A Markov decision process model for equitable distribution of supplies under uncertainty

Many individuals suffering from food insecurity obtain assistance from governmental programs and nonprofit agencies such as food banks. Much of the food distributed by food banks come from donations which are received from various sources in uncertain quantities at random points in time. This paper presents a model that can assist food banks in distributing these uncertain supplies equitably and measure the performance of their distribution efforts. We formulate this decision problem as a discrete-time, discrete state Markov decision process that considers stochastic supply, deterministic demand and an equity-based objective. We investigate three different allocation rules and describe the optimal policy as a function of available inventory. We also provide county level estimates of unmet need and determine the probability distribution associated with the number of underserved counties. A numerical study is performed to show how the allocation policy and unmet need are impacted by uncertain supply and deterministic, time-varying demand. We also compare different allocation rules in terms of equity and effectiveness.