Optimal control of a dynamic production-inventory system with various cost criteria
In this article, we investigate the dynamic control problem of a production-inventory system. Here, demands arrive at the production unit according to a Poisson process and are processed in an FCFS manner. The processing time of the customer’s demand is exponentially distributed. Production manufact...
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| Veröffentlicht in: | Annals of operations research Jg. 337; H. 1; S. 75 - 103 |
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| Abstract | In this article, we investigate the dynamic control problem of a production-inventory system. Here, demands arrive at the production unit according to a Poisson process and are processed in an FCFS manner. The processing time of the customer’s demand is exponentially distributed. Production manufacturers produce items on a make-to-order basis to meet customer demands. The production is run until the inventory level becomes sufficiently large. We assume that the production time of an item follows an exponential distribution and that the amount of time for the produced item to reach the retail shop is negligible. In addition, we assume that no new customer joins the queue when there is void inventory. Moreover, when a customer is waiting in an infinite FIFO queue for service, he/she does not leave the queue even if the inventory is exhausted. This yields an explicit product-form solution for the steady-state probability vector of the system. The optimal policy that minimizes the discounted/average/pathwise average total cost per production is derived using a Markov decision process approach. We find an optimal policy using value/policy iteration algorithms. Numerical examples are discussed to verify the proposed algorithms. |
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| AbstractList | In this article, we investigate the dynamic control problem of a production-inventory system. Here, demands arrive at the production unit according to a Poisson process and are processed in an FCFS manner. The processing time of the customer’s demand is exponentially distributed. Production manufacturers produce items on a make-to-order basis to meet customer demands. The production is run until the inventory level becomes sufficiently large. We assume that the production time of an item follows an exponential distribution and that the amount of time for the produced item to reach the retail shop is negligible. In addition, we assume that no new customer joins the queue when there is void inventory. Moreover, when a customer is waiting in an infinite FIFO queue for service, he/she does not leave the queue even if the inventory is exhausted. This yields an explicit product-form solution for the steady-state probability vector of the system. The optimal policy that minimizes the discounted/average/pathwise average total cost per production is derived using a Markov decision process approach. We find an optimal policy using value/policy iteration algorithms. Numerical examples are discussed to verify the proposed algorithms. |
| Audience | Academic |
| Author | Golui, Subrata Sobhanan, Abhay Pal, Chandan Manikandan, R. |
| Author_xml | – sequence: 1 givenname: Subrata surname: Golui fullname: Golui, Subrata organization: Department of Mathematics, Indian Institute of Technology Guwahati – sequence: 2 givenname: Chandan surname: Pal fullname: Pal, Chandan organization: Department of Mathematics, Indian Institute of Technology Guwahati – sequence: 3 givenname: R. orcidid: 0000-0002-0408-1712 surname: Manikandan fullname: Manikandan, R. email: mani@cukerala.ac.in organization: Department of Mathematics, Central University of Kerala – sequence: 4 givenname: Abhay surname: Sobhanan fullname: Sobhanan, Abhay organization: Department of Industrial and Management Systems Engineering, University of South Florida |
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| Cites_doi | 10.1007/s10479-013-1437-x 10.1007/978-981-15-5951-8_14 10.1007/978-3-030-54987-9 10.1002/047001363X 10.1007/s001860400369 10.1007/s00245-013-9208-2 10.1111/poms.13819 10.1002/9781394174201 10.1287/opre.40.4.808 10.1016/j.ijpe.2010.10.011 10.1080/15326340701645975 10.1002/9780470316887 10.1007/BF01125431 10.1080/15326349908807558 10.1080/17442508.2013.872644 10.1080/07362994.2015.1050674 10.1007/s11134-006-8710-5 10.1080/17442508.2018.1521413 10.1080/07408179308964320 10.1155/JAMSA/2006/69068 10.1287/opre.42.2.337 10.1002/9781119755234.ch6 10.2307/1427522 10.1287/moor.11.2.208 10.1007/978-3-642-02547-1 10.1080/07362990600753635 10.1137/140972640 10.1007/BF02060488 10.1016/S0377-2217(01)00257-0 10.1007/s00186-022-00779-9 10.1016/j.ejor.2013.01.041 10.1111/poms.13820 10.1287/moor.11.2.193 10.1007/978-1-4612-0729-0 10.1007/s00170-010-2883-0 |
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| Keywords | Controlled Markov chain Cost criterion Policy iteration algorithm Primary 93E20 60J27 Value iteration algorithm Secondary 49L20 Production-inventory system |
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TijmsHenk CA first course in stochastic models2003Wiley10.1002/047001363X PereraSCSethiSPA survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)-type policies-the continuous-time caseProduction and Operations Management202210.1111/poms.13819 SchwarzMSauerCDadunaHKulikRSzekliRM/M/1 queueing systems with inventoryQueueing Systems200654557810.1007/s11134-006-8710-5 A Piunovsky (5716_CR34) 2020 M Saffari (5716_CR37) 2011; 53 A Federgruen (5716_CR8) 1992; 40 C Pal (5716_CR30) 2019; 91 KS Kumar (5716_CR23) 2013; 68 S Chakravarthy (5716_CR7) 1986 B Pal (5716_CR31) 2012; 219 SR Chakravarthy (5716_CR6) 2022 5716_CR17 5716_CR38 SP Meyn (5716_CR27) 1993; 25 SC Perera (5716_CR32) 2022 O Berman (5716_CR3) 1999; 15 5716_CR36 A Krishnamoorthy (5716_CR20) 2013; 228 M Schwarz (5716_CR40) 2006; 54 AZ Melikov (5716_CR26) 1992; 28 A Federgruen (5716_CR10) 1986; 11 A Krishnamoorthy (5716_CR22) 2021 A Federgruen (5716_CR9) 1986; 11 MK Ghosh (5716_CR11) 2014; 86 N Zhao (5716_CR45) 2011; 129 MF Neuts (5716_CR29) 1994 K Sigman (5716_CR42) 1992; 40 O Berman (5716_CR2) 1993; 25 Q-M He (5716_CR14) 2002; 141 KL Helmes (5716_CR16) 2015; 53 M Schwarz (5716_CR41) 2007; 23 MF Neuts (5716_CR28) 1989 KS Kumar (5716_CR24) 2015; 33 XP Guo (5716_CR13) 2009 S Golui (5716_CR12) 2022; 95 A Krishnamoorthy (5716_CR19) 2015; 233 SC Perera (5716_CR33) 2022 HM Veatch (5716_CR44) 1994; 42 O Berman (5716_CR4) 2004; 60 Henk C Tijms (5716_CR43) 2003 ML Puterman (5716_CR35) 1994 5716_CR25 B Sarkar (5716_CR39) 2012; 218 SR Chakravarthy (5716_CR5) 2022 A Krishnamoorthy (5716_CR18) 2006; 24 5716_CR1 A Krishnamoorthy (5716_CR21) 2006 Q-M He (5716_CR15) 2001; 32 |
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| SubjectTerms | Algorithms Business and Management Combinatorics Control systems Customer services Customers Dynamic control Inventory Inventory control Inventory management Iterative algorithms Markov processes Mathematical optimization Methods Operations Research/Decision Theory Optimal control Original Research Probability distribution functions Queues Statistical analysis Theory of Computation Value analysis (Cost control) |
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| Title | Optimal control of a dynamic production-inventory system with various cost criteria |
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