Abstract
In this paper, we study the competition of healthcare institutions for medical supplies in emergencies caused by natural disasters. In particular, we develop a two-stage stochastic programming model in a generalized Nash equilibrium framework. It provides the optimal amount of medical supplies from warehouses to hospitals, in order to minimize both the purchasing cost and the transportation costs. For effective disaster planning, we allow for real-time information spreading and up-to-date disaster evaluation. Thus, each institution deals with a two-stage stochastic programming model that takes into account the unmet demand at the first stage, and the consequent penalty. Then, the institutions simultaneously solve their own stochastic optimization problems and reach a stable state governed by the stochastic generalized Nash equilibrium concept. Moreover, we formulate the problem as a two-stage variational inequality. We also present an alternative two-stage variational inequality formulation using the Lagrangian relaxation approximation.
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Acknowledgements
The research was partially supported by the research projects “Problemi di equilibrio: metodi variazionali e teoria dei giochi” GNAMPA-INdAM and “Programma ricerca di ateneo UNICT 2020–22 linea 2-OMNIA” University of Catania. These supports are gratefully acknowledged.
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Fargetta, G., Scrimali, L. (2021). A Two-Stage Variational Inequality for Medical Supply in Emergency Management. In: Cerulli, R., Dell'Amico, M., Guerriero, F., Pacciarelli, D., Sforza, A. (eds) Optimization and Decision Science. AIRO Springer Series, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-86841-3_8
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