Using optimal control to optimize the extraction rate of a durable non-renewable resource with a monopolistic primary supplier
The problem dealt with in this paper is that of optimizing the path of the extraction rate (and, consequently, the price) for the monopolistic owner of the primary sources of a totally or partially durable non-renewable resource (such as precious metals or gemstones) in a continuous-time frame, assu...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2022 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/374811 |
| Acesso em linha: | https://hdl.handle.net/2117/374811 https://dx.doi.org/10.3934/jimo.2021110 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Control theory Mathematical optimization Durable non-renewable resources Monopoly Optimal control Control, Teoria de Optimització matemàtica Classificació AMS::49 Calculus of variations and optimal control optimization::49K Necessary conditions and sufficient conditions for optimality optimization::49N Miscellaneous topics Àrees temàtiques de la UPC::Informàtica::Automàtica i control |
| Resumo: | The problem dealt with in this paper is that of optimizing the path of the extraction rate (and, consequently, the price) for the monopolistic owner of the primary sources of a totally or partially durable non-renewable resource (such as precious metals or gemstones) in a continuous-time frame, assuming that there is an upper bound on the extraction rate and with an interest rate equal to zero. The durability of the resource implies that, unlike the case of non-durable resources, at any time there is a stock of already-used amounts of the resource that are still potentially reusable, in addition to the resource available in the ground for extraction. The problem is addressed using the Maximum Principle of Pontryagin in the framework of optimal control theory, which allows identifying the patterns that the optimal policies can adopt. In this framework, the Hamiltonian is linear in the control input, which implies a bang-bang control policy governed by a switching surface. There is an underlying geometry to the problem that determines the solutions. It is characterized by the switching surface, its time derivative, the intersection point (if any) and the bang-bang trajectories through this point. |
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