Value of Image-based Yield Prediction: Multi-location Newsvendor Analysis

Consider an agricultural processing company, which wants to pre-purchase crop from different locations before a harvesting season in order to maximize the total expected profit from all outputs subject to multiple resource constraints. The yields for different outputs are random and depend on the location. By remotely sensing from satellites or locally sensing from unmanned aerial vehicle, the firm may employ an image-based yield prediction model at the pre-purchase time. The distribution of the yield differs by a location. With the sensed data, the company updates the distribution of the yield using a regression model, whose explanatory variable is a vegetation index from image processing. At a more favorable location, the distribution of the yield is stochastically larger. The objective of this paper is to quantify the added value of image sensing in predicting crop yield. Specifically, the posterior yield distribution from image processing is used as an input to the multi-location newsvendor model with random yields. The optimal expected profit given the posterior distribution is compared to that with only the prior distribution of the yield. The difference between the total expected profits with the prior and posterior distributions is defined as the value of the sample information. We derive the type-1 and -2 errors as a function of the standard error of the estimate. In the numerical example, we show that the value of the sample information tends to be increasing (with diminishing return) as the yield prediction model becomes more accurate.