DYNAMIC PROGRAMMING: HAS ITS DAY ARRIVED?

A look at John Kennedy's recent review article on dynamic programming (DP) applications in agriculture, forestry, and fisheries leaves no doubt that DP is a useful analytical and numerical technique [Kennedy]. However, the method appears to be in more common use among Australian than American agricultural economists, particularly in the farm management/production economics area. When John Allison and I published "Farm Management Decisions with Dynamic Programming " [Burt and Allison] twenty years ago, I though DP would be as routinely used by now as linear programming (LP), but this is obviously not the case. After outlining the fundamental principles of DP, the apparent lack of its popularity among research agricultural economists will be addressed. For simplicity in exposition, consider a dynamic process which can be described by a single state variable and a first order difference equation,

[1]  H. Simon,et al.  Dynamic Programming Under Uncertainty with a Quadratic Criterion Function , 1956 .

[2]  Dieter Bartmann,et al.  A method of bisection for discounted Markov decision problems , 1979, Z. Oper. Research.

[3]  Jo van Nunen,et al.  A set of successive approximation methods for discounted Markovian decision problems , 1976, Math. Methods Oper. Res..

[4]  Pinhas Zusman,et al.  Simulation: A Tool for Farm Planning under Conditions of Weather Uncertainty , 1965 .

[5]  N. J. Dudley,et al.  Optimal Stochastic Control of U.S. Wheat Stocks and Exports , 1980 .

[6]  Oscar R. Burt,et al.  Farm Management Decisions With Dynamic Programming , 1963 .

[7]  John O.S. Kennedy,et al.  Applications of Dynamic Programming to Agriculture, Forestry and Fisheries: Review and Prognosis , 1981 .

[8]  R. Bellman.  Dynamic programming. , 1957, Science.

[9]  Kenneth J. Arrow.  STATISTICS AND ECONOMIC POLICY , 1957 .

[10]  Ronald A. Howard,et al.  Dynamic Programming and Markov Processes , 1960 .

[11]  Oscar R. Burt,et al.  Optimal Resource Use Over Time with an Application to Ground Water , 1964 .

[12]  Evan L. Porteus.  Bounds and Transformations for Discounted Finite Markov Decision Chains , 1975, Oper. Res..

[13]  Michael Athans.  The Discrete Time Linear-Quadratic-Gaussian Stochastic Control Problem , 1972 .

[14]  C. Hildreth.  Problems of Uncertainty in Farm Planning , 1957 .

[15]  Michael D. Intriligator,et al.  Mathematical optimization and economic theory , 1971 .

[16]  Richard E. Howitt,et al.  Resource Production Under Uncertainty: A Stochastic Control Approach to Timber Harvest Scheduling , 1980 .

[17]  C. R. Taylor,et al.  Approximately Optimal Carryover Levels for Wheat in the United States , 1979 .

[18]  Averill M. Law,et al.  The art and theory of dynamic programming , 1977 .

[19]  H. Theil.  A Note on Certainty Equivalence in Dynamic Planning , 1957 .