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Ryu, Jun-Hyung, Vivek Dua, and Efstratios N. Pistikopoulos. "A bilevel programming framework for enterprise-wide process networks under uncertainty." Computers & Chemical Engineering 28, no. 6-7 (2004): 1121–29. http://dx.doi.org/10.1016/j.compchemeng.2003.09.021.
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Alnowibet, Khalid A., Ahmad M. Alshamrani, and Adel F. Alrasheedi. "A Bilevel Stochastic Optimization Framework for Market-Oriented Transmission Expansion Planning Considering Market Power." Energies 16, no. 7 (2023): 3256. http://dx.doi.org/10.3390/en16073256.
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Market power, defined as the ability to raise prices above competitive levels profitably, continues to be a prime concern in the restructured electricity markets. Market power must be mitigated to improve market performance and avoid inefficient generation investment, price volatility, and overpayment in power systems. For this reason, involving market power in the transmission expansion planning (TEP) problem is essential for ensuring the efficient operation of the electricity markets. In this regard, a methodological bilevel stochastic framework for the TEP problem that explicitly includes the market power indices in the upper level is proposed, aiming to restrict the potential market power execution. A mixed-integer linear/quadratic programming (MILP/MIQP) reformulation of the stochastic bilevel model is constructed utilizing Karush−Kuhn−Tucker (KKT) conditions. Wind power and electricity demand uncertainty are incorporated using scenario-based two-stage stochastic programming. The model enables the planner to make a trade-off between the market power indices and the investment cost. Using comparable results of the IEEE 118-bus system, we show that the proposed TEP outperforms the existing models in terms of market power indices and facilitates open access to the transmission network for all market participants.
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Park, Minyoung, and Amelia Regan. "Capacity Modeling in Transportation." Transportation Research Record: Journal of the Transportation Research Board 1906, no. 1 (2005): 97–104. http://dx.doi.org/10.1177/0361198105190600112.
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A conceptual framework is presented for modeling the capacity of multimodal freight transportation networks. A review is provided on the evolution of capacity models for use in transportation systems planning and investment, and recent advances toward a system-oriented, multimodal capacity model are discussed in depth. A logical network capacity model based on bilevel programming is proposed.
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Fernandez-Blanco, Ricardo, José M. Arroyo, and Natalia Alguacil. "A Unified Bilevel Programming Framework for Price-Based Market Clearing Under Marginal Pricing." IEEE Transactions on Power Systems 27, no. 1 (2012): 517–25. http://dx.doi.org/10.1109/tpwrs.2011.2161348.
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Zang, Guangzhi, Meng Xu, and Ziyou Gao. "High-occupancy Vehicle Lanes and Tradable Credits Scheme for Traffic Congestion Management: A Bilevel Programming Approach." PROMET - Traffic&Transportation 30, no. 1 (2018): 1–10. http://dx.doi.org/10.7307/ptt.v30i1.2300.
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High-occupancy vehicle (HOV) lanes, which are designed so as to encourage more people to use high-capacity travel modes and thus move more people in a single roadway lane, have been implemented as a lane management measure to deal with the growing traffic congestion in practice. However, the implementation has shown that some HOV lanes are not able to achieve the expected effects without proper HOV lane settings. In this study, the tradable credits scheme (TCS) is introduced to improve the HOV lane management and an optimal capacity of HOV lanes in a multilane highway is investigated to match TCSs. To approach the investigation, a bilevel programming model is proposed. The upper-level represents the decision of the highway authority and the lower-level follows the commuters’ user equilibrium with deterministic demand. The potential influence of TCSs is further investigated within the proposed framework. A modified genetic algorithm is proposed to solve the bilevel programming model. Numerical examples demonstrate that combining TCSs with the HOV lane management can obviously mitigate traffic congestion.
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Chen, Hui-Ju. "A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems." Systems Science & Control Engineering 8, no. 1 (2020): 488–99. http://dx.doi.org/10.1080/21642583.2020.1805815.
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Burgard, Anthony P., Priti Pharkya, and Costas D. Maranas. "Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization." Biotechnology and Bioengineering 84, no. 6 (2003): 647–57. http://dx.doi.org/10.1002/bit.10803.
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Epshteyn, A., and G. DeJong. "Generative Prior Knowledge for Discriminative Classification." Journal of Artificial Intelligence Research 27 (September 25, 2006): 25–53. http://dx.doi.org/10.1613/jair.1934.
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We present a novel framework for integrating prior knowledge into discriminative classifiers. Our framework allows discriminative classifiers such as Support Vector Machines (SVMs) to utilize prior knowledge specified in the generative setting. The dual objective of fitting the data and respecting prior knowledge is formulated as a bilevel program, which is solved (approximately) via iterative application of second-order cone programming. To test our approach, we consider the problem of using WordNet (a semantic database of English language) to improve low-sample classification accuracy of newsgroup categorization. WordNet is viewed as an approximate, but readily available source of background knowledge, and our framework is capable of utilizing it in a flexible way.
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Yang, Xia, Chenyang Wang, Xiaozheng He, Hedi Zhang, and Guangming Xu. "Location Optimization for Community Smart Parcel Lockers Based on Bilevel Programming." Journal of Advanced Transportation 2023 (June 2, 2023): 1–18. http://dx.doi.org/10.1155/2023/1998188.
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With the rapid development of e-commerce and the dramatic upsurge in direct-to-consumer deliveries, the last-mile problem has become increasingly apparent. With the distinct advantages of bringing economies of scale and providing 24/7 contactless self-service, smart parcel lockers play a critical role in solving the last-mile problem. However, due to a lack of planning, myopia expansion, and an ambiguous profit model, smart parcel locker suppliers in China have been suffering huge economic losses, restricting their further development. In the study, on the basis of an in-depth analysis of the cost elements and major revenue sources of smart parcel lockers, we propose a bilevel programming model to optimize the location of community smart parcel lockers with the upper-level model maximizing the profit of a third-party smart parcel locker supplier and the lower-level model maximizing user satisfaction. Then, a solution algorithm based on the genetic algorithm is proposed. Finally, some numerical experiments are carried out based on a medium-scale residential community in Jiading District, Shanghai. The sensitivity analyses conducted in this study reveal how the user satisfaction evaluation and the investment budget influence the expected profit. The modelling framework and numerical results can provide third-party smart parcel locker suppliers with significant theoretical support and practical guidance on planning the investment budget and optimizing the smart parcel locker locations to maximize their profit.
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Kalashnikov, Vyacheslav V., and Roger Z. Ríos-Mercado. "A natural gas cash-out problem: A bilevel programming framework and a penalty function method." Optimization and Engineering 7, no. 4 (2006): 403–20. http://dx.doi.org/10.1007/s11081-006-0347-z.
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Baskan, Ozgur. "A Multiobjective Bilevel Programming Model for Environmentally Friendly Traffic Signal Timings." Advances in Civil Engineering 2019 (October 20, 2019): 1–13. http://dx.doi.org/10.1155/2019/1638618.
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Rapid urbanization and mobility needs of road users increase traffic congestion and delay on urban road networks. Thus, local authorities aim to reduce users’ total travel time through providing a balance between traffic volume and capacity. To do this, they optimize traffic signal timings, which is one of the most preferred methods, and thus they can increase the reserve capacity of a road network. However, more travel demand along with more reserve capacity leads to vehicle emissions problem which has become quite dangerous for road users, especially in developing countries. Therefore, this study presents a multiobjective bilevel programming model which considers both the maximization of reserve capacity of a road network and the minimization of vehicle emissions by aiming to achieve environmentally friendly signal timings. At the upper level, Pareto-optimal solutions of the proposed multiobjective model are found based on differential evolution algorithm framework by using the weighted sum method. Stochastic traffic assignment problem is presented at the lower level to evaluate the users’ reactions. Two signalized road networks are chosen to show the effectiveness of the proposed model. The first one is a small network consisting two signalized intersections that are used to show the effect of the weighting factor on the proposed multiobjective model. The other road network with 96 O-D pairs and 9 signalized intersections is chosen as the second numerical application to investigate the performance of the proposed model on relatively large road networks. It is believed that results of this study may provide useful insights to local authorities who are responsible for regulating traffic operations with environmental awareness at the same time.
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Haghighi, Yadollah, Bahman Bahmani-Firouzi, and Mehdi Nafar. "A Partnership of Virtual Power Plant in Day-Ahead Energy and Reserve Markets Based on Linearized AC Network-Constrained Unit Commitment Model." International Transactions on Electrical Energy Systems 2022 (September 6, 2022): 1–16. http://dx.doi.org/10.1155/2022/5650527.
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This paper presents coordinated energy management as a virtual power plant (VPP) framework with a wind farm, a storage system, and a demand response program in the transmission network according to the cooperation of VPPs in day-ahead energy and reserve markets. This strategy is based on a bilevel method, where it maximizes the expected VPP revenue in the proposed markets subject to constraints of renewable and flexible sources and the VPP reserve model in the upper-level problem. Also, a market-clearing model based on network-constrained unit commitment (NCUC) is explained in the lower-level problem so that it minimizes the expected operating cost of generation units constrained to a linearized AC-NCUC model. The scenario-based stochastic programming (SBSP) models the uncertainties of loads and WF power generation. Then, the master/slave decomposition method solves the bilevel problem to achieve an optimal solution at a low computational time. Also, since the lower-level problem is mixed-integer linear programming, the Benders decomposition algorithm is adopted to solve this problem. Finally, the suggested approach is implemented on IEEE test networks in GAMS software, and numerical results confirm the efficiency of the coordinated VPP management in DA energy and reserve markets and its capabilities in improving network operation.
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Zhang, Ting, Ting Qu, George Q. Huang, Xin Chen, and Zongzhong Wang. "Sizing, pricing and common replenishment in a headquarter-managed centralized distribution center." Industrial Management & Data Systems 116, no. 6 (2016): 1086–104. http://dx.doi.org/10.1108/imds-08-2015-0343.
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Purpose – Commonly shared logistics services help manufacturing companies to cut down redundant logistics investments while enhance the overall service quality. Such service-sharing mode has been naturally adopted by group companies to form the so-called headquarter-managed centralized distribution center (HQ-CDC). The HQ-CDC manages the common inventories for the group’s subsidiaries and provides shared storage services to the subsidiaries through appropriate sizing, pricing and common replenishment. Apart from seeking a global optimal solution for the whole group, the purpose of this paper is to investigate balanced solutions between the HQ-CDC and the subsidiaries. Design/methodology/approach – Two decision models are formulated. Integrated model where the group company makes all-in-one decision to determine the space allocation, price setting and the material replenishment on behalf of HQ-CDC and subsidiaries. Bilevel programming model where HQ-CDC and subsidiaries make decisions sequentially to draw a balance between their local objectives. From the perspective of result analysis, the integrated model will develop a managerial benchmark which minimizes the group company’s total cost, while the bilevel programming model could be used to measure the interactive effects between local objectives as well as their final effect on the total objective. Findings – Through comparing the numerical results of the two models, two major findings are obtained. First, the HQ-CDC’s profit is noticeably improved in the bilevel programming model as compared to the integrated model. However, the improvement of HQ-CDC’s profit triggers the cost increasing of subsidiaries. Second, the analyses of different sizing and pricing policies reveal that the implementation of the leased space leads to a more flexible space utilization in the HQ-CDC and the reduced group company’s total cost especially in face of large demand and high demand fluctuation. Research limitations/implications – Several classical game-based decision models are to be introduced to examine the more complex relationships between the HQ-CDC and the subsidiaries, such as Nash Game model or Stackelberg Game model, and more complete and meaningful managerial implications may be found through result comparison with the integrated model. The analytical solutions may be developed to achieve more accurate results, but the mathematical models may have to be with easier structure or tighter assumptions. Practical implications – The group company should take a comprehensive consideration on both cost and profit before choosing the decision framework and the coordination strategy. HQ-CDC prefers a more flexible space usage strategy to avoid idle space and to increase the space utilization. The subsidiaries with high demand uncertainties should burden a part of cost to induce the subsidiaries with steady demands to coordinate. Tanshipments should be encouraged in HQ-CDC to reduce the aggregate inventory level as well as to maintain the customer service level. Social implications – The proposed decision frameworks and warehousing policies provide guidance for the managers in group companies to choose the proper policy and for the subsidiaries to better coordinate. Originality/value – This research studies the services sharing on the warehouse sizing, pricing and common replenishment in a HQ-CDC. The interactive decisions between the HQ-CDC and the subsidiaries are formulated in a bilevel programming model and then analyzed under various practical scenarios.
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Yue, Dajun, and Fengqi You. "Stackelberg-game-based modeling and optimization for supply chain design and operations: A mixed integer bilevel programming framework." Computers & Chemical Engineering 102 (July 2017): 81–95. http://dx.doi.org/10.1016/j.compchemeng.2016.07.026.
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Zou, Yuan, Dong-ge Li, and Xiao-song Hu. "Optimal Sizing and Control Strategy Design for Heavy Hybrid Electric Truck." Mathematical Problems in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/404073.
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Due to the complexity of the hybrid powertrain, the control is highly involved to improve the collaborations of the different components. For the specific powertrain, the components' sizing just gives the possibility to propel the vehicle and the control will realize the function of the propulsion. Definitely the components' sizing also gives the constraints to the control design, which cause a close coupling between the sizing and control strategy design. This paper presents a parametric study focused on sizing of the powertrain components and optimization of the power split between the engine and electric motor for minimizing the fuel consumption. A framework is put forward to accomplish the optimal sizing and control design for a heavy parallel pre-AMT hybrid truck under the natural driving schedule. The iterative plant-controller combined optimization methodology is adopted to optimize the key parameters of the plant and control strategy simultaneously. A scalable powertrain model based on a bilevel optimization framework is built. Dynamic programming is applied to find the optimal control in the inner loop with a prescribed cycle. The parameters are optimized in the outer loop. The results are analysed and the optimal sizing and control strategy are achieved simultaneously.
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Tawfik, Christine, and Sabine Limbourg. "Pricing Problems in Intermodal Freight Transport: Research Overview and Prospects." Sustainability 10, no. 9 (2018): 3341. http://dx.doi.org/10.3390/su10093341.
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The aim of this paper is to consider the topic of pricing decisions in the context of intermodal transport as a subject of significant influence on intermodality’s success and the move towards environment friendly modes to bring about a European sustainable transport system. We review the state of research in intermodal pricing from an Operational Research (OR) perspective as a subject with a vital link to energy consumption and sustainability assessment. In particular, we study freight transport within a revenue-maximizing perspective. Driven by the political incentives to enhance its challenged market position, we direct our discussion to the particular gap in optimization approaches that tackle service prices as explicit tactical decisions from the carriers’ point of view. A suggestion to utilize the bilevel programming framework in the present context is put forward, as well as an account of its widely successful application to similar hierarchical decision schemes. Different approaches to express the shippers’ behaviour—the potential intermodal transport customers—within the lower level problem are proposed, along with the modelling implications of different possible objectives as well as the multimodal network structures.
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Zhang, Kaike, Xueping Li, and Mingzhou Jin. "Efficient Solution Methods for a General r-Interdiction Median Problem with Fortification." INFORMS Journal on Computing 34, no. 2 (2022): 1272–90. http://dx.doi.org/10.1287/ijoc.2021.1111.
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This study generalizes the r-interdiction median (RIM) problem with fortification to simultaneously consider two types of risks: probabilistic exogenous disruptions and endogenous disruptions caused by intentional attacks. We develop a bilevel programming model that includes a lower-level interdiction problem and a higher-level fortification problem to hedge against such risks. We then prove that the interdiction problem is supermodular and subsequently adopt the cuts associated with supermodularity to develop an efficient cutting-plane algorithm to achieve exact solutions. For the fortification problem, we adopt the logic-based Benders decomposition (LBBD) framework to take advantage of the two-level structure and the property that a facility should not be fortified if it is not attacked at the lower level. Numerical experiments show that the cutting-plane algorithm is more efficient than benchmark methods in the literature, especially when the problem size grows. Specifically, with regard to the solution quality, LBBD outperforms the greedy algorithm in the literature with an up-to 13.2% improvement in the total cost, and it is as good as or better than the tree-search implicit enumeration method. Summary of Contribution: This paper studies an r-interdiction median problem with fortification (RIMF) in a supply chain network that simultaneously considers two types of disruption risks: random disruptions that occur probabilistically and disruptions caused by intentional attacks. The problem is to determine the allocation of limited facility fortification resources to an existing network. It is modeled as a bilevel programming model combining a defender’s problem and an attacker’s problem, which generalizes the r-interdiction median problem with probabilistic fortification. This paper is suitable for IJOC in mainly two aspects: (1) The lower-level attacker’s interdiction problem is a challenging high-degree nonlinear model. In the literature, only a total enumeration method has been applied to solve a special case of this problem. By exploring the special structural property of the problem, namely, the supermodularity of the transportation cost function, we developed an exact cutting-plane method to solve the problem to its optimality. Extensive numerical studies were conducted. Hence, this paper fits in the intersection of operations research and computing. (2) We developed an efficient logic-based Benders decomposition algorithm to solve the higher-level defender’s fortification problem. Overall, this study generalizes several important problems in the literature, such as RIM, RIMF, and RIMF with probabilistic fortification (RIMF-p).
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Gao, Jiyao, and Fengqi You. "Economic and Environmental Life Cycle Optimization of Noncooperative Supply Chains and Product Systems: Modeling Framework, Mixed-Integer Bilevel Fractional Programming Algorithm, and Shale Gas Application." ACS Sustainable Chemistry & Engineering 5, no. 4 (2017): 3362–81. http://dx.doi.org/10.1021/acssuschemeng.7b00002.
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Chen, Lili, Zhen Wang, Fenghua Li, Yunchuan Guo, and Kui Geng. "A Stackelberg Security Game for Adversarial Outbreak Detection in the Internet of Things." Sensors 20, no. 3 (2020): 804. http://dx.doi.org/10.3390/s20030804.
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With limited computing resources and a lack of physical lines of defense, the Internet of Things (IoT) has become a focus of cyberattacks. In recent years, outbreak propagation attacks against the IoT have occurred frequently, and these attacks are often strategical. In order to detect the outbreak propagation as soon as possible, t embedded Intrusion Detection Systems (IDSs) are widely deployed in the IoT. This paper tackles the problem of outbreak detection in adversarial environment in the IoT. A dynamic scheduling strategy based on specific IDSs monitoring of IoT devices is proposed to avoid strategic attacks. Firstly, we formulate the interaction between the defender and attacker as a Stackelberg game in which the defender first chooses a set of device nodes to activate, and then the attacker selects one seed (one device node) to spread the worms. This yields an extremely complex bilevel optimization problem. Our approach is to build a modified Column Generation framework for computing the optimal strategy effectively. The optimal response of the defender’s problem is expressed as mixed-integer linear programming (MILPs). It is proved that the solution of the defender’s optimal response is a NP-hard problem. Moreover, the optimal response of defenders is improved by an approximate algorithm--a greedy algorithm. Finally, the proposed scheme is tested on some randomly generated instances. The experimental results show that the scheme is effective for monitoring optimal scheduling.
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Alesiani, Francesco. "Implicit Bilevel Optimization: Differentiating through Bilevel Optimization Programming." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 12 (2023): 14683–91. http://dx.doi.org/10.1609/aaai.v37i12.26716.
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Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential objective for the Machine Learning community. Previously proposed approaches only consider single-level programming. In this paper, we extend existing single-level optimization programming approaches and thus propose Differentiating through Bilevel Optimization Programming (BiGrad) for end-to-end learning of models that use Bilevel Programming as a layer. BiGrad has wide applicability and can be used in modern machine learning frameworks. BiGrad is applicable to both continuous and combinatorial Bilevel optimization problems. We describe a class of gradient estimators for the combinatorial case which reduces the requirements in terms of computation complexity; for the case of the continuous variable, the gradient computation takes advantage of the push-back approach (i.e. vector-jacobian product) for an efficient implementation. Experiments show that the BiGrad successfully extends existing single-level approaches to Bilevel Programming.
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Borrero, Juan S., Oleg A. Prokopyev, and Denis Sauré. "Learning in Sequential Bilevel Linear Programming." INFORMS Journal on Optimization, January 27, 2022. http://dx.doi.org/10.1287/ijoo.2021.0063.
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We consider a framework for sequential bilevel linear programming in which a leader and a follower interact over multiple time periods. In each period, the follower observes the actions taken by the leader and reacts optimally, according to the follower’s own objective function, which is initially unknown to the leader. By observing various forms of information feedback from the follower’s actions, the leader is able to refine the leader’s knowledge about the follower’s objective function and, hence, adjust the leader’s actions at subsequent time periods, which ought to help in maximizing the leader’s cumulative benefit. We show that greedy and robust policies adapted from previous work in the max-min (symmetric) setting might fail to recover the optimal full-information solution to the problem (i.e., a solution implemented by an oracle with complete prior knowledge of the follower’s objective function) in the asymmetric case. In contrast, we present a family of greedy and best-case policies that are able to recover the full-information optimal solution and also provide real-time certificates of optimality. In addition, we show that the proposed policies can be computed by solving a series of linear mixed-integer programs. We test policy performance through exhaustive numerical experiments in the context of asymmetric shortest path interdiction, considering various forms of feedback and several benchmark policies.
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Khorramfar, Rahman, Osman Y. Özaltın, Karl G. Kempf, and Reha Uzsoy. "Managing Product Transitions: A Bilevel Programming Approach." INFORMS Journal on Computing, June 30, 2022. http://dx.doi.org/10.1287/ijoc.2022.1210.
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We model the hierarchical and decentralized nature of product transitions using a mixed-integer bilevel program with two followers, a manufacturing unit and an engineering unit. The leader, corporate management, seeks to maximize revenue over a finite planning horizon. The manufacturing unit uses factory capacity to satisfy the demand for current products. The demand for new products, however, cannot be fulfilled until the engineering unit completes their development, which, in turn, requires factory capacity for prototype fabrication. We model this interdependency between the engineering and manufacturing units as a generalized Nash equilibrium game at the lower level of the proposed bilevel model. We present a reformulation where the interdependency between the followers is resolved through the leader’s coordination, and we derive a solution method based on constraint and column generation. Our computational experiments show that the proposed approach can solve realistic instances to optimality in a reasonable time. We provide managerial insights into how the allocation of decision authority between corporate leadership and functional units affects the objective function performance. This paper presents the first exact solution algorithm to mixed-integer bilevel programs with interdependent followers, providing a flexible framework to study decentralized, hierarchical decision-making problems.
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Nisha, Tarannum, Duong Tung Nguyen, and Vijay K. Bhargava. "A Bilevel Programming Framework for Joint Edge Resource Management and Pricing." IEEE Internet of Things Journal, 2022, 1. http://dx.doi.org/10.1109/jiot.2022.3152139.
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Kozanidis, George, and Eftychia Kostarelou. "An Exact Solution Algorithm for Integer Bilevel Programming with Application in Energy Market Optimization." Journal of Optimization Theory and Applications, March 20, 2023. http://dx.doi.org/10.1007/s10957-023-02166-8.
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AbstractWe develop an exact cutting plane solution algorithm for a special class of bilevel programming models utilized for optimal price-bidding of energy producers in day-ahead electricity markets. The proposed methodology utilizes a suitable reformulation in which a key prerequisite for global optimality, termed bilevel feasibility, is relaxed. Solving the problem to global optimality involves finding the price-offers of the strategic producer (upper-level decision variables) which maximize his self-profit upon clearing of the market and identification of the optimal energy quantity distribution (lower-level decision variables). To exclude from consideration the encountered bilevel infeasible solutions, the algorithm employs a special type of valid cuts drawn from the theory of integer parametric programming. The generation of these cuts involves finding the truly optimal lower-level solution using the strategic price-offers at the bilevel infeasible solution subject to exclusion and devising range intervals for these offers such that the optimality of this solution is retained when each of them lies in its corresponding interval. Each cut imposes a suitable part of this solution, under the condition that each price-offer belongs to its associated interval, which renders the bilevel infeasible solution invalid. We establish the theoretical framework for the development of the proposed algorithm, we illustrate its application on a small case study, and we present extensive computational results demonstrating its behavior and performance on random problem instances. These results indicate that the algorithm is capable of solving to global optimality considerably larger problems than those that a previous elementary version of the same algorithm could solve. This constitutes significant research contribution, considering the lack of generic optimization software for bilevel programming, as well as the fact that the applicability of specialized algorithms on problems of realistic size is rather limited.
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Cesarone, Francesco, Lorenzo Lampariello, Davide Merolla, Jacopo Maria Ricci, Simone Sagratella, and Valerio Giuseppe Sasso. "A bilevel approach to ESG multi-portfolio selection." Computational Management Science 20, no. 1 (2023). http://dx.doi.org/10.1007/s10287-023-00458-y.
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AbstractWe rely on bilevel programming to model the problem of financial service providers that, in order to meet stakeholders’ demands and regulatory requirements, aim at incentivizing accounts’ holders to construct ESG-oriented portfolios so that the overall ESG impact of the firm is optimized, while the preferences of accounts’ owners are still satisfied. We analyze this complicated framework from a theoretical point of view and identify sufficient conditions that make it numerically tractable via a novel, specifically tailored algorithm, whose convergence properties are studied. Numerical testing on real-world data confirms the theoretical insights and shows that our model can be solved even when dealing with considerable problem sizes.
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Goyal, Akshit, Yiling Zhang, and Chuan He. "Decision Rule Approaches for Pessimistic Bilevel Linear Programs Under Moment Ambiguity with Facility Location Applications." INFORMS Journal on Computing, July 10, 2023. http://dx.doi.org/10.1287/ijoc.2022.0168.
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We study a pessimistic stochastic bilevel program in the context of sequential two-player games, where the leader makes a binary here-and-now decision, and the follower responds with a continuous wait-and-see decision after observing the leader’s action and revelation of uncertainty. We assume that only the information regarding the mean, covariance, and support is known. We formulate the problem as a distributionally robust (DR) two-stage problem. The pessimistic DR bilevel program is shown to be equivalent to a generic two-stage distributionally robust stochastic (nonlinear) program with both a random objective and random constraints under proper conditions of ambiguity sets. Under continuous distributions, using linear decision rule approaches, we construct upper bounds on the pessimistic DR bilevel program based on (1) a 0-1 semidefinite programming (SDP) approximation and (2) an exact 0-1 copositive programming reformulation. When the ambiguity set is restricted to discrete distributions, an exact 0-1 SDP reformulation is developed, and explicit construction of the worst-case distribution is derived. To further improve the computation of the proposed 0-1 SDPs, a cutting-plane framework is developed. Moreover, based on a mixed-integer linear programming approximation, another cutting-plane algorithm is proposed. Extensive numerical studies are conducted to demonstrate the effectiveness of the proposed approaches on a facility location problem. History: Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0168 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0168 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
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Biswas, Arpan, Yong Chen, Nathan Gibson, and Christopher Hoyle. "Bilevel Flexible-Robust Optimization for Energy Allocation Problems." ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg 6, no. 3 (2020). http://dx.doi.org/10.1115/1.4046269.
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Abstract A common issue in energy allocation problems is managing the tradeoff between selling surplus energy to maximize short-term revenue, versus holding surplus energy to hedge against future shortfalls. For energy allocation problems, this surplus represents resource flexibility. The decision maker has an option to sell or hold the flexibility for future use. As a decision in the current period can affect future decisions significantly, future risk evaluation of uncertainties is recommended for the current decision in which a traditional robust optimization is not efficient. Therefore, an approach to flexible-robust optimization has been formulated by integrating a real options (RO) model with the robust optimization framework. In the energy problem, the real option model evaluates the future risk, and provides the value of holding flexibility, whereas the robust optimization quantifies uncertainty and provides a robust solution of net revenue by selling flexibility. This problem is solved using bilevel programming and a complete general mathematical formulation of bilevel flexible-robust optimization model is presented for multireservoir systems and results shown to provide an efficient decision making process in energy sectors. To reduce the computational expense, mathematical techniques have been used in the proposed model to reduce the dimension in the quantification and propagation of uncertainties.
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Garcia, Daniel J., Mojtaba Mozaffar, Huaqing Ren, et al. "Sustainable Manufacturing With Cyber-Physical Discrete Manufacturing Networks: Overview and Modeling Framework." Journal of Manufacturing Science and Engineering 141, no. 2 (2018). http://dx.doi.org/10.1115/1.4041833.
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Cyber-physical systems (CPS) enable unprecedented communication between product designers and manufacturers. Effective use of these technologies both enables and requires a new paradigm of methods and models to identify the most profitable and environmentally friendly production plans for a manufacturing network. The operating system for cyber-physical manufacturing (OSCM) and the paired network operations administration and monitoring (NOAM) software are introduced. These technologies guide our development of a mixed integer bilevel programming (BP) model that models the hierarchy between designers and manufacturers as a Stackelberg game while considering multiple objectives for each of them. Designers select and pay manufacturers, while manufacturers decide how to execute the order with the payment provided by the designer. To solve the model, a tailored solution method combining a decomposition-based approach with approximation of the lower level Pareto-optimal solution set is proposed. The model is applied to a case study based on a network of manufacturers in Wisconsin and Illinois. With the proposed model, designers and manufacturers alike can take full advantage of CPS to increase profits and decrease environmental impacts.
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Tanınmış, Kübra, and Markus Sinnl. "A Branch-and-Cut Algorithm for Submodular Interdiction Games." INFORMS Journal on Computing, May 12, 2022. http://dx.doi.org/10.1287/ijoc.2022.1196.
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Many relevant applications from diverse areas such as marketing, wildlife conservation, and defending critical infrastructure can be modeled as interdiction games. In this work, we introduce interdiction games whose objective is a monotone and submodular set function. Given a ground set of items, the leader interdicts the usage of some of the items of the follower in order to minimize the objective value achievable by the follower, who seeks to maximize a submodular set function over the uninterdicted items subject to knapsack constraints. We propose an exact branch-and-cut algorithm for this kind of interdiction game. The algorithm is based on interdiction cuts, which allow the leader to capture the follower’s objective function value for a given interdiction decision of the leader and exploit the submodularity of the objective function. We also present extensions and liftings of these cuts and discuss additional preprocessing procedures. We test our solution framework on the weighted maximal covering interdiction game and the bipartite inference interdiction game. For both applications, the improved variants of our interdiction cut perform significantly better than the basic version. For the weighted maximal covering interdiction game for which a mixed-integer bilevel linear programming (MIBLP) formulation is available, we compare the results with those of a state-of-the-art MIBLP solver. Whereas the MIBLP solver yields a minimum of 54% optimality gap within one hour, our best branch-and-cut setting solves all but four of 108 instances to optimality with a maximum of 3% gap among unsolved ones.
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Lin, Shi-Woei, and Januardi Januardi. "Willingness-to-pay experimental model for Stackelberg dual channel pricing decision." International Journal of Retail & Distribution Management, September 27, 2022. http://dx.doi.org/10.1108/ijrdm-10-2021-0495.
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PurposeThis study proposes and demonstrates a novel approach to analyzing customer channel preferences and willingness-to-pay (WTP) in the dual sales channel (DSC) system involving direct online channels and conventional offline retailers, and to how the pricing decisions are made under specific game competition.Design/methodology/approachQuestionnaire survey based on central composite experiment design was utilized to obtain primary data. The model for customer channel preferences and WTP was then built by using multinomial logistic regression. The propensity of a customer to make purchases in either channel estimated by using the logit model was inserted in the bilevel programming model to formulate and solve for the Stackelberg competition where the conventional retailer acted as a leader.FindingsThe study found that channel prices have nonlinear impacts on WTP and channel preference. The empirical results complement the mathematical formulation well where high-order own-price and cross-price effects on channel selection are generally not analytical tractable. Under the Stackelberg competition, the traditional retailer (as the leader) still achieves higher profits than the online facility.Practical implicationsThe proposed framework provides an empirical approach that can easily address the competition model in the sales channel when complicated own-price or cross-price effects are present.Originality/valueThe present work provides a novel approach to analyze customer preference and WTP of the DSC systems. This alternative method simplifies the procedure for investigating and estimating price sensitivity, especially when the online and offline prices affect customer WTP and channel preferences nonlinearly. This model is also utilized in the game competition to facilitate data-driven price decision making to better formulate and understand real-world DSC problems.