An influence diagram is a widely-used graphical model for representing and solving problems of sequential decision making under imperfect information. A closely-related model for the same class of problems is a partially observable Markov decision process (POMDP). This dissertation leverages the relationship between these two models to develop improved algorithms for solving influence diagrams. The primary contribution is to generalize two classic dynamic programming algorithms for solving influence diagrams, Arc Reversal and Variable Elimination, by integrating them with a dynamic programming technique originally developed for solving POMDPs. This generalization relaxes constraints on the ordering of the steps of these algorithms in a way that dramatically improves scalability, especially in solving complex, multi-stage decision problems. A secondary contribution is the adoption of a more compact and intuitive representation of the solution of an influence diagram, called a strategy. Instead of representing a strategy as a table or as a tree, a strategy is represented as an acyclic graph, which can be exponentially more compact, making the strategy easier to interpret and understand.

This research focuses on developing a crop decision planning model to help farmers make decisions for an upcoming crop year. The decisions consist of which crops to plant, the amount of land to allocate to each crop, when to grow, when to harvest, and when to sell. The objective is to maximize the overall profit subject to available resources under yield and price uncertainties. To help achieve this objective, we develop yield and price forecasting models to estimate the probable outcomes of these uncertain factors. The output from both forecasting models are incorporated into the crop decision planning model which enables the farmers to investigate and analyze the possible scenarios and eventually determine the appropriate decisions for each situation. This dissertation has three major components, yield forecasting, price forecasting, and crop decision planning. For yield forecasting, we propose a crop-weather regression model under a semiparametric framework. We use temperature and rainfall information during the cropping season and a GDP macroeconomic indicator as predictors in the model. We apply a functional principal components analysis technique to reduce the dimensionality of the model and to extract meaningful information from the predictors. We compare the prediction results from our model with a series of other yield forecasting models. For price forecasting, we develop a futures-based model which predicts a cash price from futures price and commodity basis. We focus on forecasting the commodity basis rather than the cash price because of the availability of futures price information and the low uncertainty of the commodity basis. We adopt a model-based approach to estimate the density function of the commodity basis distribution, which is further used to estimate the confidence interval of the commodity basis and the cash price. Finally, for crop decision planning, we propose a stochastic linear programming model, which provides the optimal policy. We also develop three heuristic models that generate a feasible solution at a low computational cost. We investigate the robustness of the proposed models to the uncertainties and prior probabilities. A numerical study of the developed approaches is performed for a case of a representative farmer who grows corn and soybean in Illinois.