Skip to main content
Erschienen in:
Buchtitelbild

2013 | OriginalPaper | Buchkapitel

Inventory Control Under Parametric Uncertainty of Underlying Models

verfasst von : Nicholas A. Nechval, Konstantin N. Nechval, Maris Purgailis

Erschienen in: IAENG Transactions on Engineering Technologies

Verlag: Springer Netherlands

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A large number of problems in inventory control, production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty of underlying models. In the present paper we consider the case, where it is known that the underlying distribution belongs to a parametric family of distributions. The problem of determining an optimal decision rule in the absence of complete information about the underlying distribution, i.e., when we specify only the functional form of the distribution and leave some or all of its parameters unspecified, is seen to be a standard problem of statistical estimation. Unfortunately, the classical theory of statistical estimation has little to offer in general type of situation of loss function. In the paper, for improvement or optimization of statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a performance index is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rules, which have smaller risk than any of the well-known decision rules. A numerical example is given.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
3.
4.
5.
Zurück zum Zitat Lariviere MA, Porteus EL (1999) Stalking information: Bayesian inventory management with unobserved lost sales. Manage Sci 45:346–363MATHCrossRef Lariviere MA, Porteus EL (1999) Stalking information: Bayesian inventory management with unobserved lost sales. Manage Sci 45:346–363MATHCrossRef
7.
Zurück zum Zitat Agrawal N, Smith SA (1996) Estimating negative binomial demand for retail inventory management with unobservable lost sales. Naval Res Logist 43:839–861MATHCrossRef Agrawal N, Smith SA (1996) Estimating negative binomial demand for retail inventory management with unobservable lost sales. Naval Res Logist 43:839–861MATHCrossRef
8.
Zurück zum Zitat Nahmias S (1994) Demand estimation in lost sales inventory systems. Naval Res Logist 41:739–757MATHCrossRef Nahmias S (1994) Demand estimation in lost sales inventory systems. Naval Res Logist 41:739–757MATHCrossRef
9.
Zurück zum Zitat Liyanage LH, Shanthikumar JG (2005) A practical inventory control policy using operational statistics. Oper Res Lett 33:341–348MathSciNetMATHCrossRef Liyanage LH, Shanthikumar JG (2005) A practical inventory control policy using operational statistics. Oper Res Lett 33:341–348MathSciNetMATHCrossRef
10.
Zurück zum Zitat Bookbinder JH, Lordahl AE (1989) Estimation of inventory reorder level using the bootstrap statistical procedure. IIE Trans 21:302–312CrossRef Bookbinder JH, Lordahl AE (1989) Estimation of inventory reorder level using the bootstrap statistical procedure. IIE Trans 21:302–312CrossRef
11.
Zurück zum Zitat Nechval NA, Nechval KN, Vasermanis EK (2003) Effective state estimation of stochastic systems. Kybernetes (An International Journal of Systems & Cybernetics) 32:666–678MathSciNetMATHCrossRef Nechval NA, Nechval KN, Vasermanis EK (2003) Effective state estimation of stochastic systems. Kybernetes (An International Journal of Systems & Cybernetics) 32:666–678MathSciNetMATHCrossRef
12.
Zurück zum Zitat Nechval NA, Berzins G, Purgailis M, Nechval KN (2008) Improved estimation of state of stochastic systems via invariant embedding technique. WSEAS Trans Math 7:141–159MathSciNet Nechval NA, Berzins G, Purgailis M, Nechval KN (2008) Improved estimation of state of stochastic systems via invariant embedding technique. WSEAS Trans Math 7:141–159MathSciNet
13.
Zurück zum Zitat Nechval NA, Nechval KN, Purgailis M (2011) Prediction of future values of random quantities based on previously observed data. Eng Lett 9:346–359 Nechval NA, Nechval KN, Purgailis M (2011) Prediction of future values of random quantities based on previously observed data. Eng Lett 9:346–359
14.
Zurück zum Zitat Nechval NA, Purgailis M, Nechval KN, Strelchonok VF (2012) Optimal predictive inferences for future order statistics via a specific loss function. IAENG Int J Appl Math 42:40–51MathSciNet Nechval NA, Purgailis M, Nechval KN, Strelchonok VF (2012) Optimal predictive inferences for future order statistics via a specific loss function. IAENG Int J Appl Math 42:40–51MathSciNet
15.
Zurück zum Zitat Nechval NA, Purgailis M, Cikste K, Berzins G, Nechval KN (2010) Optimization of statistical decisions via an invariant embedding technique. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2010, WCE 2010, London, 30 June–2 July 2010, pp 1776–1782 Nechval NA, Purgailis M, Cikste K, Berzins G, Nechval KN (2010) Optimization of statistical decisions via an invariant embedding technique. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2010, WCE 2010, London, 30 June–2 July 2010, pp 1776–1782
16.
Zurück zum Zitat Nechval NA, Purgailis M, Cikste K, Nechval KN (2010) Planning inspections of fatigued aircraft structures via damage tolerance approach. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2010, WCE 2010, London, 30 June–2 July 2010, pp 2470–2475 Nechval NA, Purgailis M, Cikste K, Nechval KN (2010) Planning inspections of fatigued aircraft structures via damage tolerance approach. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2010, WCE 2010, London, 30 June–2 July 2010, pp 2470–2475
17.
Zurück zum Zitat Nechval NA, Purgailis M, Nechval KN, Rozevskis U (2011) Optimization of prediction intervals for order statistics based on censored data. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2011, WCE 2011, London, 6–8 July 2011, pp 63–69 Nechval NA, Purgailis M, Nechval KN, Rozevskis U (2011) Optimization of prediction intervals for order statistics based on censored data. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2011, WCE 2011, London, 6–8 July 2011, pp 63–69
18.
Zurück zum Zitat Nechval NA, Nechval KN, Purgailis M (2011) Statistical inferences for future outcomes with applications to maintenance and reliability. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2011, WCE 2011, London, 6–8 July 2011, pp 865–871 Nechval NA, Nechval KN, Purgailis M (2011) Statistical inferences for future outcomes with applications to maintenance and reliability. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2011, WCE 2011, London, 6–8 July 2011, pp 865–871
19.
Zurück zum Zitat Nechval NA, Purgailis M, Nechval KN, Bruna I (2012) Optimal inventory control under parametric uncertainty via cumulative customer demand. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2012, WCE 2012, London, 4–6 July 2012, pp 6–11 Nechval NA, Purgailis M, Nechval KN, Bruna I (2012) Optimal inventory control under parametric uncertainty via cumulative customer demand. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2012, WCE 2012, London, 4–6 July 2012, pp 6–11
20.
Zurück zum Zitat Nechval NA, Purgailis M, Nechval KN, Bruna I (2012) Optimal prediction intervals for future order statistics from extreme value distributions. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2012, WCE 2012, London, 4–6 July 2012, pp 1340–1345 Nechval NA, Purgailis M, Nechval KN, Bruna I (2012) Optimal prediction intervals for future order statistics from extreme value distributions. In: Lecture notes in engineering and computer science: Proceedings of the world congress on engineering 2012, WCE 2012, London, 4–6 July 2012, pp 1340–1345
21.
Zurück zum Zitat Nechval NA, Nechval KN, Purgailis M (2011) Inspection policies in service of fatigued aircraft structures. In: Ao S-I, Gelman L (eds) Electrical engineering and applied computing, vol 90. Springer, Berlin, pp 459–472CrossRef Nechval NA, Nechval KN, Purgailis M (2011) Inspection policies in service of fatigued aircraft structures. In: Ao S-I, Gelman L (eds) Electrical engineering and applied computing, vol 90. Springer, Berlin, pp 459–472CrossRef
22.
Zurück zum Zitat Nechval NA, Nechval KN, Purgailis M (2013) Weibull prediction limits for a future number of failures under parametric uncertainty. In: Ao S-I, Gelman L (eds) Electrical engineering and intelligent systems, vol 130, LNEE. Springer, Berlin, pp 273–284 Nechval NA, Nechval KN, Purgailis M (2013) Weibull prediction limits for a future number of failures under parametric uncertainty. In: Ao S-I, Gelman L (eds) Electrical engineering and intelligent systems, vol 130, LNEE. Springer, Berlin, pp 273–284
Metadaten
Titel
Inventory Control Under Parametric Uncertainty of Underlying Models
verfasst von
Nicholas A. Nechval
Konstantin N. Nechval
Maris Purgailis
Copyright-Jahr
2013
Verlag
Springer Netherlands
DOI
https://doi.org/10.1007/978-94-007-6190-2_1