  In this paper, we present a novel modelling perspective to the food-bank
donation allocation problem under equity and efficiency performance measures.
Using a penalty factor in the objective function, our model explicitly accounts
for both efficiency and equity, simultaneously. We give the tightest lower and
upper bounds of the penalty factor, which can conveniently characterize
closed-form optimal solutions for the perfect efficiency and perfect equity
cases. Testing our model on the full spectrum of our penalty factor, using real
data from Feeding America, we demonstrate that the solutions from our model
dominate those of a benchmark from the literature in terms of equity,
efficiency, and utilization equity (utiloquity). Our sensitivity analysis
demonstrates that the society should put its priority on helping eliminate
poverty before investing on capacity expansions in charity organizations like
food-banks. This will ensure that adding more capacity to the network will
always lead to a decrease in the price of equity for the food-banks. On the
other hand, we observed that encouraging the society towards charitability is
always beneficial for the food-banks, albeit with diminishing returns. Finally,
our experiments demonstrate that reducing poverty, as the most important
element in achieving higher equity, is dependent on reducing demand
variability, as opposed to the average level of demand.
