Predicting Farms’ Donations to Food Banks using the Analytic Hierarchical Process and Dempster Shafer Theory

We present an analysis of factors contributing to the annual level of donation of sweet potatoes in 2010-2016 to a North Carolina food bank. Our approach follows that of Su et al., who used the Analytic Hierarchy Process (AHP) and Dempster-Shafer theory (DST) to assess annual grain security in China for 1997-2007. We first identified the indices (or factors or criteria) that influence the level of donation and their “directions:” positive (the more the better), negative, or non-directional (average is best). We divided the range of each index into degrees (intervals) then applied AHP to get weights for the indices. To apply DST, we defined a frame of discernment that would generate focal elements that could be assigned to degrees of the indices. Then, using the index weights, we defined a BPA (basic probability function) for each year. Since for each year we had multiple pieces of possibly conflicting evidence, we used Dempster’s rule to combine each BPA with itself several times. In the resulting BPA, the focal element with greatest mass was taken as the prediction for the donation level for that year. We partitioned the range of the donation data into degrees to compare observations with the focal elements in the BPA. Predicted donation degrees matched observed degrees reasonably well if degree boundaries are well chosen. Analysis of apparent anomalies suggested a more sophisticated approach and the need to involve other information sources. This approach allows one to experiment in a principled way (and without assumptions about probability distributions) with the relative importance of the multiple factors that affect the predicted quantity and so to understand how these factors together contribute to that quantity. It is suggested for gaining preliminary insight, which may be exploited in the application of more rigid analytic techniques.