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Economic Geography Volume 46, 1970 - Issue sup1: PROCEEDINGS International Geographical Union Commission on Quantitative Methods
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Original Articles

Dynamic Programming and Geographical Systems

Ross D. MacKinnonUniversity of Toronto
Pages 350-366 | Published online: 09 Jun 2016

List of Works Cited

GENERAL

  • Aris, R. Discrete Dynamic Programming. New York: Blaisdell, 1964.
  • Beckmann, M. J. Dynamic Programming of Economic Decisions. New York: Springer-Verlag, 1968.
  • Bellman, H. E. Dynamic Programming. Princeton: Princeton University Press, 1957.
  • Bellman, R. Adaptive Control Processes: a Guided Tour. Princeton: Princeton University Press, 1961.
  • Bellman, R. Some Vistas of Modern Mathematics. Lexington: University of Kentucky Press, 1968.
  • Bellman, R. and S. E. Dreyfus. Applied Dynamic Programming. Princeton: Princeton University Press, 1962.
  • Bellman, R. and R. Kalaba. Dynamic Programming and Modern Control Theory. New York: Academic Press, 1965.
  • Bellman, R. and R. Karush. “Dynamic Programming: a Bibliography of Theory and Application,” Memorandum RM- 3951-PR. Rand Corporation, 1964.
  • Bellmore, M., G. Howard, and G. L. Nemhauser. “Dynamic Programming Computer Model 4,” Department of Operations Research and Industrial Engineering: The Johns Hopkins University (July, 1966).
  • Deledicq, A. “Programmation Dynamique Discrete,” Revue Française de l'Information et de Recherche Operationelle, 2 (1968), pp. 13–32.
  • Denardo, E. V. and L. G. Mitten. “Elements of Sequential Decision Processes,” Journal of Industrial Engineering, 18 (1967), pp. 106–12.
  • Derman, C. “Markovian Decision Processes—Average Cost Criterion,” Mathematics of the Decision Sciences, Part 2. Edited by G. B. Dantzig and A. F. Vernott, Jr. Providence: American Mathematical Society, 1968. pp. 139–48.
  • Dreyfus, S. “Dynamic Programming,” Progress in Operations Research. Edited by R. L. Ackoff. Vol. I. New York: Wiley, 1961. pp. 211–42.
  • Dreyfus, S. E. Dynamic Programming and the Calculus of Variations. New York: Academic Press, 1965.
  • Hadley, R. Nonlinear and Dynamic Programming. Reading: Addison-Wesley, 1964.
  • Hellier, F. S. and G. J. Lieberman. Introduction to Operations Research. San Francisco: Holden-Day, 1967.
  • Howard, R. A. Dynamic Programming and Markov Processes. Cambridge: MIT Press, 1960.
  • Howard, R. A. “Dynamic Programming,” Management Science, 12 (1966), pp. 317–48.
  • Jacobs, O. L. R. An Introduction to Dynamic Programming. London: Chapman and Hall, 1967.
  • Kaufmann, A. Graphs, Dynamic Programming and Finite Games. New York: Academic Press, 1967.
  • Kaufmann, A. and R. Cruon. Dynamic Programming: Sequential Scientific Management. New York: Academic Press, 1967.
  • Larson, R. E. State Increment Dynamic Programming. New York: Elsevier, 1968.
  • Nemhauser, G. L. Introduction to Dynamic Programming. New York: Wiley, 1966.
  • White, D. J. Dynamic Programming. San Francisco: Holden-Day, 1969.
  • Wilde, D. J. and C. S. Beightler. Foundations of Optimization. Englewood Cliffs: Prentice-Hall, 1967.

TRANSPORTATION

  • Bellman, R. “Notes on the Theory of Dynamic Programming: Transportation Models,” Management Science. 4 (1958), pp. 191–5.
  • Bellman, R. “Dynamic Programming Treatment of the Traveling Salesman Problem,” Journal of the Association of Computing Machinery, 9 (1962), pp. 61–3.
  • Bellman, R. and K. L. Cooke. “The Konigsberg Bridges Problems Generalized,” Journal of Mathematical Analysis and Applications, 25 (1969), pp. 1–7.
  • Bellmore, M. and G. L. Nemhauser. “The Traveling Salesman Problem: A Survey,” Operations Research, 16 (1968), pp. 538–58.
  • Bergendahl, G. “A Combined Linear and Dynamic Programming Model for Interdependent Road Investment Planning,” Transportation Research, 3 (1969), pp. 211–28.
  • Cooke, K. L. and E. Halsey. “The Shortest Route Through a Network with Time-Dependent Internodal Transit Times,” Journal of Mathematical Analysis and Applications, 14 (1966), pp. 493–8.
  • Dreyfus, S. E. “An Appraisal of Some Shortest Path Algorithms,” Operations Research, 17 (1969), pp. 395–412.
  • Funk, M. L. and F. A. Tillman. “Optimal Construction Staging by Dynamic Programming,” ASCE Journal of the Highway Division, 94 (November, 1968), pp. 255–65.
  • Gonzalez, R. H. “Solution of the Traveling Salesman Problem by Dynamic Programming on the Hypercube,” Technical Report No. 18. Cambridge: MIT Operations Research Center, 1962.
  • Groboillot, J. L. and L. Gallas. “Optimalisation d'un Project Routier Par Recherche du Plus Court Chemin dans un Graphe à Trois Dimensions,” Revue Française d'Informatique et Recherche Operationelle, 1 (1967), pp. 99–121.
  • Gulbrandsen, O. “Optimal Priority Rating of Resources-Allocation by Dynamic Programming,” Transportation Science, 1 (1967), pp. 251–60.
  • Joksch, H. C. “The Shortest Route Problem with Constraints,” Journal of Mathematical Analysis and Applications, 14 (1966), pp. 191–9.
  • Kalaba, R. “Graph Theory and Automatic Control,” Applied Combinatorial Mathematics. Edited by E. F. Beckenbach. New York: Wiley 1964. pp. 237–52.
  • Kumar, S. “Optimal Location of Recovery Points for Vehicular Traffic Subject to Two Types of Failures,” Canadian Operational Research Society Journal, 6 (1968), pp. 38–43.
  • MacKinnon, R. D. “System Flexibility within a Transportation Context,” Unpublished Ph.D. dissertation, Northwestern University, 1968.
  • Marble, D. F. “A Theoretical Exploration of Individual Travel Behavior,” Quantitative Geography Part I: Economic and Cultural Topics. Edited by W. L. Garrison and D. F. Marble. Evanston: Department of Geography, Northwestern University, 1967. pp. 33–53.
  • Midler, J. L. “A Stochastic Multiperiod Multimode Transportation Model,” Transportation Science, 3 (1969), pp. 8–29.
  • Morlok, E. K. “Goal-Directed Transportation Planning Model,” Research Report. Evanston: Transportation Center, Northwestern University, January, 1969.
  • Morlok, E. K. and R. F. Sullivan. “The Optimal Fixed Network Development Model,” Research Report. Evanston: Transportation Center, Northwestern University, April, 1969.
  • Nemhauser, G. L. “Scheduling Local and Express Service,” Transportation Science, 3 (1969), pp. 164–75.
  • Pollack, M. “Solutions of the kth Best Route Through a Network—a Review,” Journal of Mathematical Analysis Appliations, 3 (1961), pp. 547–59.
  • Roberts, P. O. “Transportation Planning: Models for Developing Countries,” Unpublished Ph.D. dissertation, Northwestern University, 1966.
  • Roberts, P. O. and M. L. Funk. “Toward Optimum Methods of Link Addition in Transportation Networks,” MIT Monograph (September, 1964).
  • Werner, C. “The Law Refraction in Transportation Geography: Its Multivariate Extension,” The Canadian Geographer, 12 (1968), pp. 28–40.
  • Wong, P. J. and R. E. Larson. “Optimization of Tree-Structured Natural Gas Transmission Networks,” Journal of Mathematical Analysis and Applications, 24 (1968), pp. 613–26.

REGIONAL AND LOCATION-ALLOCATION PROBLEMS

  • Bellman, R. “An Application of Dynamic Programming to Location-Allocation Problems,” Society Industrial and Applied Mathematics Review, 17 (1965), pp. 126–8.
  • Burt, O. and C. Harris, Jr. “Appointment of the U.S. House of Representatives: a Minimum Range, Integer Solution, Allocation Problem,” Operations Research, 11 (1963), pp. 648–52.
  • Erlenkotter, D. “Two Producing Areas—Dynamic Programming Solutions,” Investments for Capacity Expansion. Edited by A. S. Manne. London: George Allen and Unwin, 1967. pp. 210–27.
  • Scott, A. J. “Location-Allocation Systems,” Geographical Analysis, forthcoming.
  • Teitz, M. B. “Toward a Theory of Urban Public Facility Location,” Papers Regional Science Association, 21 (1968), pp. 35–52.

NATURAL RESOURCE MANAGEMENT

  • Arimizu, T. “Working Group Matrix in Dynamic Model of Forest Management,” Journal of Japanese Forestry Society, 40 (1958), p. 185.
  • Bellman, R. and R. Kalaba. “Some Mathematical Aspects of Optimal Predation in Ecology and Boviculture,” Proceedings of the National Academy of Science, 46 (1960).
  • Beard, L. R. “Optimization Techniques for Hydrologic Engineering,” Water Resources Research, 3 (1967), pp. 809–15.
  • Boughton, W. C. “Optimizing the Gradients of Channels by Dynamic Programming,” Journal of the Institute of Engineers, 38 (1966), pp. 303–6.
  • Buras, N. “Conjunctive Operation of Dams and Aquifers,” ASCE Journal of the Hydraulics Division, 89, November, 1963.
  • Burt, O. R. “Optimal Resource Use Over Time with an Application to Ground Water,” Management Science, 11 (1964), pp. 80–93.
  • Burt, O. R. “Economic Control of Groundwater Reserves,” Journal of Farm Economics, 48 (1966), pp. 632–47.
  • Butcher, W. S. “Stochastic Dynamic Programming and the Assessment of Risk,” Proceedings of National Symposium on the Analysis of Water Resource Systems, Denver, 1968.
  • Butcher, W. S. “Mathematical Models for Optimizing the Allocation of Stored Water,” The Use of Analog and Digital Computers in Hydrology. Tucson: Symposium of International Association of Scientific Hydrology, 1968.
  • Hall, W. A. “Aqueduct Capacity Under Optimum Benefit Policy,” ASCE Journal of Irrigation Drainage Division, 87 (1961), pp. 1–11.
  • Hall, W. A. “Aqueduct Capacity Under an Optimum Benefit Policy,” Transactions American Society of Engineers, 128 (1963), pp. 162–72.
  • Hall, W. A. “A Method for Allocating Costs of a Water Supply Canal,” Journal of Farm Economics, 45 (1963), pp. 713–20.
  • Hall, W. A. “Optimum Design of a Multiple-Purpose Reservoir,” ASCE Journal of the Hydraulics Division, 90 (July, 1964), pp. 141–9.
  • Hall, W. A. and N. Buras. “The Dynamic Programming Approach to Water Resources Development,” Journal of Geographical Research, 66 (1961), pp. 517–20.
  • Hall, W. A. and W. S. Butcher. “Optimal Timing of Irrigation,” ASCE Journal of Irrigation and Drainage Division, 94 (June, 1968), pp. 267–74.
  • Hall, W. A., W. S. Butcher, and A. Essogbue. “Optimization of the Operation of Multipurpose Reservoir by Dynamic Programming,” Water Resources Research, 4 (1968), pp. 471–7.
  • Hall, W. A. and D. T. Howell. “The Optimization of Single Purpose Reservoir Design with the Application of Dynamic Programming,” Journal of Hydrology, 1 (1963), pp. 355–63.
  • Hall, W. A. and T. G. Roefs. “Hydropower Project Output Optimization,” ASCE Journal of the Power Division, 92 (January, 1966), pp. 67–79.
  • Liebman, J. C. and W. R. Lynn. “The Optimal Allocation of Stream Dissolved Oxygen,” Water Resources Research, 2 (1966), pp. 581–91.
  • Little, J. D. C. “The Use of Storage Water in a Hydroelectric System,” Operations Research, 3 (1955), pp. 187–97.
  • Loucks, D. P. “A Comment on Optimization Methods for Branching Multistage Water Resource Systems,” Water Resources Research, 4 (1968), pp. 447–50.
  • Meier, W. L. and C. S. Beightler. “An Optimization Method for Branching Multistage Water Resource Systems,” Water Resources Research, 3 (1967), pp. 645–52.
  • Schweig, Z. and J. A. Cole. “Optimal Control of Linked Reservoirs,” Water Resources Research, 4 (1968), pp. 479–97.
  • Watt, K. E. F. “Dynamic Programming, ‘Look-Ahead Programming,’ and the Strategy of Insect Pest Control,” The Canadian Entomologist, 95 (1963), pp. 525–36.
  • Watt, K. E. F. Ecology and Resource Management. New York: McGraw-Hill, 1968.
  • Young, G. K., Jr. “Finding Reservoir Operating Rules,’ ASCE Journal of the Hydraulics Division, 43 (Nov. 1967), pp. 297–321.

AGRICULTURAL ECONOMICS

  • Burt, O. R. “Operations Research Techniques in Farm Management: Potential Contributions,” Journal of Farm Economics, 47 (1965), pp. 1418–26.
  • Burt, O. R. “Control Theory for Agricultural Policy: Methods and Problems in Operational Models,” American Journal of Farm Economics, 51 (1969), pp. 394–404.
  • Burt, O. R. and J. R. Allison. “Farm Management Decisions with Dynamic Programming,” Journal of Farm Economics, 45 (1963), pp. 121–36.
  • Day, R. H. Recursive Programming and Production Response. Amsterdam: North Holland Publishing Co., 1963.
  • Day, R. H. and E. H. Tinney. “A Dynamic Von Thünen Model,” Geographical Analysis, 1 (1969), pp. 137–51.
  • Fox, K. A. “The Potential Role of Control Theory in Policy Formulation for the U.S. Agricultural Industry,” American Journal of Agricultural Economics, 51 (1969), pp. 383–409.
  • Loftsgard, L. D. and E. O. Heady. “Application of Dynamic Programming Models for Optimal Farm and Home Plans,” Journal of Farm Economics, 41 (1959), pp. 51–62.
  • Tintner, G. “What Does Control Theory Have to Offer?” American Journal of Agricultural Economics, 51 (1969), pp. 383–93.

MISCELLANEOUS

  • Bellman, R. E. “Bottleneck Problems Functional Equations, and Dynamic Programming,” Econometrica, 23 (1955), pp. 37–87.
  • Bellman, R. and R. Kalaba. “On kth Best Policies,” Journal of the Society of Industrial and Applied Mathematics, 8 (1960), pp. 582–8.
  • Dorfman, R. “An Economic Interpretation of Optimal Control Theory,” Discussion Paper No. 54. Cambridge: Harvard Institute of Economic Research, 1968.
  • Emerson, M. J. “Dynamic Programming and Export Base Theory,” Paper presented at the Eighth Annual Meeting, Western Regional Science Association, February, 1969.
  • Murphy, Roy E. Adaptive Processes in Economic Systems. New York: Academic Press, 1965.
  • Schlager, K. J. “A Land Use Plan Design Model,” Journal of the American Institute of Planners, 31 (1965).
  • Schlager, K. J. “A Recursive Programming Theory of the Residential Land Development Process,” Highway Research Record No. 126. Washington D. C.: Highway Research Board, 1966.
  • Schlager, K. J. “Land-Use Planning Design Models,” ASCE Journal of the Highway Division, 93 (1967), pp. 135–42.
  • Scott, A. J. Combinatorial Programming, Spatial Analysis and Planning. New York: Wiley, forthcoming.
  • Southeastern Wisconsin Regional Planning Commission, “A Mathematical Approach to Urban Design,” SWRPC Technical Report No. 3. Waukesha, Wisconsin, 1966.
  • White, D. J. “Forecasts and Decisionmaking,” Journal of Mathematical Analysis and Applications, 14 (1966), pp. 163–73.
  • Ying, C. C. “Learning by Doing—an Adaptive Approach to Multiperiod Decisions,” Operations Research, 15 (1967), pp. 797–812.

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