Koenen Melissa F, Geelen Romée, Balvert Marleen, Fleuren Hein
Department of Econometrics and Operations Research, Tilburg School of Economics and Management, Tilburg University, Tilburg, Netherlands.
Zero Hunger Lab, Tilburg School of Economics and Management, Tilburg University, Tilburg, Netherlands.
Front Nutr. 2024 Sep 18;11:1425749. doi: 10.3389/fnut.2024.1425749. eCollection 2024.
Optimization techniques, such as linear programming, can be used to estimate the minimum cost of a nutrient-adequate food basket, to determine if individuals or households can afford nutritious diets. These cost estimates typically account for seasonal fluctuations but often overlook significant disruptions in the availability of affordable nutritious food that can severely impact food and nutrition security.
This paper proposes a tree-based method, the binary search tree, to assess the resilience of the cost estimate of the minimum-cost food basket. In particular, this method aims to identify indispensable foods in these baskets - those whose unavailability would lead to a substantial cost increase. The binary search tree operates by iteratively excluding essential food items while ensuring the construction of minimum-cost nutritious baskets. It considers all relevant combinations of foods up to a specified size and avoids unnecessary optimizations, thereby saving computation time. We describe how the resulting tree can be evaluated and condensed to capture only the necessary information for decision makers. The construction and evaluation of the binary search tree are independent of the (dietary) restrictions or type of optimization model (i.e., linear, non-linear or integer) included.
In general, the binary search tree can identify all (combinations of) foods whose exclusion leads to a significant cost increase of a nutritious food basket. Furthermore, it can detect possible substitute effects between foods and identify key limiting nutrients. A case study is presented in which the binary search tree is applied to data from Ebonyi, Nigeria, modeled using linear programming. We report all combinations of up to five foods that, when unavailable, can impact food and nutrition security in Ebonyi.
The BST can provide insights into local food and nutrition security when facing drastic disruptions in access to nutritious foods by identifying indispensable foods. Its results can be used to inform and design interventions in the context of humanitarian operations.
优化技术，如线性规划，可用于估计营养充足的食物篮的最低成本，以确定个人或家庭是否能够负担得起营养饮食。这些成本估计通常会考虑季节性波动，但往往忽略了可负担得起的营养食品供应的重大中断，而这种中断可能会严重影响粮食和营养安全。
本文提出了一种基于树的方法——二叉搜索树，以评估最低成本食物篮成本估计的恢复力。具体而言，该方法旨在识别这些食物篮中不可或缺的食物——那些无法获得会导致成本大幅增加的食物。二叉搜索树通过迭代排除必需食物项目来运作，同时确保构建最低成本的营养食物篮。它会考虑指定规模内所有食物的相关组合，避免不必要的优化，从而节省计算时间。我们描述了如何评估和精简所得的树，以仅获取决策者所需的信息。二叉搜索树的构建和评估与所包含的（饮食）限制或优化模型类型（即线性、非线性或整数）无关。
一般来说，二叉搜索树可以识别所有（组合的）食物，排除这些食物会导致营养食物篮成本大幅增加。此外，它可以检测食物之间可能的替代效应，并识别关键的限制营养素。本文给出了一个案例研究，其中将二叉搜索树应用于来自尼日利亚埃邦伊的数据，并使用线性规划进行建模。我们报告了多达五种食物的所有组合，当这些食物无法获得时，可能会影响埃邦伊的粮食和营养安全。
二叉搜索树可以通过识别不可或缺的食物，在面临获取营养食物的剧烈中断时，为当地粮食和营养安全提供见解。其结果可用于为人道主义行动中的干预措施提供信息和设计方案。
