Overview of Stochastic Scheduling Problems

A single machine is available to process a collection J of jobs. The machine is free to switch between jobs at any time, but processing must respect a set Γof precedence constraints. Jobs evolve stochastically and earn rewards as they are processed, not otherwise. The theoretical framework of forwards induction/Gittins indexation is used to develop approaches to strategy evaluation for quite general (J,Γ). The performance of both forwards induction strategies and a class of quasi-myopic heuristics is assessed.

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Some indexable families of restless bandit problems

Advances in Applied Probability ◽

10.1239/aap/1158684996 ◽

2006 ◽

Vol 38 (3) ◽

pp. 643-672 ◽

Cited By ~ 32

Author(s):

K. D. Glazebrook ◽

D. Ruiz-Hernandez ◽

C. Kirkbride

Keyword(s):

Index Theory ◽

Stochastic Scheduling ◽

Gittins Index ◽

Scheduling Problems ◽

Bandit Problems ◽

Index Policy ◽

Restless Bandit ◽

Machine Maintenance ◽

State Evolution ◽

Strong Performance

In 1988 Whittle introduced an important but intractable class of restless bandit problems which generalise the multiarmed bandit problems of Gittins by allowing state evolution for passive projects. Whittle's account deployed a Lagrangian relaxation of the optimisation problem to develop an index heuristic. Despite a developing body of evidence (both theoretical and empirical) which underscores the strong performance of Whittle's index policy, a continuing challenge to implementation is the need to establish that the competing projects all pass an indexability test. In this paper we employ Gittins' index theory to establish the indexability of (inter alia) general families of restless bandits which arise in problems of machine maintenance and stochastic scheduling problems with switching penalties. We also give formulae for the resulting Whittle indices. Numerical investigations testify to the outstandingly strong performance of the index heuristics concerned.

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Performance comparison of approximate dynamic programming techniques for dynamic stochastic scheduling

An International Journal of Optimization and Control Theories & Applications (IJOCTA) ◽

10.11121/ijocta.01.2021.00987 ◽

2021 ◽

Vol 11 (2) ◽

pp. 178-185

Author(s):

Yasin Göçgün

Keyword(s):

Dynamic Programming ◽

Approximate Dynamic Programming ◽

Relevant Literature ◽

Stochastic Scheduling ◽

Performance Comparison ◽

Direct Search ◽

Basis Functions ◽

Scheduling Problems ◽

Programming Techniques ◽

Dynamic Stochastic

This paper focuses on the performance comparison of several approximate dynamic programming (ADP) techniques. In particular, we evaluate three ADP techniques through a class of dynamic stochastic scheduling problems: Lagrangian-based ADP, linear programming-based ADP, and direct search-based ADP. We uniquely implement the direct search-based ADP through basis functions that differ from those used in the relevant literature. The class of scheduling problems has the property that jobs arriving dynamically and stochastically must be scheduled to days in advance. Numerical results reveal that the direct search-based ADP outperforms others in the majority of problem sets generated.

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On Bayesian models in stochastic scheduling

Journal of Applied Probability ◽

10.2307/3213458 ◽

1977 ◽

Vol 14 (3) ◽

pp. 556-565 ◽

Cited By ~ 48

Author(s):

J. C. Gittins ◽

K. D. Glazebrook

Keyword(s):

Bayesian Models ◽

Stochastic Scheduling ◽

Scheduling Problems ◽

Prior Distributions ◽

Statistical Problems ◽

Random Times

The D.A.I. theorem of Gittins and Jones has proved a powerful tool in solving sequential statistical problems. A generalisation of this theorem is presented. This generalisation enables us to solve certain stochastic scheduling problems where the items or jobs to be scheduled have random times to completion, the random times having distributions dependent upon parameters to which prior distributions are allocated. Such problems are of interest in many areas where scheduling is important.

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Bounds for discounted stochastic scheduling problems

Journal of Applied Probability ◽

10.1017/s0021900200042704 ◽

1991 ◽

Vol 28 (04) ◽

pp. 791-801

Author(s):

K. D. Glazebrook

Keyword(s):

Resource Allocation ◽

Policy Evaluation ◽

Stochastic Scheduling ◽

Upper Bounds ◽

The Other ◽

Stochastic Environment ◽

Scheduling Problems ◽

Total Reward

Suppose that π is a policy for resource allocation in a stochastic environment and π ∗ is an optimal policy. Two existing procedures for policy evaluation are described and compared. Both of these evaluate π by means of upper bounds on R(π ∗) – R(π), the total reward lost when making resource allocations according to π rather than π∗. The bounds developed by these two methods are called Type 1 and Type 2. We demonstrate by example that neither of these procedures dominates the other in the sense of always yielding tighter bounds. A modification to Type 2 bounds is proposed resulting in an improved procedure which always dominates the Type 1 approach.

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