Supply Constrained Location‐Distribution in Not‐for‐Profit Settings

Inspired by the World Food Programme's activity in the post‐civil war food crisis in Angola, this study proposes a systematic approach to address the location distribution problem in not‐for‐profit settings, where a limited volume of supply has to be allocated to different demand regions. The use of utility functions is key in our framework because it allows the decision‐maker to establish priorities by representing the heterogeneous effects of distributing supply to different demand locations (location effect) and to different individuals in the same demand location (diminishing returns effect). We propose the use of two fractional objectives with the utility functions embedded into them: an efficiency measure and a new inequity measure related to the Gini coefficient. The suggested problem has the form of a bi‐objective integer linear fractional program and our resolution optimization technique is designed to solve for multiple fractional objective measures. Novel analytical results for the worst‐case performance of the proposed resolution technique are provided. Our numerical experiments assess computational efficiency and provide concrete managerial prescriptions. Finally, an illustrative application of our approach in the context of the food crisis in Angola is presented based on an efficiency‐inequity trade‐off analysis.