An index policy for a stochastic scheduling model with improving/deteriorating jobs

Abstract

Abstract:We consider stochastic scheduling models which have the natural character that jobs improve while being processed, but deteriorate (and may possibly leave the system altogether) while processing is diverted elsewhere. Such restless bandit problems are shown to be indexable in the sense of Whittle. A numerical study which elucidates the strong performance of the resulting index policy is complemented by a theoretical study which demonstrates the optimality of the index policy under given conditions and which develops performance guarantees for the index heuristic more generally.

Learning in a Changing World: Restless Multiarmed Bandit With Unknown Dynamics

“…Weber and Weiss in 1990 showed that Whittle index policy is asymptotically optimal under certain conditions [27], [28]. In the finite regime, the strong performance of Whittle index policy has been demonstrated in numerous examples (see, e.g., [29]- [32]). …”

Taxonomy for integrating scheduling theory and human factors: Review and research opportunities

“…The deterministic framework integrates the structure of scheduling models with sequence-dependent processing times (Sections 4.1 and 4.2), scheduling models with rate-modifying activities (Section 4.3), and work-rest models (Section 2.4). Similarly, the stochastic modeling framework involves scheduling models with random machine breakdowns and deterioration processes (Glazebrook and Mitchell, 2002;Lee and Lin, 2001); scheduling models with sequence-dependent processing times (Sections 4.1 and 4.2); and work-rest scheduling models (Section 2.4). Although the proposed stochastic modeling framework includes models with random parameters such as task processing time, due date, etc., the emphasis is stochastic processes that represent resource failure or deterioration and the corresponding maintenance scheduling policies.…”

“…The case of task processing times depending on the number of executed tasks and task content was introduced by Alidaee and Ahmadian (1996). Glazebrook and Mitchell (2002) modeled deteriorating and improving jobs using Markov decision processes. They developed an index based scheduling policy and evaluated its performance with a numerical study.…”

Index policies for the routing of background jobs

“…Further, Weber and Weiss [24,25] have established a form of asymptotic optimality for Whittle's index policy under given conditions. A developing body of evidence testifies to the strong performance of such index policies in a range of application contexts (see, e.g., Ansell, Glazebrook, Niño-Mora, and O'Keeffe [1] and Glazebrook and Mitchell [8]). …”