مدل فرایند تصمیم گیری مارکوف به منظور پخش منصفانه منابع تحت شرایط عدم قطعیت A Markov decision process model for equitable distribution of supplies under uncertainty

1. Introduction Food insecurity is defined as the situation where people are not able to access enough food at all times for an active, healthy life (USDAERS, 2006). The occurrence of food insecurity in the United States (U.S.) is significant, affecting approximately 48.1 million Americans, 15.3 million children and 32.8 million adults. Furthermore, a 2014 study on household food insecurity reported that 14% of U.S. households were unable to access enough food at all times (Coleman-Jensen, Rabbitt, Gregory, & Singh, 2015). The U.S. Government has established several public assistance programs to address this problem. These programs provide financial assistance, supplemental food, and nutrition support to individuals and states to increase access to healthy food for low-income households. Some of the most well-known programs are the Supplemental Nutrition Assistance Program (SNAP), the Women, Infants, and Children (WIC) program, and The Emergency Food Assistance Program (TEFAP) (see fns.usda.gov/ programs-and-services for a comprehensive list). In addition to government funded programs, non-profit organizations, such as Feeding America, also help to address the food insecurity problem. Feeding America (FA), the nation’s leading domestic hungerrelief organization, seeks to eliminate hunger by providing food ∗ Corresponding author. E-mail address: lbdavis@ncat.edu (L.B. Davis). to those in need through a nationwide network of about 200 member food banks and distribution centers across the country (FeedingAmerica, 2014). FA, as the parent food bank, provides administrative support, training of personnel, standards for food safety and food distribution to its member food banks. The local food banks, although partnering with FA, remain largely independent with their own management systems and budget. They solicit funds, food and supplies from individuals, groups, farmers, local manufacturers and retailers. These donations represent sources of supply that enable them to meet the demand of the people at risk of hunger. Hence, supplies to the food bank are based on the goodwill of donors who are not obligated to give at any particular time or in any particular quantity. Consequently, donations may be infrequent, almost expired which makes them inappropriate for consumption after a few days, or may not be what is actually needed. Nevertheless, food banks need to be able to adequately manage their inventory to ensure equitable distribution of supplies since meeting the demands by aid recipients is not possible with limited supply. This paper presents a decision model that assists food banks in equitable allocation of uncertain, donated supplies. We define equity as a function of the pounds distributed per person in poverty (PPIP). FA proposed this indicator as a way to measure the performance of its members. The benchmark is to distribute at least 75 pounds of food products for each person in poverty over a 12-month period. We use PPIP to measure equitable distribution practices within the food bank’s service area and also identify deviations from the performance goal set by FA. The decision making problem is formulated as a discrete-time, discrete state (DTDS) Markov decision process (MDP).