Dynamic programming approach to optimal inventory processes with delay in delivery
Author:
Richard Bellman
Journal:
Quart. Appl. Math. 18 (1961), 399-403
MSC:
Primary 90.00
DOI:
https://doi.org/10.1090/qam/118516
MathSciNet review:
118516
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Abstract: The usual dynamic programming approach to inventory processes with delays in delivery leads to functions of many variables. This multi-dimensionality prevents the straightforward utilization of digital computers.
- Kenneth J. Arrow, Theodore Harris, and Jacob Marschak, Optimal inventory policy, Econometrica 19 (1951), 250–272. MR 44094, DOI https://doi.org/10.2307/1906813
- Richard Bellman, Dynamic programming, Princeton University Press, Princeton, N. J., 1957. MR 0090477
R. Bellman, Dynamic programming and the computational solution of feedback design control processes, Conference on Computers in Control, AIEE, October 16–18, 1957, Atlantic City, New Jersey
- Richard Bellman, Some new techniques in the dynamic programming solution of variational problems, Quart. Appl. Math. 16 (1958), 295–305. MR 102032, DOI https://doi.org/10.1090/S0033-569X-1958-0102032-9
- Richard Bellman, On a dynamic programming approach to the caterer problem. I, Management Sci. 3 (1957), 270–278. MR 91222, DOI https://doi.org/10.1287/mnsc.3.3.270
- R. Bellman, I. Glicksberg, and O. Gross, On the optimal inventory equation, Management Sci. 2 (1955), 83–104. MR 74761, DOI https://doi.org/10.1287/mnsc.2.1.83
A. Dvoretzky, J. Kiefer and J. Wolfowitz, The inventory problem, I, II, Econometrica 20, 187–222 (1952)
T. M. Whitin, The theory of inventory management, Princeton University Press, Princeton, New Jersey, 1953
- Kenneth J. Arrow, Samuel Karlin, and Herbert Scarf, Studies in the mathematical theory of inventory and production, Stanford Mathematical Studies in the Social Sciences, I, Stanford University Press, Stanford, Calif., 1958. MR 0094248
K. D. Arrow, T. E. Harris, and J. Marschak, Optimal inventory policy, Econometrica 19,250–272 (1951)
R. Bellman, Dynamic programming, Princeton University Press, Princeton, New Jersey, 1957
R. Bellman, Dynamic programming and the computational solution of feedback design control processes, Conference on Computers in Control, AIEE, October 16–18, 1957, Atlantic City, New Jersey
R. Bellman, Some new techniques in the dynamic programming solution of variational problems, Quart. Appl. Math., 16 295–305 (1958)
R. Bellman, On a dynamic programming approach to the caterer problem—I, Management Science 3, 270–278 (1957)
R. Bellman, I. Glicksberg and O. Gross, On the optimal inventory equation, Management Science 2, 83–104 (1955)
A. Dvoretzky, J. Kiefer and J. Wolfowitz, The inventory problem, I, II, Econometrica 20, 187–222 (1952)
T. M. Whitin, The theory of inventory management, Princeton University Press, Princeton, New Jersey, 1953
H. Scarf, S. Karlin and K. J. Arrow, Studies in the mathematical theory of inventory and production, Stanford Univ. Press, 1958
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Article copyright:
© Copyright 1961
American Mathematical Society
