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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| Published in | Journal of optimization theory and applications Vol. 167; no. 2; pp. 716 - 732 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.11.2015
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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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| AbstractList | 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. |
| Author | Ahmadi-Javid, Amir Malhamé, Roland |
| Author_xml | – sequence: 1 givenname: Amir surname: Ahmadi-Javid fullname: Ahmadi-Javid, Amir email: ahmadi_javid@aut.ac.ir organization: Department of Industrial Engineering, Amirkabir University of Technology – sequence: 2 givenname: Roland surname: Malhamé fullname: Malhamé, Roland organization: GERAD and Department of Electrical Engineering, Ecole Polytechnique de Montréal |
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| CitedBy_id | crossref_primary_10_1007_s00291_018_0542_2 crossref_primary_10_1137_16M1058492 crossref_primary_10_1007_s00180_020_01019_6 crossref_primary_10_1016_j_jfranklin_2021_07_050 crossref_primary_10_1111_poms_14077 |
| Cites_doi | 10.1016/S0378-4266(02)00271-6 10.1109/9.554397 10.1111/1467-9965.00068 10.1023/A:1022696215389 10.1109/9.1270 10.1137/1.9780898718751 10.1109/TAC.1986.1104206 10.1287/opre.36.4.532 10.1137/S0363012993243629 10.1287/moor.1050.0186 10.1007/s10626-006-0002-z 10.1109/9.341793 10.1080/07408170801975040 10.1109/9.341795 10.1109/TAC.2004.835592 10.1109/CDC.2011.6160663 10.1109/TAC.2007.906229 10.1287/msom.4.2.133.281 10.1109/9.250488 |
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| DOI | 10.1007/s10957-014-0668-6 |
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| Keywords | 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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| SubjectTerms | 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 |
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| Title | Optimal Control of a Multistate Failure-Prone Manufacturing System under a Conditional Value-at-Risk Cost Criterion |
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