Rollout Algorithms for 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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Automated Design of Production Scheduling Heuristics: A Review

10.26686/wgtn.13151315.v1 ◽

2020 ◽

Author(s):

J Branke ◽

S Nguyen ◽

CW Pickardt ◽

Mengjie Zhang

Keyword(s):

Production Scheduling ◽

State Of The Art ◽

Stochastic Scheduling ◽

Automated Design ◽

Application Area ◽

Scheduling Problems ◽

Open Questions ◽

Powerful Approach ◽

Critical Issues ◽

Future Work

© 1997-2012 IEEE. Hyper-heuristics have recently emerged as a powerful approach to automate the design of heuristics for a number of different problems. Production scheduling is a particularly popular application area for which a number of different hyper-heuristics have been developed and are shown to be effective, efficient, easy to implement, and reusable in different shop conditions. In particular, they seem to be a promising way to tackle highly dynamic and stochastic scheduling problems, an aspect that is specifically emphasized in this survey. Despite their success and the substantial number of papers in this area, there is currently no systematic discussion of the design choices and critical issues involved in the process of developing such approaches. This paper strives to fill this gap by summarizing the state-of-the-art approaches, suggesting a taxonomy, and providing the interested researchers and practitioners with guidelines for the design of hyper-heuristics in production scheduling. This paper also identifies challenges and open questions and highlights various directions for future work.

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