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-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.

• 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