Dept. of Industrial Engineering - Ph.D. / Sc.D.No Descriptionhttps://hdl.handle.net/11693/138862023-11-29T02:14:34Z2023-11-29T02:14:34Z521Markov decision process formulations for management of pumped hydro energy storage systemsToufani, Parinazhttps://hdl.handle.net/11693/1124012023-07-11T00:03:40Z2023-06-01T00:00:00Zdc.title: Markov decision process formulations for management of pumped hydro energy storage systems
dc.contributor.author: Toufani, Parinaz
dc.description.abstract: Renewable energy sources have received much attention to mitigate the high dependence on fossil fuels and the resulting environmental impacts. Since the variability and intermittency of such renewable sources lower the reliability and security of energy systems, they should often be accompanied by efficient and flexible storage units. This dissertation focuses on pumped hydro energy storage (PHES) facilities, which are one of the most commonly used large-scale storage technologies. We study the energy generation and storage problem for PHES facilities with two connected reservoirs, where water is pumped from the lower reservoir to the upper reservoir to store energy during low-demand/low-electricity price periods, and released back to the lower reservoir to generate energy during high-demand/high-electricity price periods. The first part of this dissertation investigates the potential benefits of transforming conventional cascading hydropower stations into PHES facilities by replacing turbines with reversible ones. The second part compares the short-term cash flows obtained from different PHES configurations (cascading vs. non-cascading facilities, upstream vs. downstream inflows, and closed-loop facilities). We formulate both problems as Markov decision processes under uncertainty in the streamflow rate and electricity price. We include the streamflow rate and electricity price as exogenous state variables in our formulation. We analytically derive bounds on the profit improvement obtained from PHES transformation in the first part and bounds on the revenue differences obtained from different configurations in the second part. In the last part, we establish several structural properties of the optimal profit function for general two-reservoir PHES systems. We show the optimality of a state-dependent threshold policy for non-cascading PHES facilities when the electricity price is always positive. Leveraging our structural results, we construct a heuristic solution method for more general settings when the electricity price can also be negative. In this dissertation, we also conduct comprehensive numerical experiments with data-calibrated time series models to provide insights into the optimal operation of PHES facilities, considering distinct seasons with different streamflow rates, different negative electricity price occurrence frequencies, and different system parameters.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2023.; Includes bibliographical references (pages 95-118).
2023-06-01T00:00:00ZEnergy operations management for renewable power producers in electricity marketsKarakoyun, Ece Çiğdemhttps://hdl.handle.net/11693/1123832023-07-08T00:06:50Z2023-05-01T00:00:00Zdc.title: Energy operations management for renewable power producers in electricity markets
dc.contributor.author: Karakoyun, Ece Çiğdem
dc.description.abstract: Renewable energy generation has grown dramatically around the world in recent years, and policies targeted at reducing greenhouse gas emissions that cause global warming are expected to ensure a consistent expansion of renewable power generation in the electricity sector. With the increasing contribution of renewable sources to the overall energy supply, renewable power producers participate in electricity markets where they are imposed to make advance commitment decisions for energy delivery and purchase. Making advance commitments, however, is a complex task due to the inherent intermittency of renewable sources, increasingly volatile electricity prices, and penalties incurred for possible energy imbalances in electricity markets. Integrating renewable sources with energy storage units is among the most effective methods to address this challenging task.
Motivated by the recent trends of paired renewable energy generators and storage units, we study the energy commitment, generation and storage problem of a wind power producer who owns a battery and participates in a spot market operating with hourly commitments and settlements. In each time period, the producer decides how much energy to commit to selling to or purchasing from the market in the next time period, how much energy to generate in the wind power plant, and how much energy to charge into or discharge from the battery. The existence of the battery not only helps smooth out imbalances caused by the fluctuating wind output but also enables the producer to respond to price changes in the market. We formulate the wind power producer's problem as a Markov decision process by taking into account the uncertainties in wind speed and electricity price.
In the first part of this dissertation, we consider two different problem settings: In the first setting, the producer may choose to deviate from her commitments based on the latest available information, using the battery to support such deviations. In the second setting, the producer is required to fulfill her commitments, using the battery as a back-up source. We numerically examine the effects of system components, imbalance pricing parameters, and negative prices on the producer's profits, curtailment decisions, and imbalance tendencies in each problem setting. We provide managerial insights to renewable power producers in their assessment of energy storage adoption decisions and to power system operators in their understanding of the producers' behavior in the market with their storage capabilities.
In the second part of this dissertation, we establish several multi-dimensional structural properties of the optimal profit function such as supermodularity and joint concavity. This enables us to prove the optimality of a state-dependent threshold policy for the storage and commitment decisions under the assumptions of a perfectly efficient system and positive electricity prices. Leveraging this policy structure, we construct two heuristic solution methods for solving the more general problem in which the battery and transmission line can be imperfectly efficient and the price can also be negative. Numerical experiments with data-calibrated instances have revealed the high efficiency and scalability of our solution procedure. In the third part of this dissertation, we characterize the optimal policy structure by taking into account the battery and transmission line efficiency losses and showing the joint concavity of the optimal profit function. In the last part of this dissertation, we consider an alternative problem setting that allows for real-time trading without making any advance commitment. We analytically compare the total cash flows of this setting to those of our original problem setting. We conclude with a numerical investigation of the effect of advance commitment decisions on the producer's energy storage and generation decisions.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2023.; Includes bibliographical references (pages 120-130).
2023-05-01T00:00:00ZThree essays in the interface of optimization with mechanism design, nonexclusive competition, and prophet inequalitiesBayrak, Halil İbrahimhttps://hdl.handle.net/11693/1105282022-09-17T00:07:02Z2022-09-01T00:00:00Zdc.title: Three essays in the interface of optimization with mechanism design, nonexclusive competition, and prophet inequalities
dc.contributor.author: Bayrak, Halil İbrahim
dc.description.abstract: Mechanism Design. We consider the mechanism design problem of a principal allocating a single good to one of several agents without monetary transfers. Each agent desires the good and uses it to create value for the principal. We designate this value as the agent's private type. Even though the principal does not know the agents' types, she can verify them at a cost. The allocation of the good thus depends on the agents' self-declared types and the results of any verification performed, and the principal's payoff matches her allocation value minus the verification costs. It is known that when the agents' types are independent, a favored-agent mechanism maximizes her expected payoff. However, this result relies on the unrealistic assumptions that the agents' types follow known independent probability distributions. We assume that the agents' types are governed by an ambiguous joint probability distribution belonging to a commonly known ambiguity set and that the principal maximizes her worst-case expected payoff. We consider three types of ambiguity sets: (i) support-only ambiguity sets, which contain all distributions supported on a rectangle, (ii) Markov ambiguity sets, characterized through first-order moment bounds, and (iii) Markov with independence ambiguity sets. For each of these ambiguity sets, we show that a favored-agent mechanism, which we characterize implicitly, is optimal and also Pareto-robustly optimal. The optimal choices of the favored agent and the threshold do not depend on the verification costs in all three cases.
Nonexclusive Competition. A freelancer with a time constraint faces offers from multiple identical parties. The quality of the service provided by the freelancer can be high or low and is only known by the freelancer. The freelancer's time cost is strictly increasing and convex. We show that a pure-strategy equilibrium exists if and only if the preferences of the high-type freelancer satisfy one of the following two distinct conditions: (i) the high-type freelancer does {not} prefer providing his services for a price equal to the expected quality at the no-trade point; (ii) the high-type freelancer prefers providing his services for a price equal to the expected quality at any feasible trade point. If (i) holds, then in equilibrium, the high-type freelancer does not trade, whereas the low-type may not trade, trade efficiently, or exhaust all of his capacity. Moreover, the buyers make zero profit from each of their traded contracts. If (ii) holds, then both types of the freelancer trade at the capacity in equilibrium. Furthermore, the buyers make zero expected profit with cross-subsidization. In any equilibrium, the aggregate equilibrium trades are unique.
Prophet Inequalities. Prophet inequalities bound the expected reward obtained in a class of stopping problems by the optimal reward of the corresponding offline problem. We show how to obtain prophet inequalities for a large class of stopping problems associated with selecting a point in a polyhedron. Our approach utilizes linear programming tools and is based on a reduced form representation of the stopping problem. We illustrate the usefulness of our approach by re-establishing three different prophet inequality results from the literature. (i) For polymatroids with nonnegative coefficients in their unique Minkowski sum of simplices, we prove the 1/2-prophet inequality. (ii) We prove the 1/n-prophet inequality when there are n stages, the stages have dependently distributed rewards, and we are restricted to choosing a strategy from an arbitrary polyhedron. (iii) When the feasible set of strategies can be described via K different constraints, we obtain the 1/(K+1)-prophet inequality.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2022.; Includes bibliographical references (pages 115-119).
2022-09-01T00:00:00ZNorm minimization-based convex vector optimization algorithmsUmer, Muhammadhttps://hdl.handle.net/11693/1104862022-09-16T06:41:58Z2022-08-01T00:00:00Zdc.title: Norm minimization-based convex vector optimization algorithms
dc.contributor.author: Umer, Muhammad
dc.description.abstract: This thesis is concerned with convex vector optimization problems (CVOP). We propose an outer approximation algorithm (Algorithm 1) for solving CVOPs. In each iteration, the algorithm solves a norm-minimizing scalarization for a reference point in the objective space. The idea is inspired by some Benson-type algorithms in the literature that are based on Pascoletti-Seraﬁni scalarization. Since this scalarization needs a direction parameter, the eﬃciency of these algorithms depend on the selection of the direction parameter. In contrast, our algorithm is free of direction biasedness since it solves a scalarization that is based on minimizing a norm. However, the structure of such algorithms, including ours, has some built-in limitation which makes it diﬃcult to perform convergence analysis. To overcome this, we modify the algorithm by introducing a suitable compact subset of the upper image. After the modiﬁcation, we have Algorithm 2 in which norm-minimizing scalarizations are solved for points in the compact set. To the best of our knowledge, Algorithm 2 is the ﬁrst algorithm for CVOPs, which is proven to be ﬁnite. Finally, we propose a third algorithm for the purposes of con-vergence analysis (Algorithm 3), where a modiﬁed norm-minimizing scalarization is solved in each iteration. This scalarization includes an additional constraint which ensures that the algorithm deals with only a compact subset of the upper image from the beginning. Besides having the ﬁniteness result, Algorithm 3 is the ﬁrst CVOP algorithm with an estimate of a convergence rate. The experimental results, obtained using some benchmark test problems, show comparable performance of our algorithms with respect to an existing CVOP algorithm based on Pascoletti-Seraﬁni scalarization.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2022.; Includes bibliographical references (pages 96-102).
2022-08-01T00:00:00ZRisk-averse multi-armed bandit problemMalekipirbazari, Miladhttps://hdl.handle.net/11693/764692022-09-15T13:21:36Z2021-08-01T00:00:00Zdc.title: Risk-averse multi-armed bandit problem
dc.contributor.author: Malekipirbazari, Milad
dc.description.abstract: In classical multi-armed bandit problem, the aim is to ﬁnd a policy maximizing the expected total reward, implicitly assuming that the decision maker is risk-neutral. On the other hand, the decision makers are risk-averse in some real life applications. In this study, we design a new setting for the classical multi-armed bandit problem (MAB) based on the concept of dynamic risk measures, where the aim is to ﬁnd a policy with the best risk adjusted total discounted outcome. We provide theoretical analysis of MAB with respect to this novel setting, and propose two diﬀerent priority-index heuristics giving risk-averse allocation indices with structures similar to Gittins index. The ﬁrst proposed heuristic is based on Lagrangian duality and the indices are expressed as the Lagrangian multiplier corresponding to the activation constraint. In the second part, we present a theoretical analysis based on Whittle’s retirement problem and propose a gener-alized version of restart-in-state formulation of the Gittins index to compute the proposed risk-averse allocation indices. Finally, as a practical application of the proposed methods, we focus on optimal design of clinical trials and we apply our risk-averse MAB approach to perform risk-averse treatment allocation based on a Bayesian Bernoulli model. We evaluate the performance of our approach against other allocation rules, including ﬁxed randomization.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2021.; Includes bibliographical references (pages 97-102).
2021-08-01T00:00:00ZDeterministic and stochastic team formation problemsBerktaş, Nihalhttps://hdl.handle.net/11693/755392022-09-15T13:19:33Z2021-01-01T00:00:00Zdc.title: Deterministic and stochastic team formation problems
dc.contributor.author: Berktaş, Nihal
dc.description.abstract: In various organizations, physical or virtual teams are formed to perform jobs that require diﬀerent skills. The success of a team depends on the technical capabilities of the team members as well as the quality of communication among the team members. We study diﬀerent variants of the team formation problem where the goal is to build the best team with respect to given criteria. First, we study a deterministic team formation problem which aims to construct a capable team that can communicate and collaborate eﬀectively. To measure the quality of communication, we assume the candidates constitute a social network and we deﬁne a cost of communication using the proximity of people in the social network. We minimize the sum of all pairwise communication costs, and we impose an upper bound on the largest communication cost. This problem is formulated as a constrained quadratic set covering problem. Our experiments show that a general-purpose solver is capable of solving small and medium-sized instances to optimality. We propose a branch-and-bound algorithm to solve larger sizes: we reformulate the problem and relax it in such a way that it decomposes into a series of linear set covering problems, and we impose the relaxed constraints through branching. Our computational experiments show that the algorithm is capable of solving large-sized instances, which are intractable for the solver.
Second, we consider a two-stage stochastic team formation problem where the objective is to minimize the expected communication cost of the team. We as-sume that for a subset of pairs the communication costs are uncertain but they have a known discrete distribution. The ﬁrst stage is a trial stage where the decision-maker chooses a limited number of pairs from this subset. The actual cost values of the chosen pairs are realized before the second stage. Hence, the uncertainty in this problem is decision-dependent, also called endogenous, be-cause the ﬁrst stage decisions determine for which parameters the uncertainty will resolve. For this problem, we give two formulations, the ﬁrst one contains a set of non-anticipativity constraints similar to the models in the related lit-erature. In the second, we are able to eliminate these constraints by changing the objective function into a quadratic one, which is linearized by a set of extra binary variables. We show that the size of instances we can solve with these for-mulations using a commercial solver is limited. Therefore, we develop a Benders’ decomposition-based branch-and-cut algorithm that exploits decision-dependent nature to partition scenarios and use tight linear relaxations to obtain strong cuts. We show the eﬃciency of the algorithm presenting results of experiments conducted with randomly generated instances.
Finally, we study a multi-stage team formation problem where the objective is to minimize the monetary cost including hiring and outsourcing costs. In this problem, stages correspond to projects which are carried out consecutively. Each project consists of several tasks each of which requires a human resource. We assume that due to incomplete information there is uncertainty in people’s performances and consequently the time a person needs to complete a task is random for some person-task pairs. When a person is assigned to a task, we learn how long it takes for this person to ﬁnish the task. Hence, the uncertainty is again decision-dependent. If the duration of a task exceeds the allowable time for a project then the manager must hire an external resource to speed up the process. We present an integer programming formulation to this problem and explain that the size of the formulation strongly depends on the number of random parameters and scenarios. While this deterministic equivalent formulation can be solved with a commercial solver for small-sized instances, it easily becomes intractable when the number of random parameters increases by one. For such cases where exact methods are not promising, we investigate heuristic methods to obtain tight bounds and near-optimal solutions. In the related literature, diﬀerent Lagrangian decomposition methods are developed for such stochastic problems. In this study, we show that the convergence of existing methods is very slow, and we propose an alternative method where a relaxation of the formulation is solved by a decomposition-based branch-and-bound algorithm.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2021.; Includes bibliographical references (pages 112-124).
2021-01-01T00:00:00ZRadio communications interdiction problemTanergüçlü, Türkerhttps://hdl.handle.net/11693/533852022-09-15T13:22:39Z2020-01-01T00:00:00Zdc.title: Radio communications interdiction problem
dc.contributor.author: Tanergüçlü, Türker
dc.description.abstract: Tactical communications have always played a pivotal role in maintaining eﬀective command and control of troops operating in hostile, extremely fragile and dynamic battleﬁeld environments. Radio communications, in particular, have served as the backbone of the tactical communications over the years and have proven to be very useful in meeting the information exchange needs of widely dispersed and highly mobile military units, especially in the rugged area. Considering the complexity of today’s modern warfare, and in particular the emerging threats from the latest electronic warfare technologies, the need for optimally designed radio communications networks is more critical than ever. Optimized communication network planning can minimize network vulnerabilities to modern threats and provide additional assurance of continued availability and reliability of tactical communications. To do so, we present the Radio Communications Interdiction Problem (RCIP) to identify the optimal locations of transmitters on the battleﬁeld that will lead to a robust radio communications network by anticipating the degrading eﬀects of intentional radio jamming attacks used by an adversary during electronic warfare. We formulate RCIP as a binary bilevel (max–min) programming problem, present the equivalent single level formulation, and propose an exact solution method using a decomposition scheme. We enhance the performance of the algorithm by utilizing dominance relations, preprocessing, and initial starting heuristics. To reﬂect a more realistic jamming representation, we introduce the probabilistic version of RCIP (P-RCIP) where a jamming probability is associated at each receiver site as a function of the prevalent jamming to signal ratios leading to an expected coverage of receivers as an objective function. We approximate the nonlinearity in the jamming probability function using a piecewise linear convex function and solve this version by adapting the decomposition algorithm constructed for RCIP. Our extensive computational results on realistic scenarios that reﬂect diﬀerent phases of a military conﬂict show the eﬃcacy of the proposed solution methods. We provide valuable tactical insights by analyzing optimal solutions on these scenarios under varying parameters. Finally, we investigate the incorporation of limited artillery assets into communications planning by formulizing RCIP with Artillery (RCIP-A) as a trilevel optimization problem and propose a nested decomposition method as an exact solution methodology. Additionally, we present computational results and tactical insights obtained from the solution of RCIP-A on predeﬁned scenarios.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2020.; Includes bibliographical references (pages 100-114).
2020-01-01T00:00:00ZEssays on bilateral trade with discrete typesMohammadinezhad, Kamyar Kargarhttps://hdl.handle.net/11693/527112022-09-15T13:21:40Z2019-10-01T00:00:00Zdc.title: Essays on bilateral trade with discrete types
dc.contributor.author: Mohammadinezhad, Kamyar Kargar
dc.description.abstract: Bilateral trade is probably the most common market interaction problem and
can be considered as the simplest form of two sided markets where a seller and
a buyer bargain over an indivisible object subject to incomplete information
on the reservation values of participants. We treat this problem as a combinatorial
optimization problem and re-establish some results of economic theory
that are well-known under continuous valuations assumptions for the case of
discrete valuations using linear programming techniques.
First, we propose mathematical formulation for the problem under dominant
strategy incentive compatibility (DIC) and ex-post individual rationality
(EIR) properties. Then we derive necessary and sufficient conditions under
which ex-post efficiency can be obtained together with DIC and EIR. We also
define a new property called Allocation Maximality and prove that the Posted
Price mechanism is the only mechanism that satisfies DIC, EIR and allocation
maximality. In the final part we consider ambiguity in the problem framework
originating from different sets of priors for agents types and derive robust
counterparts.
Next, we study the bilateral trade problem with an intermediary who wants
to maximize her expected gains. Using network programming we transform
the initial linear program into one from which the structure of mechanism is
transparent. We then relax the risk-neutrality assumption of the intermediary
and consider the problem from the perspective of risk-averse intermediary. The
effects of risk-averse approach are presented using computational experiments.
Finally, we broaden the scope of the problem and discuss the case in which
the seller is also a producer at the same time and consider benefit and cost
functions for the respective parties. Starting by a non-convex optimization
problem, we obtain an equivalent convex optimization problem from which
the problem is solved easily. We also reconsider the same problem under
dominant strategy incentive compatibility and ex-post individual rationality
constraints to preserve the practicality of all obtained solutions.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2019.; Includes bibliographical references (pages 80-86).
2019-10-01T00:00:00ZOptimizing airline operations under uncertaintyAydıner, Özge Şafakhttps://hdl.handle.net/11693/520812022-09-16T06:46:15Z2019-06-01T00:00:00Zdc.title: Optimizing airline operations under uncertainty
dc.contributor.author: Aydıner, Özge Şafak
dc.description.abstract: Fluctuations in passenger demand, airport congestion, and high fuel costs are
the main threats to airlines' profit, thereby need to be carefully addressed in airline
scheduling problems. This study takes an advantage of aircraft cruise speed
control in several scheduling problems to keep the cost of fuel manageable. We
first generate a
flight schedule by integrating strategic departure time decisions,
tactical
eeting and routing decisions and more operational
flight timing decisions
under stochastic demand and non-cruise times. Our model differs from the existing
studies by including aircraft cruise speed decisions to compensate for increase
in non-cruise time variations due to the airport congestion. To e ciently solve
the problem, we provide a scenario group-wise decomposition algorithm. Then,
we consider a new problem which aims to accommodate new flights into an existing
flight schedule in a short time. We suggest some operational changes such
as controlling the aircraft cruise speed, re-timing
flight departures and swapping
aircraft to open up time for new
flights. However, nonlinear fuel cost function,
and binary assignment and swapping decisions significantly increase the computational
burden of solving scheduling problems. In this thesis, we propose strong
mixed integer conic quadratic formulations. Finally, we extend the problem by
including a strategic decision to lease an aircraft for introducing new
flights. More
importantly, we consider the effects of departure time decisions on the probability
distribution of random demand. We propose a bounding method based on scenario
group-wise decomposition for stochastic programs with decision dependent
probabilities.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2019.; Includes bibliographical references (pages 165-176).
2019-06-01T00:00:00ZNetwork design problems and value of control mechanisms in power systemsPeker Sarhan, Meltemhttps://hdl.handle.net/11693/520392022-09-16T06:46:14Z2019-05-01T00:00:00Zdc.title: Network design problems and value of control mechanisms in power systems
dc.contributor.author: Peker Sarhan, Meltem
dc.description.abstract: Power systems planning and operations is one of the most challenging problems
in energy field due to its complex, large-scale and nonlinear nature. Operating
power systems with uncertainties and disturbances such as failure of system
components increases complexity and causes difficulties in sustaining a supplydemand
balance in power systems without jeopardizing grid reliability. To handle
with the uncertainties and operate power systems without endangering grid reliability,
utilities and system operators implement various control mechanisms
such as energy storage, transmission switching, renewable energy curtailment
and demand-side management. In this thesis, we first propose a multi-period
mathematical programming model to discuss the effect of transmission switching
decisions on power systems expansion planning problems. We then explore
the value of control mechanisms for integrating renewable energy sources into
power systems. We develop a two-stage stochastic programming model that cooptimizes
investment decisions and transmission switching operations. Later, we
analyze the effect of demand-side management programs on peak load management.
We provide a conceptual framework for quantifying the incentives paid to
the consumers to reshape their load profiles while taking hourly electrical power
generation costs as reference points. Finally, we study reliability aspect of the
power system planning and consider unexpected failures of components. We provide
a two-stage stochastic programming model and discuss value of transmission
switching on grid reliability.
dc.description: Cataloged from PDF version of article.; Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2019.; Includes bibliographical references (pages 123-137).
2019-05-01T00:00:00Z