Optimal strategies in a production-inventory control model

We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch over from the different production rates but it is mandatory...

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Autores principales: Azcue, Pablo, Muler, Nora, Frostig, Esther
Formato: info:eu-repo/semantics/preprint submittedVersion
Lenguaje:Inglés
Publicado: 2023
Materias:
Production-inventory control model
Cumulative process of customer demand
Storage maximum capacity
Expected discounted cumulative costs
Variational inequalities
Costs of the band strategies
Acceso en línea:https://repositorio.utdt.edu/handle/20.500.13098/11848
https://doi.org/10.1007/s11009-023-10024-3
Aporte de:
Repositorio Digital Universidad Torcuato Di Tella de Universidad Torcuato Di Tella
id I57-R163-20.500.13098-11848
record_format dspace
spelling I57-R163-20.500.13098-118482023-07-28T14:43:47Z Optimal strategies in a production-inventory control model Azcue, Pablo Muler, Nora Frostig, Esther Production-inventory control model Cumulative process of customer demand Storage maximum capacity Expected discounted cumulative costs Variational inequalities Costs of the band strategies We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch over from the different production rates but it is mandatory to switch-off when the inventory process reaches the storage maximum capacity. We consider holding, production, shortage penalty and switching costs. This model was introduced by Doshi, Van Der Duyn Schouten and Talman in 1978. In their paper they found a formula for the long-run average expected cost per unit time as a function of two critical levels, in this paper we consider expected discounted cumulative costs instead. We seek to minimize this discounted cost over all admissible switching strategies. We show that the optimal cost functions for the different production rates satisfy the corresponding Hamilton-Jacobi-Bellman system of equations in a viscosity sense and prove a verification theorem. The way in which the optimal cost functions solve the different variational inequalities gives the switching regions of the optimal strategy, hence it is stationary in the sense that depends only on the current production rate and inventory level. We define the notion of finite band strategies and derive, using scale functions, the formulas for the different costs of the band strategies with one or two bands. We also show that there are examples where the switching strategy with two critical levels is not optimal. Este documento es una versión del artículo publicado en Methodology and Computing in Applied Probability, 25(1) https://doi.org/10.1007/s11009-023-10024-3 2023-05-31T17:57:01Z 2023-05-31T17:57:01Z 2020 info:eu-repo/semantics/preprint info:eu-repo/semantics/submittedVersion https://repositorio.utdt.edu/handle/20.500.13098/11848 https://doi.org/10.1007/s11009-023-10024-3 eng Methodology and Computing in Applied Probability volume 25, Article number: 43 (2023) https://doi.org/10.1007/s11009-023-10024-3 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-sa/2.5/ar/ 31 p. application/pdf application/pdf
institution Universidad Torcuato Di Tella
institution_str I-57
repository_str R-163
collection Repositorio Digital Universidad Torcuato Di Tella
language Inglés
orig_language_str_mv eng
topic Production-inventory control model
Cumulative process of customer demand
Storage maximum capacity
Expected discounted cumulative costs
Variational inequalities
Costs of the band strategies
spellingShingle Production-inventory control model
Cumulative process of customer demand
Storage maximum capacity
Expected discounted cumulative costs
Variational inequalities
Costs of the band strategies
Azcue, Pablo
Muler, Nora
Frostig, Esther
Optimal strategies in a production-inventory control model
topic_facet Production-inventory control model
Cumulative process of customer demand
Storage maximum capacity
Expected discounted cumulative costs
Variational inequalities
Costs of the band strategies
description We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch over from the different production rates but it is mandatory to switch-off when the inventory process reaches the storage maximum capacity. We consider holding, production, shortage penalty and switching costs. This model was introduced by Doshi, Van Der Duyn Schouten and Talman in 1978. In their paper they found a formula for the long-run average expected cost per unit time as a function of two critical levels, in this paper we consider expected discounted cumulative costs instead. We seek to minimize this discounted cost over all admissible switching strategies. We show that the optimal cost functions for the different production rates satisfy the corresponding Hamilton-Jacobi-Bellman system of equations in a viscosity sense and prove a verification theorem. The way in which the optimal cost functions solve the different variational inequalities gives the switching regions of the optimal strategy, hence it is stationary in the sense that depends only on the current production rate and inventory level. We define the notion of finite band strategies and derive, using scale functions, the formulas for the different costs of the band strategies with one or two bands. We also show that there are examples where the switching strategy with two critical levels is not optimal.
format info:eu-repo/semantics/preprint
submittedVersion
author Azcue, Pablo
Muler, Nora
Frostig, Esther
author_facet Azcue, Pablo
Muler, Nora
Frostig, Esther
author_sort Azcue, Pablo
title Optimal strategies in a production-inventory control model
title_short Optimal strategies in a production-inventory control model
title_full Optimal strategies in a production-inventory control model
title_fullStr Optimal strategies in a production-inventory control model
title_full_unstemmed Optimal strategies in a production-inventory control model
title_sort optimal strategies in a production-inventory control model
publishDate 2023
url https://repositorio.utdt.edu/handle/20.500.13098/11848
https://doi.org/10.1007/s11009-023-10024-3
work_keys_str_mv AT azcuepablo optimalstrategiesinaproductioninventorycontrolmodel
AT mulernora optimalstrategiesinaproductioninventorycontrolmodel
AT frostigesther optimalstrategiesinaproductioninventorycontrolmodel
_version_ 1782030105684475904

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