We consider the burglar problem in which a burglar can either retire or choose among different types of burglaries, with each type having its own success probability and reward distribution. Some general structural re...
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We consider the burglar problem in which a burglar can either retire or choose among different types of burglaries, with each type having its own success probability and reward distribution. Some general structural results are established and, in the case of exponentially distributed reward distributions, a solution technique is presented. The burglar problem's relationship to a stochastic knapsack problem with a random exponentially distributed knapsack capacity is shown. (C) 2014 Wiley Periodicals, Inc.
dynamic Adaptive Streaming over HTTP (DASH) is a recent MPEG standard for IP video delivery whose aim is the convergence of existing adaptive-streaming proprietary solutions. However, it does not impose any adaptation...
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dynamic Adaptive Streaming over HTTP (DASH) is a recent MPEG standard for IP video delivery whose aim is the convergence of existing adaptive-streaming proprietary solutions. However, it does not impose any adaptation logic for selecting the quality of the media segments requested by the client, which is crucial to cope effectively with bandwidth fluctuations, notably in wireless channels. We therefore propose a solution to this control problem through stochastic dynamic programming (SDP). This approach requires a probabilistic characterization of the system, as well as the definition of a cost function that the control strategy aims to minimize. This cost function is designed taking into account factors that may influence the quality perceived by the users. Unlike previous works, which compute control policies online by learning from experience, our algorithm solves the control problem offline, leading promptly to better results. In addition, we compared our algorithm to others during a streaming simulation and we analyzed the objective results by means of a Quality of Experience (QoE) oriented metric. Moreover, we conducted subjective tests to complete the evaluation of the performance of our algorithm. The results show that our proposal outperforms the other approaches in terms of both the QoE-oriented metric and the subjective evaluation.
The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a ...
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The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct monotone traveling wave solutions and identify parametric regions for which the traveling wave solution has a positive or negative wave speed.
Rollout algorithms have enjoyed success across a variety of domains as heuristic solution procedures for stochasticdynamic programs (SDPs). However, because most rollout implementations are closely tied to specific p...
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Rollout algorithms have enjoyed success across a variety of domains as heuristic solution procedures for stochasticdynamic programs (SDPs). However, because most rollout implementations are closely tied to specific problems, the visibility of advances in rollout methods is limited, thereby making it difficult for researchers in other fields to extract general procedures and apply them to different areas. We present a rollout algorithm framework to make recent advances in rollout methods more accessible to researchers seeking heuristic policies for large-scale, finite-horizon SDPs. We formalize rollout variants exploiting the pre- and post-decision state variables as a means of overcoming computational limitations imposed by large state and action spaces. We present a unified analytical discussion, generalizing results from the literature and introducing new results that relate the performance of the rollout variants to one another. Relative to the literature, our policy-based approach to presenting and proving results makes a closer connection to the underpinnings of dynamicprogramming. Finally, we illustrate our framework and analytical results via application to a dynamic and stochastic multi-compartment knapsack problem. (C) 2016 Published by Elsevier B.V.
World Endurance Championship (WEC) racing events are characterised by a relevant performance gap among competitors. The fastest vehicles category, consisting in LMP1 race hybrid vehicles, has to respect energy usage c...
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World Endurance Championship (WEC) racing events are characterised by a relevant performance gap among competitors. The fastest vehicles category, consisting in LMP1 race hybrid vehicles, has to respect energy usage constraints set by the technical regulation. Considering absence of competitors, i.e. traffic conditions, the optimal energy usage strategy for lap time minimisation is typically computed through a constrained optimisation problem. To the best of our knowledge, the majority of state-of-the-art works neglects competitors. This leads to a mismatch with the real world, where traffic generates considerable time losses. To bridge this gap, we propose a new framework to offline compute optimal strategies for the powertrain energy management considering competitors. Through analysis of the available data from previous events, statistics on the sector times and overtaking probabilities are extracted to encode the competitors' behaviour. Adopting a multi-agent model, the statistics are then used to generate realistic Monte Carlo (MC) simulation of their position along the track. The simulator is then adopted to identify the optimal strategy as follows. We develop a longitudinal vehicle model for the ego-vehicle and implement an optimisation problem for lap time minimisation in absence of traffic, based on Genetic Algorithms. Solving the optimisation problem for a variety of constraints generates a set of candidate optimal strategies. stochastic dynamic programming is finally employed to online choose the best strategy at the beginning of each lap, considering the competitors' initial position and their forecast future motion provided by the MC simulator. Our approach, validated on data from a real stint of race, allows to significantly reduce the lap time.
From health care to maintenance shops, many systems must contend with allocating resources to customers or jobs whose initial service requirements or costs change when they wait too long. We present a new queueing mod...
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From health care to maintenance shops, many systems must contend with allocating resources to customers or jobs whose initial service requirements or costs change when they wait too long. We present a new queueing model for this scenario and use a Markov decision process formulation to analyze assignment policies that minimize holding costs. We show that the classic c mu rule is generally not optimal when service or cost requirements can change. Even for a two-class customer model where a class 1 task becomes a class 2 task upon waiting, we show that additional orderings of the service rates are needed to ensure the optimality of simple priority rules. We then show that seemingly-intuitive switching curve structures are also not optimal in general. We study these scenarios and provide conditions under which they do hold. Lastly, we show that results from the two-class model do not extend to when there are n >= 3 customer classes. More broadly, we find that simple priority rules are not optimal. We provide sufficient conditions under which a simple priority rule holds. In short, allowing service and/or cost requirements to change fundamentally changes the structure of the optimal policy for resource allocation in queueing systems.
This paper addresses a scheduling problem where patients with different priorities are scheduled for elective surgery in a surgical facility. which has a limited capacity. When the capacity is available, patients with...
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This paper addresses a scheduling problem where patients with different priorities are scheduled for elective surgery in a surgical facility. which has a limited capacity. When the capacity is available, patients with a higher priority are selected from the waiting list and put on the schedule. At the beginning of each period, a decision of the number of patients to be scheduled is made based on the trade-offs between the cost for overtime work and the cost for surgery postponement. A stochastic dynamic programming model is formulated to address this problem. A structural analysis of the proposed model is conducted to understand the properties of an optimal schedule policy. Based on the structural analysis, bounds on feasible actions are incorporated into a value iteration algorithm, and a brief computation experiment shows the improvement in computational efficiency. Numerical examples show that the consideration of patient priority results in significant differences in surgery schedules from the schedule that ignores the patient priority. (C) 2009 Elsevier Ltd. All rights reserved.
Several projects in the European Union (EU) are currently under development to implement the carbon capture, transport and storage (CCS) technology on a large scale and may be subject to public funding under EU suppor...
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Several projects in the European Union (EU) are currently under development to implement the carbon capture, transport and storage (CCS) technology on a large scale and may be subject to public funding under EU support initiatives. These CCS projects may develop any combination of three types of operating levels: pilot, demonstration and full-scale, representing progressing levels of electric power generation capability. Several projects have commenced at the demonstration level, with full-scale commercial levels planned for approximately 2020. Taking the perspective of a funding agency, we employ a real options framework for determining an optimal project selection and funding strategy for the development of full-scale CCS plants. Specifically, we formulate and solve a stochasticdynamic program (SDP) for obtaining optimal funding solutions in order to achieve at least one successfully operating full-scale CCS plant by a target year. The model demonstrates the improved risk reduction by employing such a multi-stage competition. We then extend the model to consider two sensitivities: (1) the flexibility to spend that budget among the time periods and (2) optimizing the budget, but specifying each time period's allocation a priori. State size and runtimes of the SDP model are provided. (C) 2013 Elsevier Ltd. All rights reserved.
This paper aims at designing optimal gear shift strategies for conventional passenger vehicles equipped with discrete ratio transmissions. In order to study quantitatively an optimal trade-off between the fuel economy...
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This paper aims at designing optimal gear shift strategies for conventional passenger vehicles equipped with discrete ratio transmissions. In order to study quantitatively an optimal trade-off between the fuel economy and the driveability, the vehicle driveability is addressed in a fuel-optimal gear shift algorithm based on dynamicprogramming by three methods: method 1, weighted inverse of power reserve;method 2, constant power reserve;method 3, variable power reserve. Furthermore, another method based on stochastic dynamic programming is proposed to derive an optimal gear shift strategy over a number of driving cycles in an average sense, hence taking into account the vehicle driveability. In contrast with the dynamic-programming-based strategy, the obtained gear shift strategy based on stochastic dynamic programming is real time implementable. A comparative analysis of all proposed gear shift methods is given in terms of the improvements in the fuel economy and the driveability. The variable-power-reserve method achieves the highest fuel economy without sacrificing the driveability.
This paper aims to promote and illustrate that the combination of classical operations research (queueing, linear and stochastic dynamic programming) and simulation (techniques and tools) can be most beneficial. First...
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This paper aims to promote and illustrate that the combination of classical operations research (queueing, linear and stochastic dynamic programming) and simulation (techniques and tools) can be most beneficial. First, an instructive example of parallel queues will be studied to address the question whether these queues should be pooled or not. This simple example already shows the necessary and fruitful combination of queueing and simulation. Next, the combined approach will be applied to and illustrated for: pooling (or not) of call centers, pooling (or not) in hospitals, checking-in at airports, flight catering, and assembly lines. The applications show that "to pool or not" is not the only question for which further research and application of a combined OR-Simulation approach can be most fruitful for 'practical optimization'. (C) 2008 Elsevier B.V. All rights reserved.
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