A Grain Storage Problem, with Random Production

A grain producer produces and stores a grain, say wheat or corn, and after each crop must decide how much to sell and how much to store. He faces a T period planning horizon, a downwards sloping demand and a storage cost, an increasing function of the amount stored. On the supply side we will assume that the area planted, the inputs such as fertilizers, labor etc. are fixed. The weather with all the unfavorable damage by frost, bugs, and burning sun will determine the final yield of the crop, i.e. we are assuming that the crop of each year is a random variable. The objective of the producer is to maximize the total expected accumulated profit. The concept of liquid stock is introduced. A sensitivity analysis is carried studying the effect of changes in the parameters of the problem on the optimal policy. (Author)