Modeling for the equitable and effective distribution of donated food under capacity constraints

Abstract

Mathematical models are presented and analyzed to facilitate a food bank's equitable and effective distribution of donated food among the population at risk for hunger. Typically exceeding the donated supply, demand is proportional to the poverty population within the food bank's service area. The food bank seeks to ensure a perfectly equitable distribution of food, i.e., each county in the service area should receive a food allocation that is exactly proportional to the county's demand such that no county is at a disadvantage compared to any other county. This objective often conflicts with the goal of maximizing effectiveness by minimizing the amount of undistributed food. Deterministic network-flow models are developed to minimize the amount of undistributed food while maintaining a user-specified upper bound on the absolute deviation of each county from a perfectly equitable distribution. An extension of this model identifies optimal policies for the allocation of additional receiving capacity to counties in the service area. A numerical study using data from a large North Carolina food bank illustrates the uses of the models.A probabilistic sensitivity analysis reveals the effect on the models' optimal solutions arising from uncertainty in the receiving capacities of the counties in the service area.

Recent advances and opportunities in sustainable food supply chain: a model-oriented review

“…They also discuss the relationships among forecast accuracy, donation behaviour, and data uncertainty, and provide insights on how to affect food bank operational decisions. Orgut et al (2016) investigate the distribution problem of donated food among people exposed to food insecurity. The objective is to balance the equity and effectiveness of distributing food to the counties in the food bank's service area with the aid of mathematical models.…”

“…Mohan, Gopalakrishnan, and Mizzi (2013) detail how an organisation is able to improve the efficiency and effectiveness of its operations by partnering with a local university which resulted in more food reaching the food insecure. Orgut et al (2016) address equitable and effective distribution of donated food under capacity constraints. Sönmez et al (2016) a model to derive general operational insights and applied the model to the food bank of the Southern Tier in New York.…”

“…They consider animal welfare by limiting the maximum trip time for animals to eight hours according to EU regulations for animal transportation. The objective function in Orgut et al (2016) minimises the amount of undistributed food at a food bank subject to a user-specified constraint on the magnitude of each county's deviation from perfect equity for equitable and effective distribution of food donations. The objective functions in dos Santos et al (2010) and Costa et al (2014) maximise the profit subject to ecologically-based constraints.…”

Analysis and prediction of food donation behavior for a domestic hunger relief organization

“…This is especially true for food aid supply chains since demand is typically larger than supply [26,27]. As a result, significant attention has been given to improving distribution practices through vehicle routing for food collection and delivery [28,29,30,31], allocation of scarce supply [32,33], and location of distribution points [34]. In these studies, supply quantities are either not explicitly considered [30,31] or assumed known and available at the time of distribution decisions [29,32,33].…”

Avaliação De Objetivos Conflitantes E Da Sensibilidade Ao Risco Na Preparação Para Um Desastre Através De Otimização Estocástica

“…A equidade pode ser definida de muitas formas através de indicadores ou funções e de uma forma geral é relacionada à justiça no atendimento, exemplos de algumas medidas podem ser vistos emMarsh & Schilling (1994). Adota-se no presente trabalho o conceito de inequidade, ou falta de equidade, como a disparidade entre os níveis de serviço no atendimento entre os nós de demanda.Algumas ilustrações de como a equidade pode ser abordada em problemas na LH podem ser vistos emTzeng et al (2007),Davis et al (2013), McCoy et al(2014) eOrgut et al (2015). A Tabela 1 mostra quais diferentes atributos entre os 3E como objetivo da otimização ou como restrição e as abordagens de aversão ao risco são encontrados em literatura.Outro trade-off que é amplamente abordado em literatura de LH, mas também na GCS, é entre a eficiência de uma operaçãocustos em gerale efetividade Rawls & Turnquist (2010).…”