Markovian decision process to find optimal policies in the management of an orange farm

This paper presents the application of a Markovian decision process to define the optimal policy in the case of an orange farm management. The problem has been proposed to be solved with two approaches: policy iteration and linear programming, which have been formulated in first instance without discount factor and then applying various discount factors ranging from 0.5 to 0.9. The policy iteration methodology has been more efficient than linear programming, since it requires fewer calculations to achieve the optimal solution. In all cases the result has been that the optimal policy is to better take care the orange farm to maximize economic benefits, which would reach an amount of 431 Mexican pesos per orange tree each year.

Linear programming; Markov chains; Markovian decision process; Optimization; Policy iteration

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