Abstract
Dynamic Programming (DP) is a useful approach to multi-stage decision problems. On the basis of Bellman’s optimality principle such a problem can be decomposed into subproblems through recursive formulae. Bellman (1957), 1957a and Dantzig (1957) introduced a DP method for integer-variable linear programs. This method yields pseudo-polynomial algorithms when the number of constraints is fixed (Papadimitriou (1981)). In the class of linear programs, problems with a staircase structure can be efficiently treated by DP methods which can be interpreted as iterative predictor-corrector processes using a pricing mechanism for subproblems at individual stages (e.g., Dantzig (1963), Ho and Manne (1974), Ho (1978), Ho and Loute (1980), Abrahamson (1981) . Various applications of DP have also been developed in production planning (Manne (1958) , Wagner and Whitin (1959), Clark and Scarf (1960), Veinott (1965), 1969), Bessler and Veinott (1966), Zangwill (1965), 1966) (1969), Konno (1973), (1988), Bitran and Yanasse (1982), Bitran et al. (1984),... In particular, polynomial algorithms have been obtained for concave cost lotsizing problems and their extensions (e.g., Wagner and Whitin (1959), Zangwill (1965), (1966), (1959), Dreyfus and Law (1977).
Chapter PDF
Keywords
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.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Konno, H., Thach, P.T., Tuy, H. (1997). Dynamic Programming Algorithms in Global Optimization. In: Optimization on Low Rank Nonconvex Structures. Nonconvex Optimization and Its Applications, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4098-4_11
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4098-4_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6835-9
Online ISBN: 978-1-4615-4098-4
eBook Packages: Springer Book Archive