No abstract

Standard models in stochastic resource allocation concern the economic processing of all jobs in some set J. We consider a set up in which tasks in various subsets of J are deemed to be alternative to one another, in that only one member of such a subset of alternative tasks will be completed during the evolution of the process. Existing stochastic scheduling methodology for single-machine problems is developed and extended to this novel class of models. A major area of application is in research planning.

Standard models in stochastic resource allocation concern the economic processing of all jobs in some set J. We consider a set up in which tasks in various subsets of J are deemed to be alternative to one another, in that only one member of such a subset of alternative tasks will be completed during the evolution of the process. Existing stochastic scheduling methodology for single-machine problems is developed and extended to this novel class of models. A major area of application is in research planning.

Nash has extended Gittins' work to describe optimal strategies for a class of generalised bandit problems. Here we use a forwards induction argument to analyse ε -optimal strategies for generalised bandit problems. An evaluation procedure for such problems is described; this may be used to analyse models in research planning and stochastic scheduling.

In many contexts in which resource allocation takes place in a stochastic environment, new jobs arrive over time. Incorporation of an arrivals process into the scheduling model significantly complicates the problem of determining optimal strategies. Earlier computational studies suggest that for a large class of single machine problems often little is lost by adopting a heuristic that (essentially) ignores the arrivals process. Cases are described in which the heuristic yields an optimal strategy and analytical tools are developed that enable its evaluation. The heuristic performs well, both when arrivals are rare and when arrivals of good jobs are frequent.