On the equity-efficiency trade-off in food-bank network operations

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.