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

In this paper, we present a novel modeling 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 both equity and efficiency, being on the Pareto frontier. Our sensitivity analysis demonstrates that assisting the food-banks should go hand-in-hand with helping eliminate poverty in the demand population. 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, our results reveal that encouraging charitability is always beneficial for the food-banks, albeit with diminishing returns. Finally, we extend our model to the case with stochastic receiving capacities and derive additional insights with regards to the inherent trade-offs between equity, efficiency, and reliability in the network.