The p-median location problem with lack of capacity

I. Martin Melero, M. Landete Ruiz, J. C. Gonçalves Dosantos, J. Sanchez Soriano

In many case studies of Location Science, a relevant topic of interest is the allocation of scarce resources among stakeholders (disaster management, design of transport networks or allocation of health coverage). However, there are no works in current literature that effectively model a large lack of capacity. Moreover, in a problem with lack of capacity, the decision maker might be able to decide where to install capacities in the facilities to be opened. In this contribution, we formulate the p-median location problem with lack of capacity, an optimisation problem that seeks to allocate scarce resources among clients and distribute capacities among potential facilities. Different models are proposed, some of which include the Game Theory properties of symmetry, order preservation and welfarism. Our proposed models outperform a canonical distribution rule based on traditional Location Science in efficient capacity use and balanced allocation of resources among the clients.

Keywords: p-median location problem, lack of capacity, proportional allocation, equal gain allocation, equal loss allocation

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June 11, 2025  10:30 AM
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