Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families

We considered the online scheduling problem of simple linear deteriorating job families on m parallel batch machines to minimize the makespan, where the batch capacity is unbounded. In this paper, simple linear deteriorating jobs mean that the actual processing time p j of job J j is assumed to be a linear function of its starting time s j , i.e., p j = α j s j , where α j > 0 is the deterioration rate. Job families mean that one job must belong to some job family, and jobs of different families cannot be processed in the same batch. When m = 1 , we provide the best possible online algorithm with the competitive ratio of ( 1 + α max ) f , where f is the number of job families and α max is the maximum deterioration rate of all jobs. When m ≥ 1 and m = f , we provide the best possible online algorithm with the competitive ratio of 1 + α max .

La storia, la morale e la politica in Tucidide

- The paper analyses Thucydides's views on history, ethics and politics trying to highlight how they affect each other. Thucydides has a tragic conception of history, according to which, notwithstanding the presence of some constants, human vicissitudes are open to unpredictability and chance. This view is closely related to Thucydides moral outlook, which is interpreted as a version of moral pluralism that recognises two mutually incompatible families of values: those related with greatness and success, and those stemming from compassion and pity. Coming to politics, it is argued that Thucydides's most valuable contribution lies in his penetrating analysis of the dynamics of power and in particular in his understanding of the fundamental importance of the dialectic between stabilizing and chaotic factors. Political thought should take account of those factors and that means that historical and empirical considerations should enter political theory no later than moral ideals and normative standards.