar 

  • Turnquist, M.A. and W.C. Jordan, A computer-based method for railroad car distribution, Final Report, DTRS5680-C-00013, U.S. Department of Transportation, Office of University Research (1982).

  • Vajda, S.,Mathematical Programming (Addison-Wesley, Reading, MA, 1961) p. 147.

    Google Scholar 

  • Veinott, Jr., A.F., Minimum concave-cost solution of Leontief substitution models of multifacility inventory systems, Oper. Res. 17(1969)262–291.

    Google Scholar 

  • Veinott, Jr., A.F. and H.M. Wagner, Optimal capacity scheduling, I and II, Oper. Res. 10(1962) 518–546.

    Google Scholar 

  • Vemuganti, R.R., M. Oblak and A. Aggarwal, Network models for fleet management, Decision Sciences 20, 1(1989)182–197.

    Google Scholar 

  • Vlach, M., Branch and bound method for the three index assignment problem, Ekonomicko-Matematicky Obzor (Czechoslovakia) 3(1967)181–191.

    Google Scholar 

  • Waddell, R., A model for equipment replacement decisions and policies, Interfaces 13, 4(1983)1.

    Google Scholar 

  • Wagner, H.M.Principles of Operations Research, 2nd ed. (Prentice-Hall, NJ, 1975).

    Google Scholar 

  • Waddell, R., A model for equipment replacement decisions and policies, Interfaces 13, 4(1983)1–7.

    Google Scholar 

  • Wagner, H.M.Principles of Operations Research, 2nd ed. (Prentice-Hall, Englewood Cliffs, NJ, 1975).

    Google Scholar 

  • Wagner, H.M. and T.M. Whitin Dynamic version of the economic lot size model, Management Science 5(1958)89–96.

    Google Scholar 

  • White, W.W., Dynamic transshipment network: An algorithm and its application to the distribution of empty containers, Networks 2(1972)211–236.

    Google Scholar 

  • White, W.W. and A.M. Bomberault, A network algorithm for empty freight car allocations, IBM Systems Journal 8 2(1969)147–169.

    Google Scholar 

  • Wilkinson, W.L., An algorithm for universal maximal dynamic flows in a network, Oper. Res. 19, 7(1971)1602–1612.

    Google Scholar 

  • Wilkinson, W.L., Min/max bounds for dynamic network flows, Naval Research Logistics Quarterly 20, 3(1973)505–516.

    Google Scholar 

  • Williams, K.B. and K.B. Haley, A practical application of linear programming in the mining industry, Oper. Res. Quart. 10, 3(1959)131–138.

    Google Scholar 

  • Yaged, Jr., B., Minimum cost routing for static network models, Networks 1(1971)139–172.

    Google Scholar 

  • Yaged, Jr., B., Minimum cost routing for dynamic network models, Networks 3(1973) 193–224.

    Google Scholar 

  • Yaged, Jr., B., Economies of scale, networks, and network cost elasticity, IEEE Trans. on Systems, Man, and Cybernetics 5(1975)30–39.

    Google Scholar 

  • Zadeh, N., On building minimum cost communications networks, Networks 3(1973)315–331.

    Google Scholar 

  • Zadeh, N. On building minimum cost communications networks over time, Networks 4(1974) 19–34.

    Google Scholar 

  • Zahorik, A., L.J. Thomas and W. Trigeiro, Network programming models for production scheduling in multi-stage, multi-item, capacitated systems Management Science 30,3(1984)308–325.

    Google Scholar 

  • Zangwill, W.I., A deterministic multiperiod production scheduling model with backloggings, Management Science 13(1966)105–119.

    Google Scholar 

  • Zangwill, W.I. Minimum concave cost flows in certain networks, Management Science 14, 7(1968) 429–450.

    Google Scholar 

  • Zangwill, W.I., A backlogging model and a multi-echelon model of a dynamic economic lot size production system — a network approach, Management Science 15, 9(1969)506–527.

    Google Scholar 

  • Zangwill, W.I., Set-up cost reduction in series facility production, Working paper, University of Chicago, Chicago, IL (January 1985).

    Google Scholar 

  • Zangwill, W.I. Eliminating inventory in a series facility production system, Management Science 33, 9(1987a) 1150–1164.

    Google Scholar 

  • Zangwill, W.I., From EOQ toward ZI, Management Science 33, 10(1987b)1209–1223.

    Google Scholar 

  • Zawack, D.J. and G.L. Thompson, A dynamic space-time network flow model for city traffic congestion. Transportation Science 21, 3(1987)153–161.

    Google Scholar 

  • Zemanian, A.H., A dynamic marketing network with monopsonistic acquisition and perfectly competitive disposition, IEEE Trans. on Circuits and Systems, CAS-30, 6(1983a)382–387.

    Google Scholar 

  • Zemanian, A.H., A dynamic marketing, storage and transportation system with perfect competition in each of its markets. IMA J. Appl. Math. 31(1983b)51–78.

    Google Scholar 

  • Zenios, S.A., Sequential and parallel algorithms for convex generalized network problems and related applications, Doctoral Dissertation, Civil Engineering Department, Princeton University, Princeton, NJ (May 1986).

    Google Scholar 

  • Zenios, S.A., An annotated bibliography on parallel optimization, ORSA Journal on Computing (1989), forthcoming.

  • Zenios, S.A. and R.A. Lasken, Nonlinear network optimization on a massively parallel connection machine. Ann. Oper. Res. 14(1988)147–165.

    Google Scholar 

  • Zenios, S.A. and J.M. Mulvey, Simulating a distributed synchronous relaxation method for convex network problems, Working Paper, Department of Civil Engineering, Princeton University, Princeton, NJ (January 1985).

    Google Scholar 

  • Zenios, S.A. and J.M. Mulvey, Nonlinear network programming on vector supercomputers: A study on the CRAY-XMP, Oper. Res. 34, 5 (1986) 667–682.

    Google Scholar 

  • Zenios, S.A. and J.M. Mulvey, A distributed algorithm for convex network optimization problems,Parallel Computing 6 (North-Holland, Amsterdam, 1988a) pp. 45–56.

    Google Scholar 

  • Zenios, S.A. and J.M. Mulvey, Vectorization and multitasking of nonlinear network programming algorithms, Math. Progr. 42, 2(1988b) 449–470.

    Google Scholar 

  • Zipkin, P., Bounds for aggregation nodes in network problems, Math. Prog. 19(1980)155–177.

    Google Scholar 

  • Zipkin, P. and P. Raimer, An improved disaggregation method for transportation problems, Math. Progr. 26, 2(1983)238–242.

    Google Scholar 

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

    Jay E. Aronson

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Prepared under National Science Foundation Grant ECS-8307549. 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.

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Aronson, J.E. A survey of dynamic network flows. Ann Oper Res 20, 1–66 (1989). https://doi.org/10.1007/BF02216922

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