The Crop Planning Decision Problem: A Comment

In the October 1969 issue of Management Science, Professor Warren Hausman presented a framework for analysis of sequential decision problems of a recurring nature (“Sequential Decision Problems: A Model to Exploit Existing Forecasters,” pp. B93-B111). His system consists of a dynamic programming decision model based upon successively revised forecasts of a key unknown variable and on the probability distribution of forecast changes. The decision system is illustrated with an application to a specific crop planning problem faced by a vegetable processor. We focus, in this comment, on the specific crop supply problem used by Hausman to illustrate the applicability of his general framework.

Hausman's assumption that crop adjustment costs are quadratic allows the following simplifications to be demonstrated:

(a) No grid search and no numerical integration is needed to solve the stated crop planning problem; a closed-form analytical solution is possible in this case.

(b) The closed-form solution does not depend on the form of the probability density function for forecast revisions, but only on its first two moments.