Browsing by Subject "Two-stage stochastic programming"

Now showing 1 - 8 of 8

Open Access
Air traffic flow management problem with stochastic capacities
(2021-09) Sertkaya, Efe
Air traﬃc systems have substantial eﬀects on transportation, logistics, and economics in a global scope. Due to both practical signiﬁcance and intellectual challenges, air traﬃc ﬂow management problems have been extensively studied for many decades. The aim of air traﬃc ﬂow management problems is to plan the ﬂow throughout the air traﬃc network while satisfying capacity constraints. In this study, we consider the case of stochastic capacities in the air traﬃc network. We propose both stochastic multistage integer and stochastic two-stage integer modeling approaches for the problem. In multistage and two-stage models, we aim to resolve the demand-capacity imbalances at each element of the air trafﬁc network. To achieve this, we decide on the take-oﬀ times and routes of each ﬂight for a given time horizon. We propose integer L-shaped and partial Benders’ decomposition approaches to solve the two-stage model. Additionally, we analyze the eﬀect of conditional value-at-risk constraints on delay time distributions. To incorporate conditional value-at-risk to solution methodologies, we propose a novel approximation technique. We present a detailed analysis of delay distributions, demonstrate the eﬀect of the approximation technique on solution quality and computational performance. For computational experiments, we explicitly describe data generation procedures to obtain realistic instances. We demonstrate that the Partial Benders’ modiﬁcation outperforms the commercial solver (CPLEX) in almost every instance.
Open Access
A chance constrained approach to optimal sizing of renewable energy systems with pumped hydro energy storage
(2022-08) Kalkan, Nazlı
Burning fossil fuels is responsible for a large portion of the greenhouse gases released into the atmosphere. In addition to their negative impacts on the environment, fossil fuels are limited, which makes the integration of renewable energy sources into the grid inevitable. However, the intermittent nature of renewable energy sources makes it challenging to regulate energy output, resulting in low system flexibility. Adoption of an energy storage system, such as pumped hydro energy storage (PHES) and batteries, is necessary to fully utilize and integrate a larger proportion of variable renewable energy sources into the grid. On the other hand, in investment planning problems, satisfying the demand for certainty for even infrequently occurring events can lead to considerable cost increases. In this study, we propose a chance constrained two-stage stochastic program for designing a hybrid renewable energy system where the intermittent solar energy output is supported by a closed-loop PHES system. The aim of this study is to minimize the total investment cost while meeting the energy demand at a predetermined service level. For our computational study, we generate scenarios for solar radiation by using an Auto-Regressive Integrated Moving Average (ARIMA) based algorithm. In order to exactly solve our large scale problem, we utilize a Benders based branch and cut decomposition algorithm. We analize the efficiency of our proposed solution method by comparing the CPU times provided by the proposed algorithm and CPLEX. The findings indicate that the proposed algorithm solves the problem faster than CPLEX.
Open Access
Nonlinear mixed integer programming models and algorithms for fair and efficient large scale evacuation planning
(2015-07) Bayram, Vedat
Shelters are safe facilities that protect a population from possible damaging effects of a disaster. Traffic management during an evacuation and the decision of where to locate the shelters are of critical importance to the performance of an evacuation plan. From the evacuation management authority's point of view, the desirable goal is to minimize the total evacuation time by computing a system optimum (SO). However, evacuees may not be willing to take long routes enforced on them by a SO solution; but they may consent to taking routes with lengths not longer than the shortest path to the nearest shelter site by more than a tolerable factor. We develop a model that optimally locates shelters and assigns evacuees to the nearest shelter sites by assigning them to shortest paths, shortest and nearest with a given degree of tolerance, so that the total evacuation time is minimized. As the travel time on a road segment is often modeled as a nonlinear function of the ow on the segment, the resulting model is a nonlinear mixed integer programming model. We develop a solution method that can handle practical size problems using second order cone programming techniques. Using our model, we investigate the trade-of between efficiency and fairness. Disasters are uncertain events. Related studies and real-life practices show that a significant uncertainty regarding the evacuation demand and the impact of the disaster on the infrastructure exists. The second model we propose is a scenario-based two-stage stochastic evacuation planning model that optimally locates shelter sites and that assigns evacuees to shelters and paths to minimize the expected total evacuation time, under uncertainty. The model considers the uncertainty in the evacuation demand and the disruption in the road network and shelter sites. We present a case study for an impending earthquake in Istanbul, Turkey. We compare the performance of the stochastic programming solutions to solutions based on single scenarios and mean values. We also propose an exact algorithm based on Benders decomposition to solve the stochastic problem. To the best of our knowledge, ours is the first algorithm that uses duality results for second order cone programming in a Benders decomposition setting. We solve practical size problems with up to 1000 scenarios in moderate CPU times. We investigate methods such as employing a multi-cut strategy, deriving pareto-optimal cuts, using a reduced primal subproblem and preemptive priority multiobjective program to enhance the proposed algorithm. Computational results confirm the efficiency of our algorithm. This research is supported by TUBITAK, The Scientific and Technological Research Council of Turkey with project number 213M434.
Open Access
Optimization of hybrid energy systems with pumped hydro storage: a case study for Turkey
(Gazi Üniversitesi Mühendislik-Mimarlık, 2019) Kocaman, Ayşe Selin
There is a need for energy models that include renewable energy sources to reduce the role of fossil fuels in electricity generation. However, renewable energy sources are intermittent and cannot be predicted precisely. Designing hybrid systems that combine alternative resources and energy storage helps reduce the intermittency of renewable sources and result in cost effective and reliable solutions. The most widely used energy storage form in the World is to store the potential energy of water in the pumped hydroelectricity systems (PHES). Pumped hydroelectricity systems can be designed in two types: mixed systems, if there is a natural water inflow to the system and pure systems, if the system is closed to water inflow. In this study, we present two-stage stochastic programming models for both types of PHES, which take into account the uncertainty of resources and electricity demand. For the first time in the literature, we consider the sizing problem of hybrid systems that include solar generation supported by pure and mixed PHES systems separately and present the results for Turkey, which currently does not have any PHES system and highly depends on fossil fuels for electricity generation, despite of the rich renewable energy potential.
Open Access
Shelter location and evacuation route assignment under uncertainty: a benders decomposition approach
(INFORMS Inst.for Operations Res.and the Management Sciences, 2018) Bayram, V.; Yaman, Hande
Shelters are safe facilities that protect a population from possible damaging effects of a disaster. For that reason, shelter location and traffic assignment decisions should be considered simultaneously for an efficient evacuation plan. In addition, as it is very difficult to anticipate the exact place, time, and scale of a disaster, one needs to take into account the uncertainty in evacuation demand, the disruption/degradation of evacuation road network structure, and the disruption in shelters. In this study, we propose an exact algorithm based on Benders decomposition to solve a scenario-based two-stage stochastic evacuation planning model that optimally locates shelters and that assigns evacuees to shelters and routes in an efficient and fair way to minimize the expected total evacuation time. The second stage of the model is a second-order cone programming problem, and we use duality results for second-order cone programming in a Benders decomposition setting. We solve practical-size problems with up to 1,000 scenarios in moderate CPU times. We investigate methods such as employing a multicut strategy, deriving Pareto-optimal cuts, and using a preemptive priority multiobjective program to enhance the proposed algorithm. We also use a cutting plane algorithm to solve the dual subproblem since it contains a constraint for each possible path. Computational results confirm the efficiency of our algorithms.
Open Access
A stochastic programming approach for Shelter location and evacuation planning
(EDP Sciences, 2018) Bayram, V.; Yaman, Hande
Shelter location and traffic allocation decisions are critical for an efficient evacuation plan. In this study, we propose a scenario-based two-stage stochastic evacuation planning model that optimally locates shelter sites and that assigns evacuees to nearest shelters and to shortest paths within a tolerance degree to minimize the expected total evacuation time. Our model considers the uncertainty in the evacuation demand and the disruption in the road network and shelter sites. We present a case study for a potential earthquake in Istanbul. We compare the performance of the stochastic programming solutions to solutions based on single scenarios and mean values
Open Access
Systemic risk measures based on value-at-risk
(2023-07) Al-Ali, Wissam
This thesis addresses the problem of computing systemic set-valued risk measures. The proposed method incorporates the clearing mechanism of the Eisenberg-Noe model, used as an aggregation function, with the value-at-risk, used as the underlying risk measure. The sample-average approximation (SAA) of the corresponding set-valued systemic risk measure can be calculated by solving a vector optimization problem. For this purpose, we propose a variation of the so-called grid algorithm in which grid points are evaluated by solving certain scalar mixed-integer programming problems, namely, the Pascoletti Serafini and norm-minimizing scalarizations. At the initialization step, we solve weighted sum scalarizations to establish a compact region for the algorithm to work on. We prove the convergence of the SAA optimal values of the scalarization problems to their respective true values. More-over, we prove the convergence of the approximated set-valued risk measure to the true set-valued risk measure in both the Wijsman and Hausdorff senses. In order to demonstrate the applicability of our findings, we construct a financial network based on the Bollob´as preferential attachment model. In addition, we model the economic disruptions using identically distributed random variables with a Pareto distribution. We conduct a comprehensive sensitivity analysis to investigate the effect of the number of scenarios, correlation coefficient, and Bollob´as network parameters on the systemic risk measure. The results highlight the minimal influence of the number of scenarios and correlation coefficient on the risk measure, demonstrating its stability and robustness, while shedding light on the profound significance of Bollob´as network parameters in determining the network dynamics and the overall level of systemic risk.
Open Access
Team orienteering problem with stochastic time-dependent travel time
(2021-07) Çelik, Şifanur
According to United Nations, human population living in urban areas is expected to increase in the coming years. This increase will have an eﬀect on the traﬃc density in the urban areas. This motivates employees whose job is to visit customers during the day, such as logistics company employees, to consider the impact of traﬃc density on the travel times while visiting customers. This study aims to ﬁnd prior optimal tours for more than one agent to visit customers and to maxi-mize total expected proﬁt within a given time limit while taking the uncertainties in travel times caused by traﬃc congestion into account. Agents are not required to visit every customer and the tour of each agent starts and ends at a certain depot node. It is assumed that the travel time to go from a customer to another customer is random and depends on the departure. We use a time-dependent travel time model that has ﬁrst-in-ﬁrst-out property while calculating the travel times. We propose a two-stage stochastic mixed-integer program to formulate the problem and suggest Integer L-shaped method in order to solve large-scale problem instances. In our computational study, we analyze the beneﬁt of using stochastic solutions, and observe that Integer L-shaped method is superior to CPLEX in terms of computational time.