Average-cost control of stochastic manufacturing systems.
type: Item
instance of: scholarly article
title: Average-cost control of stochastic manufacturing systems.
zbMATH Open document ID: 1078.93004
DOI: 10.1007/0-387-27615-7
author: Q. Zhang
author: Suresh P. Sethi
author: Hanqin Zhang
published in: Stochastic Modelling and Applied Probability
publication date: 2005-06-06T00:00:00Z
review text: This book is a study on the optimal control of manufacturing systems subject to breakdowns and repairs. The first and the third author published another monograph on a similar subject [Hierarchical decision making in stochastic manufacturing systems. Basel: Birkhäuser (1994; Zbl 0923.90002)]. They considered a discounted cost criterion; now the cost is a long-run average cost with emphasis on stationary behaviour described by stationary distributions. Other related studies of other authors involve singular perturbations in Markov decision problems, diffusion approximations (Kushner,\dots), and time-scale separation for hierarchical decision making (Gershwin,\dots), where asymptotic results associated to slow processes lead to certain decisions, and other decisions are then devised to handle short-term fluctuations. The book could be brought into the context of the first type of studies, but within the perspective of stochastic optimal control and not Markov decision processes. The second approach raises issues regarding approximation capability for near-optimal policies. Here, great care is given to near to optimal approximating configurations; it is desired that slight changes in performance are associated to slight changes in policy, so that computation of performing policies can be handled realistically. The third approach is related to the book cited above. First, the authors describe the types of manufacturing systems that they consider: parallel machines (producing multiple products or a single product), a single product dynamic flowshop (series connection of producing units), a dynamic flowshop (parallel machines with a feedback-type structure). Second, the authors consider the existence and characterization of optimal control using the Hamilton-Jacobi-Bellman equation and a verification theorem. A chapter deals with risk sensitive control in the context of parallel machines. Third, since optimal solutions, as a rule, cannot be computed, the authors consider …
reviewed by: A. Akutowicz
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 90B25
Mathematics Subject Classification ID: 90B30
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 90B36
Mathematics Subject Classification ID: 93C70
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 93A13
zbMATH DE Number: 2173790
zbMATH Keywords: reliability
zbMATH Keywords: optimal control of manufacturing systems
zbMATH Keywords: breakdowns
zbMATH Keywords: repairs
zbMATH Keywords: long-run average cost
zbMATH Keywords: near-optimal policies
zbMATH Keywords: parallel machines
zbMATH Keywords: dynamic flowshop
zbMATH Keywords: Hamilton-Jacobi-Bellman equation
zbMATH Keywords: verification theorem
zbMATH Keywords: risk sensitive control
zbMATH Keywords: convergence rate
zbMATH Keywords: error estimates
zbMATH Keywords: Markov chains
zbMATH Keywords: stochastic optimal control
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/0-387-27615-7
OpenAlex ID: W587814406
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description: scientific article; zbMATH DE number 2173790