In recent years, supply chains have become increasingly globalized. As a consequence, the world's supply of all types of parts has become more susceptible to disruptions. Some of these disruptions are extreme and ...
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In recent years, supply chains have become increasingly globalized. As a consequence, the world's supply of all types of parts has become more susceptible to disruptions. Some of these disruptions are extreme and may have global implications. Our research is based on the supply risk management problem faced by a manufacturer. We model the problem as a dynamic program, design and implement approximate dynamic programming (ADP) algorithms to solve it, to overcome the well-known curses of dimensionality. Using numerical experiments, we compare the performance of different ADP algorithms. We then design a series of numerical experiments to study the performance of different sourcing strategies (single, dual, multiple, and contingent sourcing) under various settings, and to discover insights for supply risk management practice. The results show that, under a wide variety of settings, the addition of a third or more suppliers brings much less marginal benefits. Thus, managers can limit their options to a backup supplier (contingent sourcing) or an additional regular supplier (dual sourcing). Our results also show that, unless the backup supplier can supply with zero lead time, using dual sourcing appears to be preferable. Lastly, we demonstrate the capability of the proposed method in analyzing more complicated realistic supply chains. (C) 2012 Elsevier Ltd. All rights reserved.
Surgical scheduling consists of selecting surgeries to be performed within a day, while jointly assigning operating rooms, starting times and the required resources. Patients can be elective or emergency/urgent. The s...
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Surgical scheduling consists of selecting surgeries to be performed within a day, while jointly assigning operating rooms, starting times and the required resources. Patients can be elective or emergency/urgent. The scheduling of surgeries in an operating theatre with common resources to emergency or urgent and elective cases is highly subject to uncertainties not only on the duration of an intervention but mainly on the arrival of emergency or urgent cases. At the beginning of the day we are given a candidate set of elective surgeries with and an expected duration and a time window the surgery must start, but the expected duration and the time window of an emergency or urgent case become known when the surgery arrives. The day is divided into decision stages. Due to the dynamic nature of the problem, at the beginning of each stage the planner can make decisions taking into account the new information available. Decisions can be to schedule arriving surgeries, and to reschedule or cancel surgeries not started yet. The objective is to minimize the total expected cost composed of terms related to refusing arriving surgeries, to canceling scheduled surgeries, and to starting surgeries out of their time window. We address the problem with an approximate dynamic programming approach embedding an integer programming formulation to support decision making. We propose a dynamic model and an approximate policy iteration algorithm making use of basis functions to capture the impact of decisions to the future stages. Computational experiments have shown with statistical significance that the proposed algorithm outperforms a lookahead reoptimization approach. (C) 2019 Elsevier Ltd. All rights reserved.
We present a numerical method for generating the state-feedback control policy associated with general undiscounted, constant-setpoint, infinite-horizon, nonlinear optimal control problems with continuous state variab...
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We present a numerical method for generating the state-feedback control policy associated with general undiscounted, constant-setpoint, infinite-horizon, nonlinear optimal control problems with continuous state variables. The method is based on approximate dynamic programming, and is closely related to approximate policy iteration. Existing methods typically terminate based on the convergence of the control policy and either require a discounted problem formulation or demand the cost function to lie in a specific subclass of functions. The presented method extends on existing termination criteria by requiring both the control policy and the resulting system state to converge, allowing for use with undiscounted cost functions that are bounded and continuous. This paper defines the numerical method, derives the relevant underlying mathematical properties, and validates the numerical method with representative examples. A MATLAB implementation with the shown examples is freely available.
This paper illustrates the development of an intelligent local area signals based controller for damping low-frequency oscillations in power systems. The controller is trained offline to perform well under a wide vari...
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This paper illustrates the development of an intelligent local area signals based controller for damping low-frequency oscillations in power systems. The controller is trained offline to perform well under a wide variety of power system operating points, allowing it to handle the complex, stochastic, and time-varying nature of power systems. Neural network based system identification eliminates the need to develop accurate models from first principles for control design, resulting in a methodology that is completely data driven. The virtual generator concept is used to generate simplified representations of the power system online using time-synchronized signals from phasor measurement units at generating stations within an area of the system. These representations improve scalability by reducing the complexity of the system "seen" by the controller and by allowing it to treat a group of several synchronous machines at distant locations from each other as a single unit for damping control purposes. A reinforcement learning mechanism for approximate dynamic programming allows the controller to approach optimality as it gains experience through interactions with simulations of the system. Results obtained on the 68-bus New England/New York benchmark system demonstrate the effectiveness of the method in damping low-frequency inter-area oscillations without additional control effort.
Problem definition: Inpatient beds are usually grouped into several wards, and each ward is assigned to serve patients from certain "primary" specialties. However, when a patient waits excessively long befor...
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Problem definition: Inpatient beds are usually grouped into several wards, and each ward is assigned to serve patients from certain "primary" specialties. However, when a patient waits excessively long before a primary bed becomes available, hospital managers have the option to assign her to a nonprimary bed. although it is undesirable. Deciding when to use such "overflow" is difficult in real time and under uncertainty. Relevance: To aid the decision making, we model hospital inpatient flow as a multiclass, multipool parallel-server queueing system and formulate the overflow decision problem as a discrete-time, infinite-horizon average cost Markov decision process (MDP). The MDP incorporates many realistic and important features such as patient arrival and discharge patterns depending on time of day. Methodology: To overcome the curse-of-dimensionality of this formulated MDP, we resort to approximate dynamic programming (ADP). A critical part in designing an ADP algorithm is to choose appropriate basis functions to approximate the relative value function. Using a novel combination of fluid control and single-pool approximation, we develop analytical forms to approximate the relative value functions at midnight, which then guides the choice of the basis functions for all other times of day. Results: We demonstrate, via numerical experiments in realistic hospital settings, that our proposed ADP algorithm is remarkably effective in finding good overflow policies. These ADP policies can significantly improve system performance over some commonly used overflow strategies-for example, in a baseline scenario, the ADP policy achieves a congestion level similar to that achieved by a complete bed sharing policy, while reduces the overflow proportion by 20%. Managerial implications: We quantify the trade-off between the overflow proportion and congestion from implementing ADP policies under a variety of system conditions and generate useful insights. The plotted efficient fro
There is growing interest in the use of grid-level storage to smooth variations in supply that are likely to arise with an increased use of wind and solar energy. Energy arbitrage, the process of buying, storing, and ...
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There is growing interest in the use of grid-level storage to smooth variations in supply that are likely to arise with an increased use of wind and solar energy. Energy arbitrage, the process of buying, storing, and selling electricity to exploit variations in electricity spot prices, is becoming an important way of paying for expensive investments into grid-level storage. Independent system operators such as the New York Independent System Operator (NYISO) require that battery storage operators place bids into an hour-ahead market (although settlements may occur in increments as small as five minutes, which is considered near "real-time"). The operator has to place these bids without knowing the energy level in the battery at the beginning of the hour and simultaneously accounting for the value of leftover energy at the end of the hour. The problem is formulated as a dynamic program. We describe and employ a convergent approximate dynamic programming (ADP) algorithm that exploits monotonicity of the value function to find a revenue-generating bidding policy;using optimal benchmarks, we empirically show the computational benefits of the algorithm. Furthermore, we propose a distribution-free variant of the ADP algorithm that does not require any knowledge of the distribution of the price process (and makes no assumptions regarding a specific real-time price model). We demonstrate that a policy trained on historical real-time price data from the NYISO using this distribution-free approach is indeed effective.
The factory logistics increases in importance as more processes and types of components are needed to produce a product. Due to the limited industrial space and stressful competitive environment, manufacturers increas...
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The factory logistics increases in importance as more processes and types of components are needed to produce a product. Due to the limited industrial space and stressful competitive environment, manufacturers increasingly outsource logistics-related activities to Third-Party Logistics (3PLs) and Supply hubs. However, the challenges, including unsynchronised decisions with other partners, non-value-added warehousing operations, and excessive space occupation, still burden manufacturers. This research proposes a cross-docking-based factory logistics unitisation process (CD-FLUP) that integrates the cross-docking technique into the assembly line feeding process and uses mobile shelves for component holding and delivery. We formulate the CD-FLUP with an integer program to minimise the total number of shelf units put into storage and the number of deliveries to assembly lines. Based on time decomposition, we propose an approximate dynamic programming (ADP) approach to solve the model efficiently. The time-varying value function approximation (VFA) developed in the proposed ADP approach reduces the approximation parameters and speeds up convergence significantly. The numerical experiment shows that the proposed ADP can generate high-quality solutions far more efficiently than a commercial solver. & COPY;2023 Elsevier B.V. All rights reserved.
The approximate dynamic programming (ADP) method based on the design and analysis of computer experiments (DACE) approach has been demonstrated as an effective method to solve multistage decision-making problems in th...
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The approximate dynamic programming (ADP) method based on the design and analysis of computer experiments (DACE) approach has been demonstrated as an effective method to solve multistage decision-making problems in the literature. However, this method is still not efficient for infinite-horizon optimization considering the required large volume of sampling in the state space and high-quality value function identification. Therefore, we propose a sequential sampling algorithm and embed it into a DACE-based ADP method to obtain a high-quality value function approximation. Considering the limitations of the traditional stopping criterion (Bellman error bound), we further propose a 45-degree line stopping criterion to terminate value iteration early by identifying an optimally equivalent value function. A comparison of the computational results with those of other three existing policies indicates that the proposed sampling algorithm and stopping criterion can determine a high-quality ADP policy. Finally, we discuss the extrapolation issue of the value function approximated by multivariate adaptive regression splines, the results of which further demonstrate the quality of the ADP policy generated in this study. (c) 2020 Elsevier Ltd. All rights reserved.
This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, t...
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This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature.
Pricing American basket option is one of the essential problems in quantitative finance. The complexity of this type of option has motivated many practitioners and researchers to develop simulation-based methods. In t...
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Pricing American basket option is one of the essential problems in quantitative finance. The complexity of this type of option has motivated many practitioners and researchers to develop simulation-based methods. In this paper, we develop an optimized radial basis function neural network (RBFNN), which is optimally tuned by the particle swarm optimization algorithm to enhance the efficiency and accuracy of approximate dynamic programming (ADP) for pricing the American basket option. Additionally, for the scenario generation, a simulation-based technique using a copula-GARCH method and Extreme Value Theory is performed to tackle the nonlinearity of dependencies between variables. The prices obtained through the proposed approach compared with those ones achieved from pure RBFNN and ADP in different situations. This is also illustrated that the obtained prices of American basket option can outperform the results obtained through the RBFNN and ADP approaches in terms of the predefined fitness measures.
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