Avoiding unfairness of Owen allocations in linear production processes

This paper deals with cooperation situations in linear production problems in which a set of goods are to be produced from a set of resources so that a certain benefit function is maximized, assuming that resources not used in the production plan have no value by themselves. The Owen set is a well-known solution rule for the class of linear production processes. Despite their stability properties, Owen allocations might give null payoff to players that are necessary for optimal production plans. This paper shows that, in general, the aforementioned drawback cannot be avoided allowing only allocations within the core of the cooperative game associated to the original linear production process, and therefore a new solution set named EOwen is introduced. For any player whose resources are needed in at least one optimal production plan, the EOwen set contains at least one allocation that assigns a strictly positive payoff to such player. © 2012 Elsevier B.V. All rights reserved.The authors want to thank the Spanish Ministry of Science and Technology for providing financial support under Grants MTM200767433 and MTM201019576, and the Junta de Andalucia/Feder (Spain) under Grant FQM5849. Special thanks are due to two anonymous referees for their valuable comments and suggestions.Perea Rojas Marcos, F.; Puerto Albandoz, J.; Fernández García, FR. (2012). Avoiding unfairness of Owen allocations in linear production processes. European Journal of Operational Research. 220(1):125-131. https://doi.org/10.1016/j.ejor.2012.01.013S125131220

What do we know about the α/β for prostate cancer?

Since last decade, the debate on the parameter which reflects prostate cancer sensitivity to fractionation in a radiotherapy treatment, the α/β, has become extensive. Unlike most tumors, the low labeling indices (LI) and large potential doubling time that characterize the prostate tumor led some authors to consider that it may behave as a late responding tissue. So far, the existing studies with regard to this subject point to a low value of α/β, around 2.7 Gy, which may be considered as a therapeutic gain in relation to surrounding normal tissues by using fewer and larger fractions. The aim of this paper is to review several estimates that have been made in the last few years regarding the prostate cancer α/β both from clinical and experimental data, as well as the set of factors that have potentially influenced these evaluations

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