DYNAMIC PROGRAMMING: HAS ITS DAY ARRIVED?

Abstract

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) Xt+ 1 = h (ut,xt, Et) where u, x, and E are the decision variable, state variable, and a random variable, respectively.Frequently, the economic criterion is a periodic cash flow, the expectation of which can be written as a function of ut and xt, i.e., G(ut,xt).A one-period discount factor appropriately defined for the length of time period t is denoted 3. Since the conditional expected periodic return function, G(ut,xt), is a random variable for periods j>t from the decision agent's point of view at time t, a

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