1,721,039 research outputs found
A multi-cluster time aggregation approach for Markov chains
Full text linkThis work focuses on the computation of the steady state distribution of a Markov chain, making use of an embedding algorithm. In this regard, a well-known approach dubbed time aggregation has been proposed in Cao et al., (2002). Roughly, the idea hinges on the partition of the state space into two subsets. The linchpin in this partitioning process is a small subset of states, selected to be the state space of the aggregated process, which will account for the state space of the embedded semi-Markov process. Although this approach has provided an interesting body of theoretical results and advanced in the study of the so-called curse of dimensionality, one is still left with a high-dimensional problem to be solved. In this paper we investigate the possibility to remedy this problem by proposing a time aggregation approach with multiple subsets. This is achieved by devising a decomposition algorithm which makes use of a partition scheme to evaluate the steady state probabilities of the chain. Besides the convergence proof of the algorithm, we prove also a result for the cardinality of the partition, vis-à-vis the computational effort of the algorithm, for the case in which the state space is partitioned in a collection of subsets of the same cardinality.</p
Effectiveness of mathematical and simulation models for improving quality of care in emergency departments: a systematic literature review
No full textThis systematic literature review aims to critically evaluate the use of mathematical and simulation models within emergency departments (EDs) and assess their potential to improve the quality of care. This review emphasises the critical need for quality enhancement in healthcare systems, specifically focusing on EDs. This review incorporates studies investigating the quality of care provided in ED settings, employing assorted mathematical and simulation models for adult populations. Based on the selected studies, a narrative approach was used to synthesise the findings, focusing on outcome classification, simulation, and modelling. There are six outcome dimensions: safety, effectiveness, patient-centeredness, timeliness, efficiency, and equity. This review analysed 112 studies, uncovering a distinct focus on a set of key performance measures within emergency department (ED) operations, accounting for 222 instances across these studies. Measures assessing timeliness were most frequent, occurring 111 times, indicating a strong emphasis on operational efficiency aspects such as waiting times and patient flow. A total of 75 examinations were conducted on efficiency-related measures, specifically focusing on identifying and addressing operational bottlenecks and optimising resource utilisation. On the other hand, safety, patient-centeredness, and effectiveness were not as commonly represented, with only three, four, and 29 instances, respectively. This review highlights the considerable potential of mathematical and simulation models to enhance ED operations, particularly regarding timeliness and efficiency. However, aspects such as patient safety, effectiveness, and patient-centredness were under-represented, while equity was absent across the studies, indicating a clear need for further research. These findings emphasise the importance of adopting a more thorough approach to evaluating and improving the quality of emergency care. Future research should also concentrate on refining data management practices, incorporating observational studies, and exploring various simulation tools to develop a more balanced and inclusive understanding of these models' applications
Optimal approximation schedules for a class of iterative algorithms, with an application to multigrid value iteration
No full textMany iterative algorithms employ operators which are difficult to evaluate exactly, but for which a graduated range of approximations exist. In such cases, coarse-to-fine algorithms are often used, in which a crude initial operator approximation is gradually refined with new iterations. In such algorithms, because the computational complexity increases over iterations, the algorithm's convergence rate is properly calculated with respect to cumulative computation time. This suggests the problem of determining an optimal rate of refinement for the operator approximation. This paper shows that, for linearly convergent algorithm, the optimal rate of refinement approaches the rate of convergence of the exact algorithm itself, regardless of the tolerance-complexity relationship. We illustrate this result with an analysis of coarse-to-fine grid algorithms for Markov decision processes with continuous state spaces. Using the methods proposed here we deduce an algorithm that presents optimal complexity results and consists solely of a non-adaptive schedule for the gradual decrease of grid size.</p
Optimal speed and hedging strategies for tramp shipping operators in volatile freight markets
No full textThe maritime shipping industry faces significant uncertainties due to the volatility of freight rates, directly impacting business operations. This paper examines the relationship between freight rate uncertainties, hedging policies, and shipping speeds using a novel stochastic optimization framework that integrates practical hedging strategies with operational speed decisions. Unlike traditional models that assume Geometric Brownian Motion (GBM) for price dynamics, our model employs an exponential Ornstein-Uhlenbeck (OU) process to capture the mean-reverting nature of freight rates, providing a more realistic representation of market behavior. Additionally, the model is compatible with Forward Freight Agreement (FFA) hedging practices and allows for partial hedging, aligning closely with realworld risk management strategies. By employing a mean-variance utility function, this research offers a toolkit for risk-averse shipping operators to incorporate risk tolerance into the speed and hedging decision-making process. Our analysis reveals that the ability to hedge future profits significantly influences current speed choices, uncovering novel insights such as the asymmetric nature of the optimal policy for laden and ballast legs and the sensitivity of the optimal hedge ratio to various risk parameters. We also establish a closed-form relationship between hedging ratios and speed through a newly developed theorem, offering practical guidance for operators. Experimental results demonstrate the model’s applicability and effectiveness when tested against real-life data, highlighting its potential to enhance both economic and operational decision-making in maritime shipping
Optimal approximation schedules for iterative algorithms with application to dynamic programming
No full textMany iterative algorithms rely on operators which may be difficult or impossible to evaluate exactly, but for which approximations are available. Furthermore, a graduated range of approximations may be available, inducing a functional relationship between computational complexity and approximation tolerance. In such a case, a reasonable strategy would be to vary tolerance over iterations, starting with a cruder approximation, then gradually decreasing tolerance as the solution is approached. In this article, it is shown that under general conditions, for linearly convergent algorithms the optimal choice of approximation tolerance convergence rate is the same linear convergence rate as the exact algorithm itself, regardless of the tolerance/complexity relationship. We illustrate this result by presenting a partial information value iteration (PIVI) algorithm for discrete time dynamic programming problems. The proposed algorithm makes use of increasingly accurate partial model information in order to decrease the computational burden of the standard value iteration algorithm. The algorithm is applied to a stochastic network example and compared to value iteration for the purpose of benchmarking.</p
Virtual interpolation of discrete multi-objective programming solutions with probabilistic operation
No full textThis work presents a novel framework to address the long term operation of a class of multi-objective programming problems. The proposed approach considers a stochastic operation and evaluates the long term average operating costs/profits. To illustrate the approach, a two-phase method is proposed which solves a prescribed number of K monoobjective problems to identify a set of K points in the Paretooptimal region. In the second phase, one searches for a set of non-dominated probability distributions that define the probability that the system operates at each point selected in the first phase, at any given operation period. Each probability distribution generates a vector of average long-term objectives and one solves for the Pareto-optimal set with respect to the average objectives. The proposed approach can generate virtual operating points with average objectives that need not have a feasible solution with an equal vector of objectives. A few numerical examples are presented to illustrate the proposed method
Learning-agent-based simulation for queue network systems
Full text linkEstablished simulation methods generally require from the modeller a broad and detailed knowledge of the system under study. This paper proposes the application of Reinforcement Learning in an Agent-Based Simulation model to enable agents to define the necessary interaction rules. The model is applied to queue network systems, which are a proxy for broader applications, in order to be validated. Simulation tests compare results obtained from learning agents and results obtained from known good rules. The comparison shows that the learning model is able to learn efficient policies on the go, providing an interesting framework for simulation.</p
Optimal testing policies for diagnosing patients with intermediary probability of disease
Full text linkThis paper proposes a stochastic shortest path approach to find an optimal sequence of tests to confirm or discard a disease, for any prescribed optimality criterion. The idea is to select the best sequence in which to apply a series of available tests, with a view at reaching a diagnosis with minimum expenditure of resources. The proposed approach derives an optimal policy whereby the decision maker is provided with a test strategy for each a priori probability of disease, aiming to reach posterior probabilities that warrant either immediate treatment or a not-ill diagnosis.</p
Optimization model to assess electric vehicles as an alternative for fleet composition in station-based car sharing systems
No full textElectromobility can be one of many solutions to the environmental challenge facing society nowadays, and the dissemination of policies towards the adoption of electric vehicles (EVs) urges the development of studies to assess their actual benefits in contrast to both conventional and other alternative technologies. This work proposes an optimization model to evaluate the influence of the selected parameters in the economic and environmental dimensions of different vehicle technologies and the optimal fleet composition for small-scale car sharing. The model is applied to car sharing system VAMO, located in Fortaleza (Brazil), and the decision variables comprise pure electric (BEV), plug-in hybrid (PHEV) and internal combustion engine (ICEV) vehicles. Baseline results are strongly influenced by the economic dimension, showing that existing infrastructure and well-established technology are great advantages for ICEVs and major barriers for EVs. In that sense, ethanol arises as a balanced alternative between costs and emissions. However, EVs represent a strong environmental appeal considering global emissions and local pollutants and even with economic losses in the short-term, investments in electromobility could come out as a positioning strategy in a future business with strong perspectives of growth, be it technological or in market share. The results suggest that all vehicle technologies will play an important role during this transition period to a desired sustainable mobility.</p
Novel time aggregation based algorithms for Markov decision processes
No full textWe present two novel approaches to accelerate the convergence of a class of Markov decision problems (MDPs) with stationary state space components, which iterate on reduced state and action spaces and converge to an optimal policy. The time aggregation based algorithm (TABA) partitions the state space into disjoint sets, one for each possible combination of the non-stationary components, and iterates in the sets. The local search policy set iteration (LSPSI) algorithm introduces a novel modified policy evaluation procedure that seamlessly performs a local search over a very large set of candidate policies, by sampling a reduced subset of actions at each state's value function update. Both approaches, as well as a combination of them, are validated by means of a mining supply chain application with a large number of stationary state components and a large set of feasible actions. The experiments suggest that the proposed frameworks are very efficient for such a class of problems
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