We develop a Design and Analysis of the Computer Experiments (DACE) approach to the stochastic unit commitment problem for power systems with significant renewable integration. For this purpose, we use a two-stage sto...
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We develop a Design and Analysis of the Computer Experiments (DACE) approach to the stochastic unit commitment problem for power systems with significant renewable integration. For this purpose, we use a two-stage stochastic programming formulation of the stochastic unit commitment-economic dispatch problem. Typically, a sample average approximation of the true problem is solved using a cutting plane method (such as the L-shaped method) or scenario decomposition (such as Progressive Hedging) algorithms. However, when the number of scenarios increases, these solution methods become computationally prohibitive. To address this challenge, we develop a novel DACE approach that exploits the structure of the first-stage unit commitment decision space in a design of experiments, uses features based upon solar generation, and trains a multivariate adaptive regression splines model to approximate the second stage of the stochastic unit commitment-economic dispatch problem. We conduct experiments on two modified IEEE-57 and IEEE-118 test systems and assess the quality of the solutions obtained from both the DACE and the L-shaped methods in a replicated procedure. The results obtained from this approach attest to the significant improvement in the computational performance of the DACE approach over the traditional L-shaped method.
In addressing the challenges of last-mile logistics, the reliability of the supply chain network becomes paramount. These challenges are intensified due to drone performance limitations and various uncertainties in su...
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In addressing the challenges of last-mile logistics, the reliability of the supply chain network becomes paramount. These challenges are intensified due to drone performance limitations and various uncertainties in supply chain operations. While recent literature recognises the potential of drones for last-mile delivery, it falls short in effectively considering these uncertainties in drone-enabled supply chain models. Our research addresses this gap with two major contributions: first, a novel stochastic mixed-integer programming model is developed to construct a feasible delivery network, including warehouses and recharging stations, enhancing both coverage and reliability. Second, a modification in the genetic algorithm by considering each scenario independently improves computational efficiency, outperforming commercial software by an average of 40% and up to 55%. Empirical findings reveal that strategic investments in system hardening can yield substantial improvements in reliability. Despite the absence of real-world stochastic parameters as a limitation, this research pioneers the design of reliable networks under uncertainties and extends drone coverage through strategic charging stations. This work sets a significant milestone for future optimization in drone logistics, offering practical implications for supply chain managers considering drone adoption.
Uncertain conditions may deeply affect the relevance of deterministic solutions proposed by optimization or equilibrium models as well as leave the decision maker in a quandary at the moment of defining policy. This c...
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This paper proposes a stochastic bilevel optimization approach to owners of pumped hydro storage systems (PHSSs) to participate in pay-as-bid power market and provide optimal bids and offers. The price offering of oth...
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This paper proposes a stochastic bilevel optimization approach to owners of pumped hydro storage systems (PHSSs) to participate in pay-as-bid power market and provide optimal bids and offers. The price offering of other generation units is modeled by stochastic programming. The upper-level of the proposed bilevel programming seeks maximization of the profit of the PHSS arbitrage, where the lower-level assures the optimal system dispatching (and market-clearing), and keeps the network security. The bilevel optimization is then transferred into a single-level equivalent via Karush-Kuhn-Tucker (KKT) complementarity conditions. The equations of the KKT conditions are linearly modeled using special ordered sets of type 1 (SOS1) variables. Furthermore, the bilinear objective function of the upper-level is approximated using McCormick envelopes relaxation method, in order to obtain the solutions as fast as possible and making the problem as mixed-integer linear programming. The proposed method is verified on the IEEE 24-bus reliability test system (RTS) considering different cases. The operation of a single PHSS is assessed in the network's normal and congested conditions. The results show that the PHSS achieve more revenue in a limited network as the offered prices go up to price cap in some periods. In the studied cases, the profit of energy arbitrage by the PHSS increases from $ 3302 in a normal network, to $ 8170 in a limited network. Moreover, the effect of wind generation uncertainty on the arbitrage problem is investigated using five sub-scenarios dedicated to wind generation. It is shown that the arbitrage profit is more sensitive on generation cost uncertainty rather than wind generation uncertainty. Furthermore, it is revealed that the expected profit in the presence of wind turbines is slightly lower than that without wind turbines. This is due to the fact that the wind generation power is always accepted and dispatched in the market and lowers the load demand a
Unexpected disruptions occur frequently in the railways, during which many train services cannot run as scheduled. This paper deals with timetable rescheduling during such disruptions, particularly in the case where a...
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Unexpected disruptions occur frequently in the railways, during which many train services cannot run as scheduled. This paper deals with timetable rescheduling during such disruptions, particularly in the case where all tracks between two stations are blocked for hours. In practice, a disruption may become shorter or longer than predicted. To take the uncertainty of the disruption duration into account, this paper formulates the timetable rescheduling as a rolling horizon two-stage stochastic programming problem in deterministic equivalent form. The random disruption duration is assumed to have a finite number of possible realizations, called scenarios, with given probabilities. Every time a prediction about the range of the disruption end time is updated, new scenarios are defined, and a two-stage stochastic model computes the optimal rescheduling solution to all these scenarios. The stochastic method was tested on a part of the Dutch railways, and compared to a deterministic rolling-horizon method. The results showed that compared to the deterministic method, the stochastic method is more likely to generate better rescheduling solutions for uncertain disruptions by less train cancellations and/or delays, while the solution robustness can be affected by the predicted range regarding the disruption end time.
Devastating effects of disasters and global crises on people increase the importance of humanitarian logistics studies for pre and post-disaster stages. Location planning of Temporary Medical Centers/field hospitals i...
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Devastating effects of disasters and global crises on people increase the importance of humanitarian logistics studies for pre and post-disaster stages. Location planning of Temporary Medical Centers/field hospitals is one of the most important problems for disaster response. We aimed to determine the location and number of temporary medical centers in case of disasters by considering the locations of the existing hospitals, casualty classification (triage), capacities of medical centers and possibilities of damage to the roads and hospitals. Besides, we aimed to assign different casualty classes to these medical centers for emergency medical response by considering the distances between disaster areas and medical centers. For this purpose, a two-stage stochastic programming model was developed. The proposed model finds an optimal TMC location solution while minimizing the total setup cost of the TMCs and the expected total transportation cost by considering casualty types, demand, possibilities of damage to the roads and hospitals, and distance between the disaster areas and the medical centers. In the model, a-reliability constraints for the expected number of unassigned casualties were also used. Besides, the model was reformulated without triage, in order to understand the impact of casualty classification on the solution of the problem. We performed a real case study for the district of Kartal expected to be widely damaged in the possible Istanbul earthquake, and a sensitivity analysis was made. The analysis of the results offer some managerial insights associated with the number of temporary medical centers' needed, their locations, and additional hospital capacity requirements.
The unit commitment problem is a typical scheduling problem in an electric power system. The problem is determining the schedules for power generating units and the generating level of each unit. In this paper, we dev...
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Community resilience planning is challenging as it involves several large-scale systems with interdependency, populations with diverse socio-economic characteristics, and numerous stakeholders. This study introduces a...
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Community resilience planning is challenging as it involves several large-scale systems with interdependency, populations with diverse socio-economic characteristics, and numerous stakeholders. This study introduces a new optimization model to decrease a community's burden in developing viable alternative sets of decisions while considering costs and risks associated with uncertain hazard events. The model captures the essential features of a community, and its scope extends beyond infrastructure and buildings to include social goals. Structural engineering and social science approaches are adapted and incorporated into the model formulation to facilitate the identification of engineering decisions meeting the social goals of minimizing population dislocation and time for recovery. A risk-averse approach frames the optimization problem as a two-stage mean-risk stochastic programming model, which enables effective planning for low-probability, high-consequence hazard events. A case study simulating flood hazards in Lumberton, North Carolina, is developed, and the model is run with the generated data set to showcase the model's capability in developing risk-informed mitigation and recovery plans to achieve resilience goals. The insights drawn from the numerical experiments show the effect of changing risk preference on community resilience metrics.
Despite concerted efforts by health authorities worldwide to contain COVID-19, the SARS-CoV-2 virus has continued to spread and mutate into new variants with uncertain transmission characteristics. Therefore, there is...
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Despite concerted efforts by health authorities worldwide to contain COVID-19, the SARS-CoV-2 virus has continued to spread and mutate into new variants with uncertain transmission characteristics. Therefore, there is a need for new data-driven models for determining optimal vaccination strategies that adapt to the new variants with their uncertain transmission characteristics. Motivated by this challenge, we derive an integrated chance constraints stochastic programming (ICC-SP) approach for finding vaccination strategies for epidemics that incorporates population demographics for any region of the world, uncertain disease transmission and vaccine efficacy. An optimal vaccination strategy specifies the proportion of individuals in a given household-type to vaccinate to bring the reproduction number to below one. The ICC-SP approach provides a quantitative method that allows to bound the expected excess of the reproduction number above one by an acceptable amount according to the decision-maker's level of risk. This new methodology involves a multi-community household based epidemiology model that uses census demographics data, vaccination status, age-related heterogeneity in disease susceptibility and infectivity, virus variants, and vaccine efficacy. The new methodology was tested on real data for seven neighboring counties in the United States state of Texas. The results are promising and show, among other findings, that vaccination strategies for controlling an outbreak should prioritize vaccinating certain household sizes as well as age groups with relatively high combined susceptibility and infectivity.
In this paper, we propose a multi-objective two-stage stochastic programming model for a multi-site supply chain planning problem under demand uncertainty. Decisions such as the amount of products to be produced, the ...
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