scholarly journals Controlling a Random Population

2020 ◽  
pp. 119-135
Author(s):  
Thomas Colcombet ◽  
Nathanaël Fijalkow ◽  
Pierre Ohlmann
Keyword(s):  
Control Problem ◽  
Stochastic Control ◽  
Markov Decision Process ◽  
Open Problem ◽  
Decision Process ◽  
State System ◽  
Finite State ◽  
Markov Decision ◽  
Stochastic Setting ◽  
Min Cut

AbstractBertrand et al. introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is decidable and EXPTIME-complete in the adversarial setting, and posed as an open problem the stochastic setting, where the agent is represented by a Markov decision process. In this paper, we show that the stochastic control problem is decidable. Our solution makes significant uses of well quasi orders, of the max-flow min-cut theorem, and of the theory of regular cost functions.

scholarly journals Controlling a random population

2021 ◽  
Vol Volume 17, Issue 4 ◽  
Author(s):  
Thomas Colcombet ◽  
Nathanaël Fijalkow ◽  
Pierre Ohlmann
Keyword(s):  
Control Problem ◽  
Stochastic Control ◽  
Open Problem ◽  
Decision Process ◽  
Flow Problem ◽  
Intermediate Problem ◽  
Finite State ◽  
Markov Decision ◽  
Stochastic Setting ◽  
Min Cut

Bertrand et al. introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is decidable and EXPTIME-complete in the adversarial setting, and posed as an open problem the stochastic setting, where the agent is represented by a Markov decision process. In this paper, we show that the stochastic control problem is decidable. Our solution makes significant uses of well quasi orders, of the max-flow min-cut theorem, and of the theory of regular cost functions. We introduce an intermediate problem of independence interest called the sequential flow problem and study its complexity.

scholarly journals Development of a Shipment Policy for Collection Centers

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1385
Author(s):  
Irais Mora-Ochomogo ◽  
Marco Serrato ◽  
Jaime Mora-Vargas ◽  
Raha Akhavan-Tabatabaei
Keyword(s):  
Climate Change ◽  
Natural Disasters ◽  
Markov Decision Process ◽  
Decision Process ◽  
Necessary Conditions ◽  
Decision Makers ◽  
Humanitarian Organizations ◽  
The World ◽  
Markov Decision ◽  
Unsatisfied Demand

Natural disasters represent a latent threat for every country in the world. Due to climate change and other factors, statistics show that they continue to be on the rise. This situation presents a challenge for the communities and the humanitarian organizations to be better prepared and react faster to natural disasters. In some countries, in-kind donations represent a high percentage of the supply for the operations, which presents additional challenges. This research proposes a Markov Decision Process (MDP) model to resemble operations in collection centers, where in-kind donations are received, sorted, packed, and sent to the affected areas. The decision addressed is when to send a shipment considering the uncertainty of the donations’ supply and the demand, as well as the logistics costs and the penalty of unsatisfied demand. As a result of the MDP a Monotone Optimal Non-Decreasing Policy (MONDP) is proposed, which provides valuable insights for decision-makers within this field. Moreover, the necessary conditions to prove the existence of such MONDP are presented.

Sign in / Sign up

Export Citation Format

Share Document