On the Egalitarian–Utilitarian spectrum in stochastic capacitated resource allocation problems

Abstract

In this paper, we study a generalized resource allocation problem where a limited resource is to be allocated to a set of agencies with stochastic receiving capacities while taking into account the decision-maker’s preference towards equity in allocation. Taking the empiric distributional nature of the capacities into account, we formulate the problem in a chance-constrained based Mixed-Integer Programming framework with user-specified reliability and tolerance levels as well as equity preference level. We show that the problem can be conveniently reduced to a linear equivalent with adjusted capacity constraints. Deriving the tightest lower and upper bounds corresponding to the utilitarian and egalitarian perspectives, respectively, we give the closed-form optimal solutions for such cases. Using real data, we test the behavior of our model with a view towards the inherent equity-efficiency as well as reliability-efficiency trade-offs. We further characterize the cost and value of information in a detailed analysis.