Optimal intervention policy for projects with growing stochastic demand
Developers of projects with a fixed capacity and an increasing demand over time will be interested in an optimal decision-making policy on when to increase capacity and by how much. Demand, X, is an increasing function with a stochastic diffusion term (Brownian Motion) and capacity, K, is a piece-wi...
- Autores:
-
Wiesner Urbina, Federico
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2024
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/74755
- Acceso en línea:
- https://hdl.handle.net/1992/74755
- Palabra clave:
- Stochastic
Quasi-Variational Inequalities
Optimal Policy
Matemáticas
Ingeniería
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 International
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Optimal intervention policy for projects with growing stochastic demand |
| dc.title.alternative.spa.fl_str_mv |
Política óptima de inversión para proyectos con demanda estocástica creciente |
| title |
Optimal intervention policy for projects with growing stochastic demand |
| spellingShingle |
Optimal intervention policy for projects with growing stochastic demand Stochastic Quasi-Variational Inequalities Optimal Policy Matemáticas Ingeniería |
| title_short |
Optimal intervention policy for projects with growing stochastic demand |
| title_full |
Optimal intervention policy for projects with growing stochastic demand |
| title_fullStr |
Optimal intervention policy for projects with growing stochastic demand |
| title_full_unstemmed |
Optimal intervention policy for projects with growing stochastic demand |
| title_sort |
Optimal intervention policy for projects with growing stochastic demand |
| dc.creator.fl_str_mv |
Wiesner Urbina, Federico |
| dc.contributor.advisor.none.fl_str_mv |
Sánchez Silva, Edgar Mauricio Junca Peláez, Mauricio José |
| dc.contributor.author.none.fl_str_mv |
Wiesner Urbina, Federico |
| dc.contributor.jury.none.fl_str_mv |
Serrano Perdomo, Rafael Antonio |
| dc.subject.keyword.eng.fl_str_mv |
Stochastic Quasi-Variational Inequalities Optimal Policy |
| topic |
Stochastic Quasi-Variational Inequalities Optimal Policy Matemáticas Ingeniería |
| dc.subject.themes.none.fl_str_mv |
Matemáticas Ingeniería |
| description |
Developers of projects with a fixed capacity and an increasing demand over time will be interested in an optimal decision-making policy on when to increase capacity and by how much. Demand, X, is an increasing function with a stochastic diffusion term (Brownian Motion) and capacity, K, is a piece-wise constant function. The difference K−X can be seen as an inventory: surplus capacity are the available units. This project seeks to analytically prove that an (s, S) policy -whereby inventory is always brought up to a level S every time that it drops under s- is an optimal decision policy, a solution to the Stochastic Control Problem. Ito Calculus is used to state Quasi-Variational Inequalities equivalent to the Hamilton-Jacobi-Bellman equation, while Green Functions and Real Analysis are used to prove the existence of solutions. Moreover, the value of s is proven to be unique. For the second part, a numerically based method using Finite Differences and Iterative Methods will be used to estimate the values of s and S, given parameters to model capacity and demand. |
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2024 |
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2024-07-29T18:04:42Z |
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2024-07-29T18:04:42Z |
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2024-07-29 |
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Trabajo de grado - Pregrado |
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info:eu-repo/semantics/bachelorThesis |
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info:eu-repo/semantics/acceptedVersion |
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http://purl.org/coar/resource_type/c_7a1f |
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eng |
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eng |
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J. R. Yzer, W. E. Walker, V. A. W. J. Marchau, and J. H. Kwakkel, “Dynamic adaptive policies: A way to improve the cost-benefit performance of megaprojects?” Environment and Planning B: Planning and Design, 2014. I. Clark, “Level of service f, is it really as bad as it gets?” Transportation Group New Zealand, 2008. J. H. Saleh, G. Mark, and N. C. Jordan, “Flexibility: A multi-disciplinary literature review and a research agenda for designing flexible engineering systems”, Journal of Engineering Design, 2009. M. Amran and N. Kulatikala, Real Options. Harvard Business School Press, 1998. M. A. Cardin, “Enabling flexibility in engineering systems: A taxonomy of procedures and a design framework,” Journal of Mechanical Design, 2014. M. Junca and M. Sánchez-Silva, “Optimal maintenance policy for a compound poisson shock process,” IEEE Transactions on Reliability, 2018. Merriam-Webster, Merriam-Webster English Dictionary. 2024. F. W. Harris, Operations and Cost (Factory Management Series). A. W. Shaw, 1915. K. Siegrist, Random: Probability, mathematical statistics, stochastic processes, https://www.randomservices.org/random/index.html. H. B. Wolfe, “A model for control of style merchandise,” Industrial Management Review, 1968. H. Schmidli, Stochastic Control in Insurance. Springer, 2008. A. Bensoussan, Dynamic Programming and Inventory Control. IOS Press, 2011. A. Bensoussan and J. L. Lions, Impulse Control and Quasi-Variational Inequalities. Gauthier-Villars, 1984. Y. Yoo, Stochastic calculus and black-scholes model, https://math.uchicago.edu/~may/REU2017/REUPapers/Yoo.pdf. S. P. Lalley, Stochastic differential equations, https://galton.uchicago.edu/~lalley/Courses/385/SDE.pdf. J. Liu, K. F. C. Yiu, and A. Bensoussan, “Optimal inventory control with jump diffusion and nonlinear dynamics in the demand,” SIAM Journal on Control and Optimization, 2018. P. D. Lax, “On the existence of green’s function,” Proceedings of the AMS, 1951. J. Liu, K. Yiu, and A. Bensoussan, “Optimality of (s, S) policies with nonlinear processes,” Discrete and Continuous Dynamical Systems - Series B, vol. 22, pp. 161–185, Dec. 2016. doi: 10.3934/dcdsb.2017008.25 V. Pando, L. A. San-Jose, and J. Sicilia, “An inventory model with stock dependent demand rate and maximization of the return on investment,” Mathematics (MDPI), 2021. |
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Attribution-NonCommercial-NoDerivatives 4.0 International |
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26 páginas |
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application/pdf |
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Universidad de los Andes |
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Matemáticas Ingeniería Civil |
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Facultad de Ciencias Facultad de Ingeniería |
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Departamento de Matemáticas Departamento de Ingeniería Civil y Ambiental |
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Universidad de los Andes |
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Sánchez Silva, Edgar Mauriciovirtual::19338-1Junca Peláez, Mauricio Josévirtual::19339-1Wiesner Urbina, FedericoSerrano Perdomo, Rafael Antonio2024-07-29T18:04:42Z2024-07-29T18:04:42Z2024-07-29https://hdl.handle.net/1992/74755instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/Developers of projects with a fixed capacity and an increasing demand over time will be interested in an optimal decision-making policy on when to increase capacity and by how much. Demand, X, is an increasing function with a stochastic diffusion term (Brownian Motion) and capacity, K, is a piece-wise constant function. The difference K−X can be seen as an inventory: surplus capacity are the available units. This project seeks to analytically prove that an (s, S) policy -whereby inventory is always brought up to a level S every time that it drops under s- is an optimal decision policy, a solution to the Stochastic Control Problem. Ito Calculus is used to state Quasi-Variational Inequalities equivalent to the Hamilton-Jacobi-Bellman equation, while Green Functions and Real Analysis are used to prove the existence of solutions. Moreover, the value of s is proven to be unique. For the second part, a numerically based method using Finite Differences and Iterative Methods will be used to estimate the values of s and S, given parameters to model capacity and demand.Pregrado26 páginasapplication/pdfengUniversidad de los AndesMatemáticasIngeniería CivilFacultad de CienciasFacultad de IngenieríaDepartamento de MatemáticasDepartamento de Ingeniería Civil y AmbientalAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Optimal intervention policy for projects with growing stochastic demandPolítica óptima de inversión para proyectos con demanda estocástica crecienteTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPStochasticQuasi-Variational InequalitiesOptimal PolicyMatemáticasIngenieríaJ. R. Yzer, W. E. Walker, V. A. W. J. Marchau, and J. H. Kwakkel, “Dynamic adaptive policies: A way to improve the cost-benefit performance of megaprojects?” Environment and Planning B: Planning and Design, 2014.I. Clark, “Level of service f, is it really as bad as it gets?” Transportation Group New Zealand, 2008.J. H. Saleh, G. Mark, and N. C. Jordan, “Flexibility: A multi-disciplinary literature review and a research agenda for designing flexible engineering systems”, Journal of Engineering Design, 2009.M. Amran and N. Kulatikala, Real Options. Harvard Business School Press, 1998.M. A. Cardin, “Enabling flexibility in engineering systems: A taxonomy of procedures and a design framework,” Journal of Mechanical Design, 2014.M. Junca and M. Sánchez-Silva, “Optimal maintenance policy for a compound poisson shock process,” IEEE Transactions on Reliability, 2018.Merriam-Webster, Merriam-Webster English Dictionary. 2024.F. W. Harris, Operations and Cost (Factory Management Series). A. W. Shaw, 1915.K. Siegrist, Random: Probability, mathematical statistics, stochastic processes, https://www.randomservices.org/random/index.html.H. B. Wolfe, “A model for control of style merchandise,” Industrial Management Review, 1968.H. Schmidli, Stochastic Control in Insurance. Springer, 2008.A. Bensoussan, Dynamic Programming and Inventory Control. IOS Press, 2011.A. Bensoussan and J. L. Lions, Impulse Control and Quasi-Variational Inequalities. Gauthier-Villars, 1984.Y. Yoo, Stochastic calculus and black-scholes model, https://math.uchicago.edu/~may/REU2017/REUPapers/Yoo.pdf.S. P. Lalley, Stochastic differential equations, https://galton.uchicago.edu/~lalley/Courses/385/SDE.pdf.J. Liu, K. F. C. Yiu, and A. Bensoussan, “Optimal inventory control with jump diffusion and nonlinear dynamics in the demand,” SIAM Journal on Control and Optimization, 2018.P. D. Lax, “On the existence of green’s function,” Proceedings of the AMS, 1951.J. Liu, K. Yiu, and A. Bensoussan, “Optimality of (s, S) policies with nonlinear processes,” Discrete and Continuous Dynamical Systems - Series B, vol. 22, pp. 161–185, Dec. 2016. doi: 10.3934/dcdsb.2017008.25V. Pando, L. A. San-Jose, and J. Sicilia, “An inventory model with stock dependent demand rate and maximization of the return on investment,” Mathematics (MDPI), 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