Optimal Control of a Multistate Failure-Prone Manufacturing System under a Conditional Value-at-Risk Cost Criterion

The aim of this paper is to establish the optimality of a hedging-point control policy in a multistate Markovian failure-prone manufacturing system with a risk-averse criterion that is defined as the conditional value-at-risk (CVaR) of the steady-state instantaneous running cost, where the system is...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 167; no. 2; pp. 716 - 732
Main Authors Ahmadi-Javid, Amir, Malhamé, Roland
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2015
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constants
Control systems
Criteria
Engineering
Manufacturing
Markov analysis
Markov processes
Mathematical models
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimal control
Optimization
Policies
Production capacity
Random variables
Risk aversion
Running
Studies
Theory of Computation
90C15 Secondary 93B52
Conditional value-at-risk
Failure-prone manufacturing system
Hedging-point control policy
Stochastic optimal control
91G99
Production control
Primary 93E20
Long-run average cost
91B06
Risk-averse criterion
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Summary:The aim of this paper is to establish the optimality of a hedging-point control policy in a multistate Markovian failure-prone manufacturing system with a risk-averse criterion that is defined as the conditional value-at-risk (CVaR) of the steady-state instantaneous running cost, where the system is subject to a constant single-product demand rate. An explicit expression for the optimal control policy is also obtained for the two-state case. The results are important from both theoretical and practical viewpoints. Indeed, the paper extends the well-known classical theoretical result on the optimality of hedging-point control policies under risk-neutral criteria, which are typically given by long-run average costs, and it develops a flexible and practical method for incorporating risk aversion into cost criteria. The approach presented here can be used to specify optimal control policies in similar manufacturing systems with CVaR criteria.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-014-0668-6