Bi-level Programming Approach Research Articles

A bilevel programming approach to price decoupling in Pay-as-Clear markets, with application to day-ahead electricity markets

Motivated by the recent crisis of the European electricity markets, we propose the concept of Segmented Pay-as-Clear (SPaC) market, introducing a new family of market clearing problems that achieve a degree of decoupling between groups of participants. This requires a relatively straightforward modification of the standard PaC model and retains its crucial features by providing both long- and short-term sound price signals. The approach is based on dynamically partitioning demand across the segmented markets, where the partitioning is endogenous, i.e., controlled by the model variables, and is chosen to minimise the total system cost. The thusly modified model leads to solving Bilevel Programming problems, or more generally Mathematical Programs with Complementarity Constraints; these have a higher computational complexity than those corresponding to the standard PaC, but in the same ballpark as the models routinely used in real-world Day Ahead Markets (DAMs) to represent “nonstandard” requirements, e.g., the unique buying price in the Italian DAM. Thus, SPaC models should still be solvable in a time compatible with market operation with appropriate algorithmic tools. Like all market models, SPaC is not immune to strategic bidding techniques, but some theoretical results indicate that, under the right conditions, the effect of these could be limited. An initial experimental analysis of the proposed models, carried out through Agent Based simulations, seems to indicate a good potential for significant system cost reductions and an effective decoupling of the two markets.

A robust, resilience and risk-aware solar energy farm location by bi-level programming approach

A robust, resilience and risk-aware solar energy farm location by bi-level programming approach

Optimal capacity configuration and dynamic pricing strategy of a shared hybrid hydrogen energy storage system for integrated energy system alliance: A bi-level programming approach

The shared energy storage system is recognized as a promising business model for the coordinated operation of integrated energy systems (IES) to improve the utilization of energy storage and the consumption of renewable energy. As the hydrogen energy gradually receives more attention, this paper constructs the structure of a hybrid hydrogen energy storage system shared by an IES alliance in a dynamic pricing mode. A bi-level optimization model for the shared hybrid hydrogen energy storage system (SHHESS) is proposed to optimize the capacity configuration decisions and the pricing strategy jointly. The upper level determines the capacity and dynamic price of SHHESS with maximum profits and the lower level obtains the optimal operation of the IES alliance minimizing the total operation costs. The proposed model is solved by an improved PSO-GA algorithm and CPLEX solver. Finally, numerical tests are conducted in different scenarios. The results show that the hybrid energy storage system improves the daily profits of SHHESS by 70.3% and 5.44%, and reduces the renewable energy curtailment by 80.93% and 48.92% respectively compared to the battery-only and hydrogen-only systems. Additionally, the daily operation cost of the IES alliance is 35.2% lower than the individual operation scenario. The proposed model confirms the feasibility and superiority of the hybrid hydrogen energy storage system in a sharing business mode.

A quadratic-linear bilevel programming approach to green supply chain management

Green Supply Chain Management requires coordinated decisions between the strategic and operational organization layers to address strict green goals. Furthermore, linking CO2 emissions to supply chain operations is not always easy. This study proposes a new mathematical model to minimize CO2 emissions in a three-layered supply chain. The model foresees using a financial budget to mitigate emissions contributions and optimize supply chain operations planning. The three-stage supply chain analyzed has inbound logistics and handling operations at the intermediate level. We assume that these operations contribute to emissions quadratically. The resulting bilevel programming problem is solved by transforming it into a nonlinear mixed-integer program by applying the Karush-Kuhn-Tucker conditions. We show, on different sets of synthetic data and on a case study, how our proposal produces solutions with a different flow of goods than a modified linear model version. This results in lower CO2 emissions and more efficient budget expenditure.

Determining an Optimal Government Subsidy Scheme for Shared Parking Management via a Bi-Level Programming Approach

A bi-level programming model is formulated to determine a government subsidy scheme for shared parking management. The government, as the upper-level decision-maker, seeks to maximize the social benefit by providing subsidy to the shared parking platform, incentivizing the platform to rent more shared parking slots, which can increase the utilization rate of idle parking slots and reduce the curbside parking cruising time of parking demanders. At the lower-level formulation, the shared parking platform, as a reseller, not only matches shared parking slot demanders but also determines which shared parking slots to rent, which is approached by a two-sided decision-making process. A “one-to-many” matching principle is adopted for the platform to maximize its revenue. A modified genetic algorithm is designed to solve the proposed model. Results indicate that the government subsidy has a positive impact on stimulating the shared parking market. Specifically, from the perspective of the government, the subsidy can increase the number of matched shared parking demanders, improve the supply of parking slots, and reduce curbside parking cruising time. From the perspective of the shared parking platform, the subsidy can lead to higher revenue.

A Bi-Level Programming Approach to Optimize Ship Fouling Cleaning

Ship fouling has significant adverse effects on vessel performance and environmental sustainability. Therefore, this research study develops a bi-level programming model to simultaneously optimize cleaning equipment deployment by cleaning service providers in the upper level and cleaning decisions by shipping companies in the lower level. To address the interaction within the bi-level problem, the model is transformed into a single-level formulation using the big-M method. This transformation greatly simplifies the complexity of the computation and reduces computation time. Numerical experiments are conducted using real-world data to evaluate the performance of the proposed models. In addition, sensitivity analyses are performed to investigate the influence of key parameters. The results indicate that cleaning service providers primarily purchase equipment in the first year based on the demand distribution. To maximize profit, they may choose to forgo a portion of the demand. The sensitivity analysis reveals that sacrificing part of the demand can lead to an additional USD 27 million in profits compared with satisfying all demand. Moreover, increasing the cleaning price reduces both demand and equipment purchases but increases total profits. Conversely, increasing purchase costs reduces profits and the total amount of equipment purchased. When service providers can no longer generate profits, they are likely to exit the market. These findings offer valuable insights for service providers and shipping companies in the practical deployment of cleaning equipment and foul cleaning decisions, respectively.

An efficient system of incentivizing truck drivers to accept night loads

ABSTRACT Night deliveries are increasingly used by motor carriers to cut costs, but many carriers struggle to secure night truck drivers because many drivers dislike night driving. Monetary incentives are offered to drivers to accept night loads, but the incentive system currently used in practice is inefficient, as it not only pays more incentives than necessary but also does not incentivize the right drivers, both of which increase costs. This paper develops a new incentive system that allows carriers to secure night drivers at lower costs. Based on the interviews conducted with seven motor carriers, as well as the analysis of large night delivery data, we propose a bi-level programming approach that (1) generates a unique incentive for each driver based on his/her night driving performance, and (2) implicitly aligns the incentive paid to each driver with his/her reservation price. Simulation experiments conducted with real-world data showed that by using our approach carriers can not only avoid over-incentivizing drivers, but also (1) incentive only the right set of drivers who can bring cost savings and (2) encourage other drivers to improve night driving. Results also showed that our approach may give cost savings of up to 2.5% over the current system.

Integrating wind energy and compressed air energy storage for remote communities: A bi-level programming approach

The integration of compressed air energy storage and wind energy offers an attractive energy solution for remote areas with limited access to reliable and affordable energy sources. This study presents a design approach for an energy system comprising wind turbines, compressed air energy storage, and diesel generators. The proposed method is based on bi-level programming, enabling the simultaneous optimization of the size and operation of the system while considering the interaction between them. Detailed mechanical design and configuration of the compressed air energy storage system are considered, including the number and size of compressors and turbines, valves, recuperator operating conditions, etc. In contrast with conventional compressed air energy storage systems, operating once a day for peak shaving, the proposed compressed air energy storage system aims to mitigate wind fluctuations. Therefore, it would operate under partial load conditions most of the time, and as a result, the system's off-design modeling is also considered. The results indicate that the proposed system is a promising, cost-effective, reliable energy solution for remote areas, significantly decreasing the average daily total cost and CO2 emissions by 69 % and 76 %, respectively. Additionally, by studying the system's performance under both design and off-design conditions, it is concluded that considering the off-design conditions is critical to ensure a more realistic performance of the system as the system is less likely to utilize the compressed air energy storage in low charging and discharging opportunities.

Setting closer targets based on non-dominated convex combinations of Pareto-efficient units: A bi-level linear programming approach in Data Envelopment Analysis

Data Envelopment Analysis (DEA) very often sets unrealistic targets, which require from the decision-making units (DMUs) a huge amount effort, perhaps non-assumable, for their achievement. For the identification of best practices in the benchmarking, this paper proposes considering as peers not only DEA efficient DMUs but also those that are Pareto efficient, and allowing for reference sets spanning convex combinations that are not dominated by observed DMUs. It is therefore an approach that somehow relaxes the convexity in DEA, and sets targets representing best practices in the sense that they define a course of action leading to results that are not worse than those of the real plans. A bi-level linear programming (BLP) DEA model is developed which finds the closest targets from a convex combination of the DMUs in a reference set satisfying such non-dominance requirement. This approach has proven to be successful in setting targets that require an effort significantly smaller than that needed to achieve the closest targets on the strong efficient frontier of both the DEA and the free disposal hull (FDH) technologies. In the empirical illustration, we have observed reductions in the order of 40 percentage points on average in the total effort required for their achievement, thus setting more realistically implementable directions for improving performance towards best practices than those provided by conventional DEA and FDH.

Optimal trauma care network redesign with government subsidy: A bilevel integer programming approach

Trauma presents a prominent health problem worldwide. However, trauma centers are often clustered in urban areas and sparsely located in rural areas. The geographic maldistribution of trauma centers leads to system-related mistriage errors. While some local governments offer subsidy to incentivize the affiliated hospital group to redesign the trauma care network, the approach is ad hoc. To address this issue, we propose a bilevel integer programming model to investigate the subsidized trauma care network redesign problem, which considers the government as the leader and the hospital group as the follower. To solve the resultant problem efficiently, we propose a branching idea to exclude additional infeasible solutions and suboptimal solutions, in turn speeding up the branch-and-bound algorithm. In a case study, we redesign a trauma care network in the midwestern area of the U.S. based on closed-form approximate functions of system-related mistriage errors. The results show that the optimal network redesign redistributes the network by slightly reducing the number of trauma centers to relieve the crowded trauma care resource, and achieves an overall improvement of about 11% over the original network.

Correction to: an efficient environmentally friendly transportation network design via dry ports: a bi-level programming approach

Correction to: an efficient environmentally friendly transportation network design via dry ports: a bi-level programming approach

Interactive Allocation of Water Pollutant Initial Emission Rights in a Basin under Total Amount Control: A Leader-Follower Hierarchical Decision Model.

The initial emission rights allocation is the key measure to achieve the goal of total amount control and deepen the emission trading system. Although many studies have focused on the modeling of initial emission rights allocation, such as using game theory and multi-objective optimization methods, few studies have observed the hierarchical relationship of mutual interference and restriction between watershed management agency and local governments in each subarea during allocation. This relationship directly affects the rationality of the results of regional emission rights allocation. In this study, a leader-follower hierarchical decision model (LFHDM) for allocating initial emission rights in a basin is developed. Based on the bilevel programming approach, the model simulates the interactive decision-making process between the watershed management agency of the upper-level model (LFHDM-U) and the local government of the lower-level model (LFHDM-L) in the allocation under total amount control. A case study of China's Yellow River Basin is conducted to demonstrate the feasibility and practicality of the model. Findings reveal that, compared with the single-level model, the developed LFHDM has higher satisfaction with the allocation scheme. Under different scenarios, the overall satisfaction of the configuration schemes of COD and NH3-N in each province and autonomous region remains above 0.9. In addition, the allocation volumes of COD and NH3-N in each province of the Yellow River Basin in planning year increase with the enhancement of allowable assimilative capacity of water bodies, but the interval gap of satisfaction with allocation schemes gradually narrows. It shows that when the allowable assimilation capacity of a water body is low, the decision-making of the allocation scheme needs to be more cautious. Moreover, for the Yellow River Basin, apart from Qinghai and Sichuan, the task of reducing water pollutants in other provinces in the next few years is very arduous. The average reduction of total COD and NH3-N in the basin is about 48% and 46%, respectively.

Optimizing inland port scale and function decisions: A bilevel programming approach

With the implementation of the Belt and Road Initiative, the inland ports planning is receiving more and more attention. In this work, we aim to determine the scale and function of different potential inland ports in a certain region while considering the cargo flow allocation schemes for the inland ports and seaports in cross-border trade. Unlike previous studies, we consider the dynamic interaction between local government and manufacturing enterprises in the inland port planning process. Based on this, we formulate a bilevel programming model for the considered inland port planning problem, where the upper-level focuses on the local government and the lower-level concentrates on the manufacturing enterprise. To solve the proposed model, we develop a hybrid heuristic algorithm by combining a genetic algorithm and an exact solution method. Furthermore, we conduct a case study of the inland ports planning for the Huaihai Economic Zone in China to verify the applicability of the proposed model and algorithm. The computational results demonstrate that the proposed optimization approach can effectively increase the cross-border transportation market share of inland ports within a limited investment amount and reduce the competition among these inland ports. Our case study also provides valuable management insights on inland port planning in terms of manufacturing enterprises weights, investment limit amount, scale effect, and cargo value weights.

Analyzing the Vulnerabilities in a Transshipment Network: A Bilevel Programming Approach

As one of the most common types of networks, transshipment networks face certain risks in their daily operations. This risk either stems from a deliberate intervention in the process or from an unpredictable natural effect. The owner of the network normally aims to minimize the total cost of the transportation, while a rival or an opponent might attempt to intervene in the process and cause an increase in the costs. Unpredictable natural setbacks, on the other hand, can also have a negative impact on the network necessitating decision-makers to be more vigilant, especially for the worst-case consequences of network disruptions. The problem can be designed as a bilevel mathematical model. In this study, we develop a bilevel max-min model considering that the arcs in a transshipment network are liable to a disruption imposed by an intervenor. We present an original model with a novel solution approach to identify vulnerabilities in the arcs of a given transshipment network. The results reveal the most vulnerable arcs in the network, which have the highest negative impact on transportation costs when a disruption occurs. The decision-makers can use such results to analyze the risk in distribution networks such as electrical grids and develop associated measures to decrease the cost and increase the flexibility of the distribution systems. The model also enables decision makers with a methodical understanding of worst cases if the distribution network is interrupted for some reason.

An efficient environmentally friendly transportation network design via dry ports: a bi-level programming approach

An efficient environmentally friendly transportation network design via dry ports: a bi-level programming approach

Bilevel programming approach for the quantitative analysis of renewable portfolio standards considering the electricity market

Many countries have introduced renewable portfolio standard (RPS) with market systems that allow transactions of renewable energy certificates (RECs) to foster investment in renewable energy (RE). The main objective of this study is to estimate long-term REC prices based on marginal-cost pricing and analyze the RPS system quantitatively. In the proposed method, a mathematical model is constructed as bilevel programming that considers the REC and electricity markets simultaneously, and the KKT conditions are used to solve the nonlinearity of the constructed model. The proposed method has the following advantages: (1) it determines the optimal capacity of RE to implement the RPS system, (2) it derives the long-term marginal cost of the REC market, and (3) it can be used to perform quantitative analyses of the RPS system. Simulation studies were performed in South Korea, and the results indicated that solar photovoltaic accounted for a major portion of the new investment. The marginal cost of the REC market and the impact of the RPS systems on retail electricity prices are estimated to be USD 14.01/REC and USD 4.59/MWh in 2031, respectively (in 2021 USD). Our study provides appropriate price signals to the market participants and serves as a reference for policymakers.

Optimization of depreciation subsidy policy strategies for electric two-wheelers for improving traffic safety

Abstract To improve the traffic safety of electric two-wheelers (ETW), China has promulgated ETW standardization policies. This policy requires local governments to take measures to guide the illegal ETWs out of use. Governments have implemented a depreciation subsidy scheme to encourage users to scrap illegal ETWs early. When designing the subsidy scheme, effectively improving the ETWs' traffic safety at the road network level while saving government expenses is essential for the sustainable implementation of the policy. This study proposes an optimization method for depreciation subsidy design incorporating traffic safety evaluation. Based on the policy scheme, this study formulates a risk assessment model for the ETW traffic network to characterize the effect of the subsidy on improving safety. Then, we use the bi-level programming approach to model the subsidy strategy design problem. The upper-level problem reflects the goal of policymakers to maximize safety improvement and minimize government expenses. The lower-level problem describes the route choices of ETW users. The optimal subsidy design under different safety-expense trade-offs is analysed based on the Nguyen and Dupuis network and a real network extracted from Changsha City in China. The results show that specific subsidy schemes effectively improve road safety without a large government spending. When the market price or service life of ETWs increases, the government spending on the same safety goal increases. The government should comprehensively consider the safety effect of financial expense and the situation of the local ETW market before selecting reasonable subsidy strategies.

Economic Dispatch of Power Retailers: A Bi-Level Programming Approach via Market Clearing Price

For power retailers in a smart grid, it is necessary to design an economic dispatch method to maintain a balance between power supply and demand on the sale side as well as obtain better economic benefits. This study concentrates on the economic dispatch of the dominant retailer in a regional market. The dominant retailer is considered to be equipped with generator resources such as distributed photovoltaics (PV), wind turbines (WT), and microturbines (MT). As one retailer cannot exactly predict the market conditions of other retailers, the retail market is considered to be modeled as a dichotomous-market model consisting of the dominant retailer market and the other retailers market. As a result, a bi-level optimal dispatch model is proposed for the dominant power retailer based on the dichotomous-market model. In the proposed model, the outer problem aims to minimize the costs of purchases under time-of-use (TOU) price given in the market clearing process, while the inner problem is formulated to simulate the process of market clearing. Furthermore, the bi-level model is converted to a single-level model via the Karush–Kuhn–Tucker (KKT) conditions and eventually solved by employing the YALMIP toolbox with Gurobi solver. Finally, a case study is conducted to validate the effectiveness and adaptability of the proposed model, and the analysis of the variables is presented.

Saving a Path and Maximizing Dynamic Contra ow: A Bilevel Programming Approach

An important aspect of evacuation planning is to save human population by sending the people in dangerous areas (sources) to the safe places (sinks). Optimization models for evacuation planning focus on regulating the tra_c ow in urban road networks so as to maximize the number of evacuees reaching the safe places or to minimize the evacuation time of evacuees. Recent studies show that reversing the direction of the usual tra_c ow in necessary road segments increases the tra_c ow and decreases the evacuation time signi_cantly. However, this may block the ow of some necessary support towards the source. Based on network ow models, we consider the problem of saving a path from a given node to the source, in a single-source-single-sink network, as a bilevel program. With an objective to minimize a function depending on ow rate and the path chosen, the upper level selects a path from a given node to the source, and the lower level maximizes the dynamic ow allowing arc reversals in the resulting network within a given time horizon. We discuss a solution strategy based on replacing the lower level problem by the corresponding KKT conditions. GANIT J. Bangladesh Math. Soc. 42.1 (2022) 010- 024

Modelling lane changing behaviors for bus exiting at bus bay stops considering driving styles: A game theoretical approach

Bus is one of the most important travel modes for citizens, but lane changing behaviors for bus exiting at bus bay stops have negative impacts on traffic flow operations. It is necessary to investigate the characteristics of drivers’ behavioral decision-makings in lane changing for bus exiting for improving public transportation operations. The interactions between passenger car drivers in target lanes and bus drivers with different driving styles (e.g., aggressive or conservative style) are analyzed based on the game theory. A two-player, non-zero-sum, non-cooperative game model with incomplete information is formulated to examine the impacts of driving styles on the lane changing behavioral decision makings. The bi-level programming approach is applied to calibrate the parameters in the formulated model with solving the Bayesian equilibria and minimizing the prediction errors. The vehicle trajectory data extracted from Lvboqiao bus bay stop, Dalian, China are used for model calibration and validation. The results reveal that the formulated model has 73.01%, 86.60% and 83.54% accuracy rates on average for predicting the passenger car, aggressive and conservative bus drivers’ behaviors, respectively. At a 95% confidence level, the time error of a lane changing behavior is statistically significant by the paired t-test. Compared with the previous research, it can be proven that the consideration of driving styles is helpful to deeply explore the interactions between passenger car and bus drivers’ behaviors. The proposed model provides decent theoretical support for the drivers to make better decision-makings, and improves the traffic safety and efficiency around bus bay stops.