Title: Minmax multi-period resources allocation problem with weighted substitutable resources

Authors: Mohamed Esalah Salah; Slah Ben Youssef; Abdelwaheb Rebai

Addresses: Faculté des Sciences Economiques et de Gestion de Sfax, Route Aéroport km 4, BP No 1088, 3018 Sfax, Tunisia ' Al-Imam Muhammad Ibn Saud Islamic University, Airport Rd, PO Box 5701, Riyadh 11432, Saudi Arabia ' Faculté des Sciences Economiques et de Gestion de Sfax, Route Aéroport km 4, BP No 1088, 3018 Sfax, Tunisia

Abstract: Minmax multi-period resources allocation problem with weighted substitutable resources is concerned with the allocation of m resources (wealth, working opportunities, healthcare, alimentary needs) among n users during t periods. The objective of this problem is to minimise the maximum performance function, knowing that certain weighted substitution between resources is possible. Today, one of the most controversial questions is how to allocate the limited amount of resources among competing users in order to realise justice between users. This question indicates that we are searching for methods to realise fairness in the allocation of limited resources. In this paper, we study some variants of minmax resources allocation problems. Then, we present the principles of distributive justice and we propose the model to formulate the minmax multi-period resources allocation problem with weighted substitutable resources. Finally, we propose an exact algorithm to solve our formulated model and we present a numerical example to test our algorithm. The obtained result is considered as a motivation to solve a real instance.

Keywords: distributive justice; equity; equality; fairness; need; resource allocation; weighted substitutable resources; wealth; working opportunities; healthcare; alimentary needs.

DOI: 10.1504/IJARGE.2015.069787

International Journal of Agricultural Resources, Governance and Ecology, 2015 Vol.11 No.1, pp.45 - 62

Available online: 11 Jun 2015 *

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