Optimal Allocation of Shared Manufacturing Resources Based on Bilevel Programming

In the shared manufacturing environment, on the basis of in-depth analysis of the shared manufacturing process and the allocation process of manufacturing resources, a bilevel programming model for the optimal allocation of manufacturing resources considering the benefits of the shared manufacturing platform and the rights of consumers is established. In the bilevel programming model, the flexible indicators representing the interests of the platform are the upper-level optimization target of the model and the Quality of Service (QoS) indicators representing the interests of consumers are the lower-level optimization goal. The weights of the upper indicators are determined by Analytic Hierarchy Process (AHP) and Improved Order Relation Analysis (Improved G1) combination weighting method and the bilevel programming model is solved by the Improved Fast Elitist Non-Dominated Sorting Genetic Algorithm (Improved NSGA-II). Finally, the effectiveness of the model is validated by a numerical example.

Efficient Solution Methods for a General r-Interdiction Median Problem with Fortification

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).

Active Safety Planning Method for Transportation Network Design

Traffic accidents are frequent although various countermeasures are introduced. Traffic safety cannot be fundamentally improved if it is not considered in the transportation network design stage. Although it is well known that traffic safety is one of the most important concerns of the public, traffic safety is not adequately accommodated in transportation planning. This paper considers traffic safety as a major criterion in designing a transportation network. It is a kind of proactive measure rather than reactive measure. A bilevel programming model system is proposed where the upper level is the urban planners’ decision to minimize the estimated total number of traffic accidents, and the lower level is the travelers’ response behaviors to achieve transportation system equilibrium. A genetic algorithm (GA) with elite strategy is proposed to solve the bilevel model. The method of successive averages (MSA) is embedded for the lower level model, which is a feedback procedure between destination choice and traffic assignment. To demonstrate the effectiveness of the proposed method and algorithm, an experimental study is carried out. The results show that these methods can be a valuable tool to design a safer transportation network although efficiency, in terms of system total travel time, is slightly sacrificed.

Bifuzzy-Bilevel Programming Model: Solution and Application

Bi-level programming is widely used in processing various questions, but it cannot deal with the complex and fuzzy information contained in problems. In order to solve such problems better with intricate and vague information that can be efficiently handled by bifuzzy theory, a bifuzzy–bilevel programming model that sets the parameters to bifuzzy variables is proposed in this paper, which can process complex realistic data more accurately and improve the feasibility and validity of bi-level programming models. To ensure the solvability of the model, the equivalent form of the bifuzzy–bilevel programming model is obtained by utilizing the expected value operator. According to the linear and nonlinear characteristics of the model, the Karush–Kuhn–Tucker condition and particle swarm optimization algorithm are employed to handle the problem, respectively. Finally, by taking the distribution center location problem of the supplier as an example, the bifuzzy–bilevel programming model is applied in practice to balance highly intricate customer demands and corporate cost minimization, obtaining the feasible solution of functions at the upper and lower levels, and the bifuzzy information in the problem can also be processed well, which proves the effectiveness of the proposed methodology.

A Continuous Transportation Network Design Problem with the Consideration of Road Congestion Charging

This paper proposes a biobjective continuous transportation network design problem concerning road congestion charging with the consideration of speed limit. The efficiency of the traffic network and the reduction of pollution in the network environment are improved by designing a reasonable road capacity enhancement and speed limit strategy. A biobjective bilevel programming model is developed to formulate the proposed network design problem. The first target of the upper problem is the optimization of road charging efficiency, and the other target is the total cost of vehicle emissions; these objectives are required to devise the optimal road capacity enhancement scheme, speed limiting schemes for different time periods, and the road pricing scheme. The lower-level problem involving travellers’ route choice behaviours uses stochastic user equilibrium (SUE) theory. Based on the nondominated sorting genetic algorithm, which is applied to solve the bilevel programming model, a numerical example is developed to illustrate the effectiveness of the proposed model and algorithm. The results show that the implementation of congestion charging measures on the congested road sections would help to alleviate road congestion in the transportation network, effectively save transportation infrastructure investment and limited urban land resources, increase fiscal revenue, and open up new sources of funds for urban infrastructure construction.

Optimal Design of Cordon Sanitaire for Regular Epidemic Control

The outbreak of COVID-19 has disrupted our regular life. Many state and local authorities have enforced a cordon sanitaire for the protection of sensitive areas. Travelers can only travel across the cordon after being qualified. This paper aims to propose a method to determine the optimal deployment of cordon sanitaire in terms of the number of parallel checkpoints at each entry link for regular epidemic control. A bilevel programming model is formulated where the lower-level is the transport system equilibrium with queueing to predict traffic inflow, and the upper-level is queueing network optimization, which is an integer nonlinear programming. The objective of this optimization is to minimize the total operation cost of checkpoints with a predetermined maximum waiting time. Note that stochastic queueing theory is used to represent the waiting phenomenon at each entry link. A heuristic algorithm is designed to solve the proposed bilevel model where the method of successive averages (MSA) is adopted for the lower-level model, and the genetic algorithm (GA) is adopted for the upper-level model. An experimental study is conducted to demonstrate the effectiveness of the proposed method and algorithm. The results show that the methods can find a good heuristic optimal solution. These methods are useful for policymakers to determine the optimal deployment of cordon sanitaire for hazard prevention and control.

Optimizing Train Timetable Based on Departure Time Preference of Passengers for High-Speed Rails

Passengers would like to choose the most suitable train based on their travel preferences, expenses, and train timetable in the high-speed railway corridor. Meanwhile, the railway department will constantly adjust the train timetable according to the distribution of passenger flows during a day to achieve the optimal operation cost and energy consumption saving plan. The question is how to meet the differential travel needs of passengers and achieve sustainable goals of service providers. Therefore, it is necessary to design a demand-oriented and environment-friendly high-speed railway timetable. This paper formulates the optimization of train timetable for a given high-speed railway corridor, which is based on the interests of both passengers and transportation department. In particular, a traveling time-space network with virtual departure arc is constructed to analyze generalized travel costs of passengers of each origin-destination (OD), and bilevel programming model is used to optimize the problem. The upper integer programming model regards the minimization of the operating cost, which is simplified to the minimum traveling time of total trains, as the goal. The lower level is a user equilibrium model which arranges each OD passenger flow to different trains. A general advanced metaheuristic algorithm embedded with the Frank–Wolfe method is designed to implement the bilevel programming model. Finally, a real-world numerical experiment is conducted to verify the effectiveness of both the model and the algorithm.

Multicriteria Intermodal Freight Network Optimal Problem with Heterogeneous Preferences under Belt and Road Initiative

In this study, we demonstrate the importance of incorporating shippers’ preference heterogeneity into the optimization of the China Railway express network. In particular, a bilevel programming model is established to minimize the total construction cost for the government in the upper level and maximize the shippers’ satisfaction in the lower level. The proposed model considers price, time, reliability, frequency, safety, flexibility, traceability, and emission. Two designs are obtained by applying the model to two scenarios, in which one is of the aggregate shipper group and the other is of the three distinct clusters. Results show that explicitly including heterogeneity in network optimization pays off in terms of the dramatic increase in shippers’ satisfaction and the share of the sustainable railway without generating extra cost for the system. The results of this study could lead to insightful implication for proper network planning for the China Railway express and some useful suggestions on the subsidies of the government.