Abstract
We analyze a mathematical programming model of a fractional flow process which consists ofn sectors and all possible time-dependent streams of flow between, into and out of the sectors. Assuming specific constraints on flow, least cost policies are determined for control of the system transactions involved over a given finite time horizon and over an infinite horizon. Several applications of the model are presented and discussed.
Similar content being viewed by others
References
D.J. Bartholemew,Stochastic models for social processes (Second Ed.) (Wiley, New York, 1973) pp. 95–136.
R.E. Bellman,Dynamic programming (Princeton University Press, 1957).
R.E. Bellman,Introduction to matrix analysis (Second Ed.) (McGraw Hill, New York, 1970) pp. 286–303.
J.S. Chipman, “The multisector multiplier”,Econometrica 18 (1950).
D. Gale, “On optimal development in a multi-sector economy”,Review of Economic Studies 34 (1967).
R.M. Goodwin, “The multiplier as matrix”,Economic Journal 59 (1949).
R.C. Grinold and R.E. Stanford, “Optimal control of a graded manpower system”, ORC Rept. 73-8, University of California, Berkeley (April 1973).
J.G. Kemeny and L. Snell,Mathematical models in the social sciences (Ginn and Co., 1962) pp. 66–71.
Kelvin Lancaster,Mathematical economics (MacMillan, 1971).
Leon S. Lasdon,Optimization theory for large scale systems (MacMillan, 1970).
L. Metzler, “A multiple region theory of income and trade”,Econometrica 18 (1950).
Masao Nakamura, “Some programming problems in population projection”,Operations Research 21 (1973).
R.E. Stanford, “Optimal control of a graded manpower system”, ORC Rept. 71-20, University of California, Berkeley (August 1971).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stanford, R.E. Analytical solution of A dynamic transaction flow problem. Mathematical Programming 10, 214–229 (1976). https://doi.org/10.1007/BF01580668
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01580668