On the scheduling of alternative stochastic jobs on a single machine

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.

Single-machine stochastic scheduling with dependent processing times

“…From Theorem 1 of Glazebrook and Fay (1987), a result for the independence case, we deduce from (6) and 7that…”

“…Here a (discounted) reward R, is earned upon the jth job completion, j = 1, 2. For examples of-such models, see Glazebrook and Fay (1987). In (2) E:J( is an expectation conditional upon the application of policy n: Note that we shall introduce job-specific reward models in Section 4.…”

“…their own right. Glazebrook and Fay (1987) study such models for the case of independent processing times. They also cite examples from research planning in which the jobs are alternative routes to some research objective, only one of which needs to be completed successfully, see Ritchie (1972).…”

On a reduction principle in dynamic programming

“…We now apply the theory of Section 2 to a model first discussed by Glazebrook and Fay (1987). In this example of MDPs in parallel, each constituent MDP may be thought of as an R&D project with two phases.…”

“…In Section 2 we give more explicit expression to the ideas described here and then proceed to give an upper bound for the loss in total expected reward incurred when making the above reduction. These results are applied in Sections 3 and 4 to two classes of decision processes previously discussed by Glazebrook (1979) and Glazebrook and Fay (1987) respectively.…”