Advertisement

Annals of Operations Research

, Volume 20, Issue 1, pp 1–66 | Cite as

A survey of dynamic network flows

  • Jay E. Aronson
Article

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.

Keywords

Flow Model Dynamic Structure Specialized Technique Dynamic Network Numerous Application 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. 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).Google Scholar
  3. 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
  4. 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
  5. 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
  6. 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.Google Scholar
  7. 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
  8. 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
  9. Ali, A.I., J.L. Kennington and B. Shetty, The equal flow problem, Eur. J. Oper. Res. 36(1988) 107–115.Google Scholar
  10. Ali, A.I., R. Padman and H. Thiagarajan, Dual algorithms for pure network problems, Oper. Res. 37, 1(1989)159–171.Google Scholar
  11. 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
  12. ARC: Analysis Research and Computation, Inc., PNET User's Guide, Austin, TX 78765 (1974).Google Scholar
  13. 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
  14. 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
  15. 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
  16. Aronson, J.E., Forward linear programming, Doctoral Dissertation, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA (April 1980a).Google Scholar
  17. 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
  18. 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
  19. Aronson, J.E., Networks tutorial, in:Proc. 1988 Annual Meeting of the Decision Sciences Institute, Las Vegas, NV (November 1988).Google Scholar
  20. 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).Google Scholar
  21. 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).Google Scholar
  22. 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).Google Scholar
  23. 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
  24. 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
  25. 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.Google Scholar
  26. 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).Google Scholar
  27. 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
  28. 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
  29. 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).Google Scholar
  30. Aronson, J.E. and G.L. Thompson, A survey on forward methods in mathematical programming, Large Scale Systems 7(1984)1–16.Google Scholar
  31. 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
  32. Assad, A.A., Analytical models in rail transportation: An annotated bibliography, INFOR 19, 1(1981)59–80.Google Scholar
  33. Assad, A.A., Multicommodity network flows: A survey, Networks 8, 1(1987)37–92.Google Scholar
  34. Baker, K.R., Scheduling a full-time workforce to meet cyclic staffing requirements, Management Science 20(1974)1561–1568.Google Scholar
  35. Baker, K.R., Workforce allocation in cyclical scheduling problems, Oper. Res. Quart. 27(1976)155.Google Scholar
  36. Baker, K.R. Workforce allocation in cyclical scheduling problems, Oper. Res. Quart. 27(1976) 155–167.Google Scholar
  37. 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
  38. Balas, E. and P. Landweer, Traffic assignment in communication satellites Oper. Res. Lett. 2(1983) 141–147.Google Scholar
  39. 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
  40. Balas, E. and M.J. Saltzman, Facets of the three-index assignment polytope, Discr. Appl. Math. (1989), forthcoming.Google Scholar
  41. Barnes, E.R., A variation on Karmarkar's algorithm for solving linear programming problems, Math. Progr. 36, 2(1986)174–182.Google Scholar
  42. 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
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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
  48. 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
  49. 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
  50. Bartholdi, J.J. and H.D. Ratliff, Unnetworks with applications to idle time scheduling, Management Science 24(1978)850–858.Google Scholar
  51. 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
  52. Bean, J.C., J.R. Birge and R.L. Smith, Aggregation in dynamic programming, Oper. Res. 35, 2(1987)215–220.Google Scholar
  53. 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
  54. 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
  55. Beckman, M.J., On the theory of traffic flows in networks, Traffic Quarterly 21(1967)109–116.Google Scholar
  56. 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
  57. Berlin, G.N., The use of directed routes for assessing escape potential, National Fire Protection Association, Boston, MA (1979).Google Scholar
  58. Bertsekas, D.P., A new algorithm for the assignment problem, Math. Progr. 21(1981)153–171.Google Scholar
  59. 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
  60. 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.Google Scholar
  61. 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).Google Scholar
  62. Bertsekas, D.P. and J. Eckstein, Dual coordinate step methods for linear network flow problems, Math. Progr. 42, 2(1988)203–243.Google Scholar
  63. 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
  64. 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
  65. 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
  66. Bertsekas, D.P. and J.N. Tsitsiklis,Parallel and Distributed Algorithms (Prentice-Hall, Englewood Cliffs NJ, 1988).Google Scholar
  67. Bhaskaran, S., S. Chand and S.P. Sethi, Decision and forecast horizon procedures in operations management, Private Communication of Research in Progress (1986).Google Scholar
  68. 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
  69. 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
  70. 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
  71. Bixby, R. and W. Cunningham, Converting linear programs to network programs, Math. Oper. Res. 5(1980)321–357.Google Scholar
  72. 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
  73. Bookbinder, J.H. and S.P. Sethi, The dynamic transportation problem: A survey, Naval Research Logistics Quarterly 27, 3(1980)447–452.Google Scholar
  74. Bowman, E.H., Production scheduling by the transportation method of linear programming, Oper. Res. 4(1956)100–103.Google Scholar
  75. Bradley, G.H., Survey of determinsitic networks, AIIE Trans. 7, 3(1975)222–234.Google Scholar
  76. 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
  77. 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
  78. 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
  79. Carey, M., A convex dynamic assignment model, Working Paper, School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburth, PA (1980).Google Scholar
  80. Carey, M., A constraint qualification for a dynamic traffic assignment model, Transportation Science 20, 1(1986)55–58.Google Scholar
  81. Carey, M., Optimal time-varying flows on congested networks, Oper. Res. 35, 1(1987)58–69.Google Scholar
  82. 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
  83. 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
  84. 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
  85. Carey, M. and A. Srinivasan, Congested network flows: Time-varying demands and start-time policies, Eur. J. Oper. Res. (1989), forthcoming.Google Scholar
  86. Chalmet, L.G., R.L. Francis and P.B. Saunders, Network models for building evacuation, Management Science 28, 1(1982)86–105.Google Scholar
  87. 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
  88. 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
  89. 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
  90. Charnes, A. and W.W. Cooper,Management Models and Industrial Applications of Linear Programming, Vol. I and II (Wiley, New York, 1961).Google Scholar
  91. 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
  92. 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
  93. Chen, B.D., Forward network programming, Doctoral Dissertation, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX (May 1985).Google Scholar
  94. Chen, C.J. and M. Engquist, A primal simplex approach to pure processing networks, Management Science 32, 12(1986)1582–1598.Google Scholar
  95. Chen, R.J. and R.R. Meyer, Parallel optimization for traffic assignment, Math. Progr. 42, 2(1988) 327–345.Google Scholar
  96. 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
  97. 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
  98. Chvátal, V.,Linear Programming (Freeman, New York, 1983).Google Scholar
  99. 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
  100. 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
  101. Corban, A., A multidimensional transportation problem, Revue Roumaine des Mathematiques Pures et Appliquees 9(1964)721–735.Google Scholar
  102. Corban, A., On a three-dimensional transportation problem, Revue Roumaine des Mathematiques Pures et Appliquees 11(1966)57–75.Google Scholar
  103. 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
  104. Crum, R.L., Cash management in the multinational firm: A constrained generalized network approach, Working Paper, University of Florida, Gainesville, FL (1976).Google Scholar
  105. 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
  106. 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.Google Scholar
  107. 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
  108. 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
  109. Cuimet, G.P., Empty freight car distribution, Master's Thesis, Queen's University, Kingston, Ontario, Canada (April 1972).Google Scholar
  110. Cunningham, W.H., A network simplex method, Math. Progr. 11(1976)105–116.Google Scholar
  111. Cunningham, W.H., Theoretical properties of the network simplex method, Math. Oper. Res. 4, 2(1979)196–208.Google Scholar
  112. Dafermos, S., An extended traffic assignment model with application to two-way traffic, Transportation Science 5(1971)366–389.Google Scholar
  113. Dafermos, S., The traffic assignment problem for multiclass-user transportation networks, Transportation Science 6(1972)73–87.Google Scholar
  114. Dafermos, S., Traffic equilibrium and variational inequalities, Transportation Science 14(1980) 42–54.Google Scholar
  115. Dafermos, S., Relaxation algorithms for the general asymmetric traffic equilibrium problem, Transportation Science 14(1982a)231–240.Google Scholar
  116. Dafermos, S., The general multimodal network equilibrium problem with elastic demands, Networks 12(1982b)57–72.Google Scholar
  117. Dafermos, S. and A. Nagurney, Sensitivity analysis for the general spatial economic equilibrium problem, Oper. Res. 32, 5(1984a)1069–1086.Google Scholar
  118. Dafermos, S. and A. Nagurney, Sensitivity analysis for the asymmetric network equilibrium problem, Math. Progr. 28, 2(1984b)174–184.Google Scholar
  119. 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
  120. 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
  121. Dantzig, G.B.,Linear Programming and Extensions (Princeton, NJ, 1963).Google Scholar
  122. 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
  123. 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
  124. 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.Google Scholar
  125. 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).Google Scholar
  126. 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
  127. 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
  128. Dijkstra, E.W., A note on two problems in connexion with graphs, Numerische Mathematik 1 (1959)269–271.Google Scholar
  129. 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
  130. Dreyfus, S.E., An appraisal of some shortest-path algorithms, Oper. Res. 17(1969)395–412.Google Scholar
  131. Dreyfus, S.E. and R.A. Wagner, The Steiner problem in graphs, Networks 1(1971)195–207.Google Scholar
  132. 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
  133. 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
  134. 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
  135. 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
  136. 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
  137. 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
  138. 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
  139. Ermol'ev, Y.M., T.A. Krivets and V.S. Petukhov, Planning of shipping empty seaborne containers, Cybernetics 12(1976)664.Google Scholar
  140. Escudero, L.F., On nonlinear replicated networks, Questiio 9(1985)55–74.Google Scholar
  141. Escudero, L.F., Performance evaluation of independent superbasic sets on nonlinear replicated networks, Eur. J. Oper. Res. 23, 3(1986)343–355.Google Scholar
  142. Evans, J.R., A single-commodity transformation for certain multicommodity networks, Oper. Res. 26, 4(1975)673–681.Google Scholar
  143. Evans, J.R., The multicommodity assignment problem: A network aggregation heuristic, Computers and mathematics with Applications, 7, 2(1981)187–194.Google Scholar
  144. 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.Google Scholar
  145. 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
  146. Federgruen, A. and H. Groenevelt, Preemptive scheduling of uniform machines by ordinary network flow techniques, Management Science 32, 3(1986)341–349.Google Scholar
  147. Feeney, G., Controlling the distribution of empty freight cars, in:Proc. 10th National Meeting (Operations Research Society of America, 1957).Google Scholar
  148. 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.Google Scholar
  149. Florez, H., Empty-container repositioning and leasing: An optimization model, Doctoral Dissertation, Polytechnic Institute of New York, New York, NY (1986).Google Scholar
  150. 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
  151. Fong, C.O. and V. Srinivasan, The multiregion dynamic capacity expansion problem: An improved heuristic, Management Science 32, 9(1986)1140–1152.Google Scholar
  152. Ford, Jr., L.R. and D.R. Fulkerson, Maximal flow through a network, Can. J. Math. 8(1956)399.Google Scholar
  153. Ford, Jr., L.R. and D.R. Fulkerson, Maximal flow through a network, Can. J. Math. 8(1956)399–404.Google Scholar
  154. Ford, Jr., L.R. and D.R. Fulkerson, Constructing maximal dynamic flows from static flows, Oper. Res. 6(1958)419–433.Google Scholar
  155. Ford, Jr., L.R. and D.R. Fulkerson,Flows in Networks (Princeton University Press, Princeton, NJ, 1962).Google Scholar
  156. Fourer, R., A simplex algorithm for piecewise-linear programming I: Derivation and proof, Math. Progr. 33, 2(1985)204–233.Google Scholar
  157. 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
  158. Fourer, R., A simplex algorithm for piecewise-linear programming II: Finiteness, feasibility and degeneracy, Math. Progr. 41, 3(1988)281–316.Google Scholar
  159. 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
  160. Frieze, A.M., A bilinear programming formulation of the 3-dimensional assignment problem, Math. Progr. 7, 3(1974)376–379.Google Scholar
  161. Frieze, A.M., Complexity of a 3-dimensional assignment problem, Eur. J. Oper. Res. 13(1983) 161–164.Google Scholar
  162. 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
  163. 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
  164. 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
  165. Gale, D., A theorem on flows in network, Pacific J. Math. 7(1957)1073–1086.Google Scholar
  166. Gale, D., Transient flows in networks, Michigan Mathematical Journal 6(1959)59–63.Google Scholar
  167. Garfinkel, R.S. and G.L. Nemhauser,Integer Programming (Wiley, New York, 1972).Google Scholar
  168. Gass, S.I.,Linear Programming: Methods and Applications, 4th ed. (McGraw-Hill, New York, 1975).Google Scholar
  169. 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
  170. Gilbert, K.C. and R.B. Hofstra, Multidimensional assignment problems, Decision Sciences 19, 2(1988)306–321.Google Scholar
  171. 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
  172. 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
  173. 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
  174. 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
  175. 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
  176. Glover, F., J. Hultz and D. Klingman, Improved computer-based planning techniques, Part I, Interfaces 8, 4(1978a)16–25.Google Scholar
  177. Glover, F., J. Hultz and D. Klingman, Improved computer-based planning techniques, Part II, Interfaces 9, 4(1979)12–20.Google Scholar
  178. 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
  179. 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
  180. 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
  181. 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
  182. 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
  183. 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
  184. Glover, F., and D. Klingman, Improved labeling of L.P. bases in networks, Omega, 23, 2(1975b)220–221.Google Scholar
  185. 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
  186. Glover, F. and D. Klingman, Network applications in industry and government, AIIE Trans. 9, 4(1977)363–376.Google Scholar
  187. 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
  188. 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
  189. 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
  190. 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
  191. 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
  192. 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).Google Scholar
  193. 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
  194. Glover, F., D. Klingman and J. Stutz, Augmented threaded index method, INFOR 12, 3(1974) 293–298.Google Scholar
  195. Glover, F. and F. Martinson, Linear programming/netform model for vegetation allocation, in:Ecological Modeling (Elsevier, Amsterdam, 1982).Google Scholar
  196. 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).Google Scholar
  197. Golden, B.L., and T.L. Magnanti, Deterministic network optimization: A bibliography, Networks 7(1977)149–183.Google Scholar
  198. 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
  199. Gotlieb, C.C., The construction of class-teacher timetables,Proc. IFIP Congress (1962) pp. 73–77.Google Scholar
  200. Gunawardane, G., A three-dimensional assignment problem, presented at the ORSA/TIMS Joint National meeting, San Diego, CA (October 1982).Google Scholar
  201. Gurel, M. and D.M. Winbigler, Container provisioning for an airline network, presented at the 32nd National Meeting, ORSA, Chicago, IL (November 1967).Google Scholar
  202. Hajek, B. and R.G. Ogier, Optimal dynamic routing in communciations networks with continuous traffic, Networks 14(1984)457–487.Google Scholar
  203. Haghani, A.E., A combined model of train routing, makeup and empty distribution, Doctoral Dissertation, Northwestern University, Evanston, IL (1986).Google Scholar
  204. 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
  205. Haley, K.B., The solid transportation problem, Oper. Res. 10(1962)448–463.Google Scholar
  206. Haley, K.B., The multi-index problem, Oper. Res. 11(1963)368–379.Google Scholar
  207. Haley, K.B., The existence of a solution to the multi-index problem, Oper. Res. Quart. 16(1965) 471–474.Google Scholar
  208. Halpern, J., A generalized dynamic network flows problem,. Networks 9, 2(1979)133–167.Google Scholar
  209. 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
  210. Halpern, J. and I. Priess, Shortest path with time constraints on movement and parking. Networks 4(1974)241–253.Google Scholar
  211. Hamacher, H., EJOR software exchange program, Eur. J. Oper. Res. 38(1989)119.Google Scholar
  212. 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
  213. 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
  214. Hein, O., Naherungsverfahren für das ‘Überschuss-Bedarf’ Problem, Angewandte Informatik 17 (1975)324–326.Google Scholar
  215. Hein, O., Naherungsverfahren für die Leerwagenverteilung, Eisenbahntechnische Rundschau 27 (1978)73–77.Google Scholar
  216. 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
  217. 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
  218. 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
  219. 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
  220. Herren, H., Computer-controlled empty wagon distribution on the SBB, Rail Int. 8(1977)25–32.Google Scholar
  221. Hillier, F.S. and G.J. Lieberman,Introduction to Operations Research, 4th ed. (Holden-Day, San Francisco, CA, 1987).Google Scholar
  222. Ho, J.K., and E. Loute, Computational experience with advanced implementation of decomposition algorithms. Math. Progr. 27, 3(1983)283–290.Google Scholar
  223. Hu, T.C. and W. Prager, Network analysis of production systems, Naval Research Logistics Quarterly 6(1959)17–23.Google Scholar
  224. 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
  225. Hultz, J., Algorithms and applications for generalized networks, Unpublished Dissertation The University of Texas at Austin, Austin, TX (1976).Google Scholar
  226. 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).Google Scholar
  227. IBM: International Business Machines Corporation, IBM Mathematical Programming System Extended/370 Program Reference Manual, White Plains, NY (December 1979).Google Scholar
  228. 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
  229. Jarvis, J.J., and H.D. Ratliff, Some equivalent objectives for dynamic network flow problems, Management Science 28, 1(1982)106–109.Google Scholar
  230. Jensen, P. and J.W. Barnes,Network Flow Programming (Wiley, New York, 1980).Google Scholar
  231. 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
  232. Jordan, W.C., The impact of uncertain demand and supply on empty rail car distribution, Doctoral Dissertation, Cornell University, Ithaca, NY (1982).Google Scholar
  233. Jordan, W.C. and M.A. Turnquist, A stochastic dynamic model for railroad car distribution, Transportation Science 17(1983)123–145.Google Scholar
  234. 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
  235. Karmarkar, N., A new polynomial-time algorithm for linear programming, Combinatorics 4(1984a) 373–395.Google Scholar
  236. Karmarkar, N., A new polynomial-time algorithm for linear programming,Proc. 16th Annual ACM Symposium on the Theory of Computing (1984b) pp. 302–311.Google Scholar
  237. 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
  238. Kennington, J.L., A survey of linear cost multicommodity network flows, Oper. Res. 26, 2(1978) 209–236.Google Scholar
  239. Kennington, J.L. and R.V. Helgason,Algorithms for Network Programming (Wiley, New York, 1980).Google Scholar
  240. 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).Google Scholar
  241. Kibby, F.R. and F.B. Potts, The minimum route problem with turn penalties and prohibitions, Transportation Research 3(1969)397–408.Google Scholar
  242. 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).Google Scholar
  243. 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).Google Scholar
  244. Klessig, R.W., An algorithm for nonlienar multicommodity flow problems, Networks 4(1974) 343–355.Google Scholar
  245. 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
  246. 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
  247. 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
  248. 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
  249. 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
  250. Klingman, D., P. Randolph and S. Fuller, A cotton ginning problem, Oper. Res. 24, 4(1976) 700–718.Google Scholar
  251. Konno, H., Minimum concave cost production systems: A further generalization of multi-echelon model. Math. Progr. 41, 2(1988)185–194.Google Scholar
  252. 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).Google Scholar
  253. 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).Google Scholar
  254. 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).Google Scholar
  255. Langley, R., Continuous and integer generalized flow problems, Unpublished Dissertation, Georgia Institute of Technology, Atlanta, GA (1973).Google Scholar
  256. Lawler, E.L.,Combinatorial Optimization, Networks and Matroids, (Holt, Rinehart and Winston, New York, 1976).Google Scholar
  257. Leue, O., Methoden zur Lösung dreidimensionaler Zuordnungsprobleme, Angewandte Informatik (April 1972) 154–162.Google Scholar
  258. 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
  259. 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
  260. Luss, H. and D.R. Smith, Multiperiod allocation of limited resources: A minimax approach, Naval Research Logistics Quarterly 35(1988)493–501.Google Scholar
  261. Mangasarian, O.L. and R.R. Meyer, eds.,Parallel Methods in Mathematical Programming, Mathematical Programming 42, 2(1988), special issue.Google Scholar
  262. Marsten, R.E., The design of the XMP linear programming library, Transactions on Mathematical Software 7, 4(1981).Google Scholar
  263. Masson, G.M., and B.W. Jordan, Jr., Generalized multi-stage connection networks, Networks 2(1972)191–209.Google Scholar
  264. 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
  265. 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
  266. McCallum, C.J., A generalized upper bounding approach to a communications network planning problem, Networks 7(1977)1–23.Google Scholar
  267. 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
  268. 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
  269. Merchant, D.K., A study of dynamic traffic assignment and control, Doctoral Dissertation, Cornell University, Ithaca, NY (1974).Google Scholar
  270. 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
  271. Merchant, D.K. and G.L. Nemhauser, Optimality conditions for a dynamic traffic assignment model, Transportation Science 12, 3(1978b)201–207.Google Scholar
  272. Meyer, R.R., Parallel algorithms for large-scale nonlinear networks, presented at the SIAM Conference on Optimization, Houston, TX (May 1987).Google Scholar
  273. 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
  274. Miller, D., J. Pekny and G.L. Thompson, Solution of large, dense transportation problems using a parallel primal algorithm, Oper. Res. Lett. (1989), forthcoming.Google Scholar
  275. Miller, L.W. Using linear programming to derive planning horizons for a production smoothing problem, Management Science 25, 12(1979)1232–1244.Google Scholar
  276. Minieka, E., Maximal, lexicographic and dynamic network flows, Oper. Res. 12, 2(1973)517–527.Google Scholar
  277. Minieka, E., Dynamic network flows with are changes, Networks 4(1974)255–265.Google Scholar
  278. 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
  279. 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
  280. Morton, T.E., Universal planning horizons for generalized convex production scheduling, Oper. Res. 26, 6(1978)1046–1057.Google Scholar
  281. Morton, T.E., Forward algorithms for forward thinking managers, in:Applications of Management Science, ed. R.L. Schultz, Vol. 1 (JAI Press, Inc., 1981).Google Scholar
  282. Mulvey, J.M. A network portfolio approach for cash flow management, J. Cash Management (1984a) 46–48.Google Scholar
  283. 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
  284. Mulvey, J.M. and S.A. Zenois, Solving large scale generalized networks, J. Information and Optimization Science 6(1985)95–112.Google Scholar
  285. 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
  286. 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
  287. 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
  288. 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
  289. 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).Google Scholar
  290. 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
  291. Nagurney, A. and J.E. Aronson, A general dynamic spatial price network equilibrium model with gains and losses, Networks (1989), forthcoming.Google Scholar
  292. Nemhauser, G.L. and L.A. Wolsey,Integer and Combinatorial Optimization (Wiley, New York, 1988).Google Scholar
  293. 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).Google Scholar
  294. 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).Google Scholar
  295. 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.Google Scholar
  296. 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
  297. Orlin, J.B., Maximum-throughput dynamic network flows, Math. Progr. 27, 2(1983)214–231.Google Scholar
  298. Orlin, J.B., Minimum convex cost dynamic network flows, Math. Oper. Res. 9, 2(1984)190–207.Google Scholar
  299. Ouimet, G.P., Empty freight car distribution, Masters Thesis, Queen's University, Kingston, Ontario, Canada (1972).Google Scholar
  300. 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
  301. Perold, A.F., Continuous linear programming, Doctoral Dissertation, Department of Operations Research, Stanford University, Stanford, CA (1978).Google Scholar
  302. Phillips, D. and A. Garcia-Diaz,Fundamentals of Network Analysis (Prentice-Hall, New York, 1981).Google Scholar
  303. Phillips, D.T., A. Ravindran and J.J. Solberg,Operations Research, Principles and Practice (Wiley, New York, 1976).Google Scholar
  304. 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
  305. Pierskalla, W.P., The tri-substitution method for the three-dimensional assignment problem, CORS Journal 5(1967a)71–81.Google Scholar
  306. 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
  307. Pierskalla, W.P., The multi-dimensional assignment problem, Oper. Res. 15, 2(1968)422–431.Google Scholar
  308. Posner, M.E. and W. Szwarc, A transportation type aggregate production model with backordering, Management Science 29, 2(1983)188–199.Google Scholar
  309. Potts, R.B. Movement of empty containers within Australia, presented to the Operations Research Society of Victoria, Melbourne, Australia (September 1970).Google Scholar
  310. Powell, W.B., A stochastic model of the dynamic vehicle allocation problem, Transportation Science 20, 2(1986)117–129.Google Scholar
  311. 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
  312. 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
  313. 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
  314. 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
  315. 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
  316. 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
  317. Premoli, A. Piecewise-linear programming: The compact (CPLP) algorithm, Math. Progr. 36, 2(1986)210–227.Google Scholar
  318. Propoi, A.I. and V. Krivonozhko, The dynamic simplex method, RM-77-24, International Institute for Applied Systems Analysis, Laxenburg, Austria (1977).Google Scholar
  319. 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
  320. Rao, V.V. and L.F. McGinnis, Optimal lot sizing in acyclic multiperiod production systems, IIE Trans. 15(1983)54–62.Google Scholar
  321. Robillard, P., Multipath traffic assignment with dynamic input flows, Transportation Research 8(1974)567–583.Google Scholar
  322. 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
  323. 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
  324. Rosenthal, R.E., Representing inverses in pure network flow optimization, Eur. J. Oper. Res. 23, 3(1986)356–366.Google Scholar
  325. Saksena, J.P. and S. Kumar, The routing problem with ‘K’ specified nodes, Oper. Res. 14(1966) 909–913.Google Scholar
  326. 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
  327. Sandbothe, R.A. and G.L. Thompson, A forward algorithm for the capacitated lot size model with stockouts, Oper. Res. (1989), forthcoming.Google Scholar
  328. 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
  329. Sethi, A.P., Algorithmic enhancements of the simplex method, Doctoral Dissertation, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA (1983).Google Scholar
  330. 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
  331. 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
  332. 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).Google Scholar
  333. Sethi, S.P. and S. Chand, Planning horizon procedures for machine replacement models, Management Science 25, 2(1979)140–151Google Scholar
  334. Shamma, M.M. A generalized assignment problem, Doctoral Dissertation, Computer Science/Operations Research Center, Southern Methodist University, Dallas, TX (March, 1971).Google Scholar
  335. 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
  336. Shanno, D.F., Computing Karmarkar projections quickly, Math. Progr. 41, 1(1988)61–72.Google Scholar
  337. Shetty, B., The equal flow problem, Doctoral Dissertation, Department of Operations Research and Engineering Management, Southern Methodist University, Dallas TX (May 1985).Google Scholar
  338. Simmonard, M.,Linear Programming (Prentice-Hall, Englewood Cliffs, NJ, 1966).Google Scholar
  339. Smith, R.L., Deferral strategies for a dynamic communications network, Networkds 9(1979)61–87.Google Scholar
  340. Srinivasan, V., A transshipment model for cash management decisions, Management Science 20, 10(1974)1350–1363.Google Scholar
  341. 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
  342. 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
  343. 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
  344. Stanley, J.D., A forward convex-simplex method, Eur. J. Oper. Res. 29(1987)328–335.Google Scholar
  345. Steinberg, E. and H.A. Napier, Optimal multi-level lot sizing for systems requirements planning, Management Science 26, 12(1980)1258–1271.Google Scholar
  346. Stone, R.E., An algorithm for solving network problems with side variables, Working paper, AT & T Bell Laboratories, Holmdel, NJ (Nov. 1988).Google Scholar
  347. Szwarc, W. and M.E. Posner, The tridiagonal transportation problem, Oper. Res. Lett. 3, 1(1984) 25–30.Google Scholar
  348. 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).Google Scholar
  349. 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
  350. Tibrewala, R., D. Philippe and J. Browne, Optimal scheduling of two idle periods, Management Science 19(1972)71–75.Google Scholar
  351. Todd, M.J., Exploiting special structure in Karmarkar's linear programming algorithm, Math. Progr. 41, 1(1988)97–113.Google Scholar
  352. Tomlin, J.A., Special ordered sets and an application to gas supply operations planning, Math. Progr. 42, 1(1988)69–84.Google Scholar
  353. 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).Google Scholar
  354. 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
  355. Tseng, P. and D.P. Bertsekas, Relaxation methods for linear programs, Math. Oper. Res. 12, 4 (1987a)569–596.Google Scholar
  356. 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
  357. 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
  358. 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
  359. 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).Google Scholar
  360. Vajda, S.,Mathematical Programming (Addison-Wesley, Reading, MA, 1961) p. 147.Google Scholar
  361. Veinott, Jr., A.F., Minimum concave-cost solution of Leontief substitution models of multifacility inventory systems, Oper. Res. 17(1969)262–291.Google Scholar
  362. Veinott, Jr., A.F. and H.M. Wagner, Optimal capacity scheduling, I and II, Oper. Res. 10(1962) 518–546.Google Scholar
  363. Vemuganti, R.R., M. Oblak and A. Aggarwal, Network models for fleet management, Decision Sciences 20, 1(1989)182–197.Google Scholar
  364. Vlach, M., Branch and bound method for the three index assignment problem, Ekonomicko-Matematicky Obzor (Czechoslovakia) 3(1967)181–191.Google Scholar
  365. Waddell, R., A model for equipment replacement decisions and policies, Interfaces 13, 4(1983)1.Google Scholar
  366. Wagner, H.M.Principles of Operations Research, 2nd ed. (Prentice-Hall, NJ, 1975).Google Scholar
  367. Waddell, R., A model for equipment replacement decisions and policies, Interfaces 13, 4(1983)1–7.Google Scholar
  368. Wagner, H.M.Principles of Operations Research, 2nd ed. (Prentice-Hall, Englewood Cliffs, NJ, 1975).Google Scholar
  369. Wagner, H.M. and T.M. Whitin Dynamic version of the economic lot size model, Management Science 5(1958)89–96.Google Scholar
  370. White, W.W., Dynamic transshipment network: An algorithm and its application to the distribution of empty containers, Networks 2(1972)211–236.Google Scholar
  371. 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
  372. Wilkinson, W.L., An algorithm for universal maximal dynamic flows in a network, Oper. Res. 19, 7(1971)1602–1612.Google Scholar
  373. Wilkinson, W.L., Min/max bounds for dynamic network flows, Naval Research Logistics Quarterly 20, 3(1973)505–516.Google Scholar
  374. 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
  375. Yaged, Jr., B., Minimum cost routing for static network models, Networks 1(1971)139–172.Google Scholar
  376. Yaged, Jr., B., Minimum cost routing for dynamic network models, Networks 3(1973) 193–224.Google Scholar
  377. Yaged, Jr., B., Economies of scale, networks, and network cost elasticity, IEEE Trans. on Systems, Man, and Cybernetics 5(1975)30–39.Google Scholar
  378. Zadeh, N., On building minimum cost communications networks, Networks 3(1973)315–331.Google Scholar
  379. Zadeh, N. On building minimum cost communications networks over time, Networks 4(1974) 19–34.Google Scholar
  380. 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
  381. Zangwill, W.I., A deterministic multiperiod production scheduling model with backloggings, Management Science 13(1966)105–119.Google Scholar
  382. Zangwill, W.I. Minimum concave cost flows in certain networks, Management Science 14, 7(1968) 429–450.Google Scholar
  383. 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
  384. Zangwill, W.I., Set-up cost reduction in series facility production, Working paper, University of Chicago, Chicago, IL (January 1985).Google Scholar
  385. Zangwill, W.I. Eliminating inventory in a series facility production system, Management Science 33, 9(1987a) 1150–1164.Google Scholar
  386. Zangwill, W.I., From EOQ toward ZI, Management Science 33, 10(1987b)1209–1223.Google Scholar
  387. 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
  388. 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
  389. 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
  390. 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
  391. Zenios, S.A., An annotated bibliography on parallel optimization, ORSA Journal on Computing (1989), forthcoming.Google Scholar
  392. 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
  393. 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
  394. 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
  395. 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
  396. Zenios, S.A. and J.M. Mulvey, Vectorization and multitasking of nonlinear network programming algorithms, Math. Progr. 42, 2(1988b) 449–470.Google Scholar
  397. Zipkin, P., Bounds for aggregation nodes in network problems, Math. Prog. 19(1980)155–177.Google Scholar
  398. Zipkin, P. and P. Raimer, An improved disaggregation method for transportation problems, Math. Progr. 26, 2(1983)238–242.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1989

Authors and Affiliations

  • Jay E. Aronson
    • 1
  1. 1.Department of Management Sciences and Information Technology, College of Business AdministrationThe University of Georgia, Brooks HallAthensUSA

Personalised recommendations