Ostrom Workshop, Indiana University, Bloomington, IN, United States of America.
Department of Geography, Indiana University, Bloomington, IN, United States of America.
PLoS One. 2019 Jul 22;14(7):e0219895. doi: 10.1371/journal.pone.0219895. eCollection 2019.
The Thrifty Food Plan (TFP) is the basis of benefit allocations within the USDA's Supplemental Nutrition Assistance Program (SNAP), which administers nearly $70 billion in benefits to over 42 million people annually. To produce the allocation of food within the TFP, the USDA uses a mathematical optimization model that solves for the daily apportionment across various food groups. The model is constrained by nutritional and consumption requirements to produce an "optimal" allocation. Despite the importance of the TFP, the computational solution developed by the USDA has received insufficient attention, with only a handful of articles written on the TFP optimization model. Here, we run three alternative objective functions that are simpler than the one used by USDA. Our first alternative objective function minimizes the sum of squared errors between the consumed market basket of goods and an allocated market basket of goods, the second alternative objective function minimizes the sum of the absolute value of the difference between the consumed market basket of goods and an allocated market basket of goods, and the third alternative objective function minimizes the weighted absolute deviation of allocations and actual consumption expressed as a proportion of observed consumption. A clear theoretical advantage of either of our methods is that they eliminate the need to arbitrarily set allocated consumption to nonzero values, as is the case for the logarithmic objective function used by USDA. In an operational sense, we find that our model formulations produce an allocation that fits actual consumption better than the objective function employed by the USDA.
节俭食品计划（TFP）是美国农业部补充营养援助计划（SNAP）中福利分配的基础，该计划每年向超过 4200 万人分配近 700 亿美元的福利。为了在 TFP 中分配食品，美国农业部使用了一种数学优化模型，该模型针对各种食品组解决了每日分配问题。该模型受到营养和消费需求的限制，以产生“最佳”分配。尽管 TFP 很重要，但美国农业部开发的计算解决方案并没有得到足够的关注，只有少数几篇文章专门讨论了 TFP 优化模型。在这里，我们运行了三个比美国农业部使用的更简单的替代目标函数。我们的第一个替代目标函数是最小化消费的商品市场篮子和分配的商品市场篮子之间的平方误差之和，第二个替代目标函数是最小化消费的商品市场篮子和分配的商品市场篮子之间的差值的绝对值之和，第三个替代目标函数是最小化分配和实际消费的加权绝对偏差，以观察到的消费为比例表示。我们方法中的任何一种都有一个明显的理论优势，即它们消除了像美国农业部使用的对数目标函数那样任意将分配消费设置为非零值的需要。在操作意义上，我们发现我们的模型配方比美国农业部使用的目标函数更能准确地分配实际消费。
