Network Design Problem Research Articles

Plan Your System and Price for Free: Fast Algorithms for Multimodal Transit Operations

We study the problem of jointly pricing and designing a smart transit system, where a transit agency (the platform) controls a fleet of demand-responsive vehicles (cars) and a fixed line service (buses). The platform offers commuters a menu of options (modes) to travel between origin and destination (e.g., direct car trip, a bus ride, or a combination of the two), and commuters make a utility-maximizing choice within this menu, given the price of each mode. The goal of the platform is to determine an optimal set of modes to display to commuters, prices for these modes, and the design of the transit network in order to maximize the social welfare of the system. In this work, we tackle the commuter choice aspect of this problem, traditionally approached via computationally intensive bilevel programming techniques. In particular, we develop a framework that efficiently decouples the pricing and network design problem: Given an efficient (approximation) algorithm for centralized network design without prices, there exists an efficient (approximation) algorithm for decentralized network design with prices and commuter choice. We demonstrate the practicality of our framework via extensive numerical experiments on a real-world data set. We moreover explore the dependence of metrics such as welfare, revenue, and mode usage on (i) transfer costs and (ii) cost of contracting with on-demand service providers and exhibit the welfare gains of a fully integrated mobility system. Funding: This work was supported by the National Science Foundation [Awards CMMI-2308750, CNS-1952011, and CMMI-2144127]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0452 .

When two chains meet: Optimizing the design of blockchain-enabled supply chain networks

Applications of the blockchain technology are rapidly emerging across sectors. By redefining information flow, blockchain technology promises to instill trust among supply chain members, improve transaction efficiency, thus reshaping the structure and configuration of supply chains. The practical exploratory use of blockchain has shown immense potential in supply chain management. In order to explore the new changes brought by blockchain technology to supply chain network design issues, this study focuses on the supply chain network design problem in the context of blockchain technology. Specifically, we consider a supply chain network comprised of a number of distribution centers (DCs) and retailers. The operation of this physical network is supported by blockchain-based information infrastructure. As the interrelated relationship between these two networks, it is necessary to optimize them simultaneously to improve the profitability and information exchange level. We propose an objective function based on previous studies to maximize the profits of the entire supply chain network, with decision variables including DC locations, retailer assignment, inventory replenishment policy, and blockchain adoption level. At the same time, to characterize the interrelation between the two networks, the demand and certain cost parameters of the model become endogenous depending on the blockchain adoption level, which significantly increases the complexity of the solution algorithm. We reformulate the model and use the polymatroid cutting plane approach to address this issue. We conducted calculations and numerical analysis. The computational results show that the proposed method can solve practically sized problems, and integrating blockchain design reduces the system-wide cost. We discuss managerial insights based on a range of numerical studies and solve a case study using publicly available instance data.

Solving discrete network design problem using disjunctive constraints

AbstractThis paper introduces a deterministic algorithm to solve the discrete network design problem (DNDP) efficiently. This non‐convex bilevel optimization problem is well‐known as an non deterministic polynomial (NP)‐hard problem in strategic transportation planning. The proposed algorithm optimizes budget allocation for large‐scale network improvements deterministically and with computational efficiency. It integrates disjunctive programming with an improved partial linearized subgradient method to enhance performance without significantly affecting solution quality. We evaluated our algorithm on the mid‐scale Sioux Falls and large‐scale Chicago networks. We assess the proposed algorithm's accuracy by examining the objective function's value, specifically the total travel time within the network. When tested on the mid‐scale Sioux Falls network, the algorithm achieved an average 46% improvement in computational efficiency, compared to the best‐performing method discussed in this paper, albeit with a 4.17% higher total travel time than the most accurate one, as the value of the objective function. In the application to the large‐scale Chicago network, the efficiency improved by an average of 99.48% while the total travel time experienced a 4.34% increase. These findings indicate that the deterministic algorithm proposed in this research improves the computational speed while presenting a limited trade‐off with solution precision. This deterministic approach offers a structured, predictable, and repeatable method for solving DNDP, which can advance transportation planning, particularly for large‐scale network applications where computational efficiency is paramount.

Designing a resilient supply chain network: A multi-objective data-driven distributionally robust optimization method

Uncertainty of supply chain disruption poses a significant challenge to decision-making in many real-life problems. In this paper, a new multi-objective data-driven distributionally robust optimization (MDDRO) model for the resilient supply chain network (RSCN) design problem under disruption scenario is developed, which includes minimizing the total cost, carbon emissions, and delivery time. In the context of supply chain disruption, it is important self-evidently that products can be supplied normally and the practical demand can be met. In handling the partial probability distribution information of the considered uncertain demand, this paper uses a data-driven Wasserstein-Moment ambiguity set (WMAS), which incorporate the Wasserstein metric and Moment information, and a robust counterpart to transform the developed model into a tractable approximation form. The finite-sample performance guarantee of the optimal solution of MDDRO model with Wasserstein-Moment ambiguous chance constraint is given. An accelerated Branch and cut algorithm (BCA) is constructed to solve the MDDRO model. Finally, through the investigation of a real-life case and sensitivity analysis of key parameters, some managerial insights are put forward.

Approximations for the Steiner Multicycle problem

The Steiner Multicycle problem consists in, given a complete graph, a weight function on its edges, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint cycles in the graph such that, for every terminal set, all of its vertices are in a same cycle of the collection. This problem generalizes the Traveling Salesman problem and, therefore, is hard to approximate in general. On the practical side, it models a collaborative less-than-truckload problem with pickup and delivery locations. Using an algorithm for the Survivable Network Design problem and T-joins, we obtain a 3-approximation for the metric case, improving on the previous best 4-approximation. Furthermore, we present an (11/9)-approximation for the particular case of the Steiner Multicycle in which each edge weight is 1 or 2. This algorithm can be adapted to obtain a (7/6)-approximation when every terminal set contains at least four vertices. Finally, we devise an O(lg⁡n)-approximation algorithm for the asymmetric version of the problem.

A topological network connectivity design problem based on spectral analysis

How to improve network connectivity and which parts of the network are vulnerable are critical issues. We begin by defining an equal distribution problem, in which supplies are distributed equally to all nodes in the network. We then derive a topological network connectivity measure from the convergence speed, which is the second minimum eigenvalue of a Laplacian network matrix. Based on the equal distribution problem, we propose a method for identifying critical links for network connectivity using the derivative of the second minimum eigenvalue. Furthermore, we develop a network design problem that maximizes topological connectivity within a budget creating strengthening network links. The problem is convex programming, and the solution is global. Furthermore, it can be converted into an identical semidefinite programming problem, which requires less computational effort. Finally, we test the developed problems on road networks in the Japanese prefectures of Ishikawa and Toyama to determine their applicability and validity.

From operational to strategic modelling: A continuous multi-scale approach for last-mile analysis

Supply chain planning requires decision-making at all levels, especially in the new normal of intervened supply networks. The integration of strategic network design and operational routing decisions has been widely studied in the literature as the location-routing problem (LRP). However, the LRP does not consider the differences in the planning horizon of each sub-problem, nor have geospatial elements been included in the distribution of demand. This paper aims to redesign the conceptual modelling of the last mile to inform strategic network design problems. A continuous multi-scale approach (CMA) is proposed by taking elements from the districting problem (DP) and continuous approximation (CA). This approach includes stochastic demand in the analysis and the effects of time windows and failed deliveries. The validation of CMA in a case of rural parcel deliveries in Belgium shows an estimate of the distance travelled similar to traditional routing algorithms in scenarios with high demand density. Likewise, the effects of time windows on the spatial configuration of multi-scale districting are explored. This approach provides insights for decision-making in strategic and tactical planning, such as sonification, differentiated services to satisfy consumer preferences, and fleet management. The limitations of the CMA lie in its implementation in purely operational scenarios since it does not offer detailed routing information. Subsequent research aims to exploit the potential of strategic last-mile modelling with effective integration into network design problems.

Exploring the pre-disaster evacuation network design problem under five traffic equilibrium models

This paper explores modeling approaches for the pre-disaster Evacuation Network Design Problem (ENDP) considering different flow equilibrium conditions. We combine this problem with the modeling idea of Continuous Network Design Problem (CNDP), which we call Continuous Evacuation Network Design Problem (CENDP) in this paper. We develop five CENDP models, which are under the consideration of User Equilibrium (UE), Stochastic User Equilibrium (SUE), Boundedly Rational User Equilibrium (BRUE), and Non-equilibrium (NONE), among which we develop two types of models based on BRUE. The modeling is mainly to consider the single objective of optimizing the total evacuation time, and then to provide reasonable road expansion solutions under certain budget constraints and different equilibrium conditions. Our main motivation for developing models is to introduce various types of equilibrium conditions into models and design algorithms to solve these problems while mining for key insights. We design the corresponding five heuristic algorithms to solve models and verify the applicability of the models and algorithms by two test networks (Nguyen-Dupuis network and Sioux-Falls network). We demonstrate whether evacuation flow equilibrium need or not need to be considered in the CENDP, the applicability of different equilibrium conditions, and the correlation between the total evacuation time, the network investment cost, and the network congestion degree. Additionally, we conduct model and algorithm tests on 40 instance networks, dividing them into medium-sized networks (20 instances) and large-sized networks (20 instances). Not only do we further validate the insights obtained from the test networks, but we also expand upon them. Specifically, the main findings of this study are as follows: (1) We demonstrate that considering evacuation flow equilibrium in CENDP is essential to reduce total evacuation time, construction costs, and mitigate congestion. (2) While increased investment in road construction can meet evacuation time requirements, it is crucial to make informed decisions, as investment alone does not directly reduce total evacuation time and congestion. (3) Optimizing road evacuation time is more effective than merely increasing road capacity for reducing total evacuation time and mitigating congestion. (4) From the perspectives of total evacuation time, investment cost, and network congestion degree, the CENDP model considering user equilibrium performs better in medium-sized networks, while the CENDP model considering stochastic user equilibrium performs better in large-sized networks. Conversely, the CENDP model that does not consider flow equilibrium performs the worst across all above three metrics. Based on this, we also provide recommendations on which model to choose for different metrics. In summary, this study not only reveals the importance of different flow equilibrium conditions in evacuation network design but also provides valuable strategic recommendations for practical applications to optimize evacuation effectiveness and resource allocation.

On-demand mobility-as-a-Service platform assignment games with guaranteed stable outcomes

Mobility-as-a-Service (MaaS) systems are two-sided markets, with two mutually exclusive sets of agents, i.e., travelers/users and operators, forming a mobility ecosystem in which multiple operators compete or cooperate to serve customers under a governing platform provider. This study proposes a MaaS platform equilibrium model based on many-to-many assignment games incorporating both fixed-route transit services and mobility-on-demand (MOD) services. The matching problem is formulated as a convex multicommodity flow network design problem under congestion that captures the cost of accessing MOD services. The local stability conditions reflect a generalization of Wardrop's principles that include operators’ decisions. Due to the presence of congestion, the problem may result in non-stable designs, and a subsidy mechanism from the platform is proposed to guarantee local stability. A new exact solution algorithm to the matching problem is proposed based on a branch and bound framework with a Frank-Wolfe algorithm integrated with Lagrangian relaxation and subgradient optimization, which guarantees the optimality of the matching problem but not stability. A heuristic which integrates stability conditions and subsidy design is proposed, which reaches either an optimal MaaS platform equilibrium solution with global stability, or a feasible locally stable solution that may require subsidy. For the heuristic, a worst-case bound and condition for obtaining an exact solution are both identified. Two sets of reproducible numerical experiments are conducted. The first, on a toy network, verifies the model and algorithm, and illustrates the differences local and global stability. The second, on an expanded Sioux Falls network with 82 nodes and 748 links, derives generalizable insights about the model for coopetitive interdependencies between operators sharing the platform, handling congestion effects in MOD services, effects of local stability on investment impacts, and illustrating inequities that may arise under heterogeneous populations.

Collaborative Service Network Design for Multiple Logistics Carriers Considering Demand Uncertainty

Collaborative designing of service networks using multiple logistics carriers can bring advantages in both economic and environmental terms, and these carriers have symmetry in their service areas. To enable such a collaborative service network and the corresponding benefits, this study proposes a problem of collaborative service network design (CSND) considering demand uncertainty. This problem is formulated as a two-stage robust optimization model using a budget uncertainty set to handle the uncertain demand. A column-and-constraint generation algorithm is developed to accurately solve the robust model. Numerical experiments show that the proposed algorithm outperforms the Benders decomposition algorithm in terms of solving efficiency and quality. Through comparative experiments, this research validates the advantages of collaborative designing and the robustness of model solutions. In addition, three allocation mechanisms are tested to investigate the importance of allocation in CSND.

A [formula omitted]-approximation algorithm for minimum power k edge disjoint st-paths

In minimum power network design problems we are given an undirected graph G=(V,E) with edge costs {ce:e∈E}. The goal is to find an edge set F⊆E that satisfies a prescribed property of minimum power pc(F)=∑v∈Vmax⁡{ce:e∈F is incident to v}. In the Min-PowerkEdge Disjointst-Paths problem F should contain k edge disjoint st-paths. The problem admits a k-approximation algorithm, and it was an open question to achieve an approximation ratio sublinear in k for simple graphs, even for unit costs. We give a 22k-approximation algorithm for general costs.

Integrating vision and lidar based hyperlocal metadata for optimal capacity expansion planning in hillside road networks

The rapidly expanding population and scarcity of affordable housing in many urban areas, such as Los Angeles, have resulted in large inventories of structures in hilly landscapes. Such urbanization has also rendered road capacities inadequate in many instances, with hazards such as floods, fires, and earthquakes posing additional risks to such inventory. Planning construction activities such as widening, structural, and geotechnical retrofits to increase capacity and resiliency by cutting through slopes and incorporating landslide protection measures requires hyperlocal information for road segments in hillside areas. Performing traditional surveys for large areas of such road networks can be both time-consuming and cost prohibitive. At the same time, data acquired from satellites may not provide the required spatial resolution for planning, especially regarding road-adjacent features such as slopes. This paper proposes a novel framework to fuse hyperlocal data regarding road and adjacent slopes gathered from the street-level mobile mapper equipped with cameras and lidar into the network design problem (NDP) to develop an optimal road width expansion plan. The hyperlocal features are derived from a colorized point cloud map and deep learning techniques to estimate the relevant features in hillside landscapes. Specifically, a deep learning-based segmentation and detection algorithms combined with novel point cloud processing techniques are used to obtain a spatially dense profile of the road and the adjacent slope. By leveraging such hyperlocal information, we explore all the potential road capacity and improvement options for road capacity expansion. Furthermore, we demonstrate the advantages of our proposed method over conventional techniques, particularly working with budget constraints. In terms of novel contributions, incorporating hyperlocal information into NDP for hillside road capacity expansion is novel, as well as algorithms to automatically detect and characterize relevant roadside features from remotely sensed lidar point clouds.

Three network design problems for community energy storage

AbstractIn this article, we develop novel mathematical models to optimize utilization of community energy storage (CES) by clustering prosumers and consumers into energy sharing communities/microgrids in the context of a smart city. Three different microgrid configurations are modeled using a unifying mixed‐integer linear programming formulation. These configurations represent three different business models, namely: the island model, the interconnected model, and the Energy Service Companies model. The proposed mathematical formulations determine the optimal households' aggregation as well as the location and sizing of CES. To overcome the computational challenges of treating operational decisions within a multi‐period decision making framework, we also propose a decomposition approach to accelerate the computational time needed to solve larger instances. We conduct a case study based on real power consumption, power generation, and location network data from Cambridge, MA. Our mathematical models and the underlying algorithmic framework can be used in operational and strategic planning studies on smart grids to incentivize the communitarian distributed renewable energy generation and to improve the self‐consumption and self‐sufficiency of the energy sharing community. The models are also targeted to policymakers of smart cities, utility companies, and Energy Service Companies as the proposed models support decision making on renewable energy related projects investments.

Approximate dynamic programming for liner shipping network design

AbstractThe global containerised trade heavily relies on liner shipping services, facilitating the worldwide movement of large cargo volumes along fixed routes and schedules. The profitability of shipping companies hinges on how efficiently they design their shipping network; a complex optimization problem known as the liner shipping network design problem (LSNDP). In recent years, approximate dynamic programming (ADP), also known as reinforcement learning, has emerged as a promising approach for large-scale optimisation. This paper introduces a novel Markov decision process for the LSNDP and investigates the potential of ADP. We show that ADP methods based on value iteration produce optimal solutions to small instances, but their scalability is hindered by high memory demands. An ADP method based on a deep neural network requires less memory and successfully obtains feasible solutions. The quality of solutions, however, declines for larger instances, possibly due to the discrete nature of high-dimensional state and action spaces.

Exact approaches to solve the Transmission Expansion Planning Problem with Re-design

Expanding electrical transmission networks is a critical challenge faced by many developing economies. This process requires extensive investments, which must be strategically and methodically planned on a large scale, often encompassing regional or national considerations. Differing from typical Network Design Problems, efficiency in a transmission network can sometimes be enhanced by strategically deactivating certain transmission lines. Thanks to that, this paper focuses on a version of the transmission expansion planning problem that allows redesign during the network expansion. We propose using two exact methodologies as alternatives to the direct use of mixed integer programming formulations with commercial solvers. These methods are an application of Benders’ decomposition and a newly developed approach named Ring Space. Through comprehensive computational experiments, we assess and compare the efficacy of these methods against the conventional application of the mathematical formulation. Additionally, this study successfully obtained new high-quality solutions and proved their optimality for a subset of benchmark instances.

Cold chain distribution network design with heterogeneous fleet under carbon reduction policy application effect

ABSTRACT To integrate cold chain distribution network design problem with heterogeneous fleet, a multi-objective optimisation model is proposed to simultaneously optimise distribution routes, the quantity of internal combustion and electric refrigerated trucks (ERTs), and the number and location of distribution centres and charging stations with time window constraints, where the cold chain distribution operating cost and the customer dissatisfaction cost are minimised. A hybrid solution methodology, combining a multi-objective artificial fish swarm algorithm with a label-based optimisation algorithm, is presented to address this model. Extensive computational experiments verify the effectiveness of the proposed method. Moreover, a sensitivity analysis, focusing on the range of ERTs, the purchase subsidy for ERTs, the carbon tax and the carbon emission quota, informs the development of diverse carbon reduction policies. A comparative analysis of the implementation effect of carbon reduction policies can provide optimisation decision support for promoting sustainability in the electrification of cold chain distribution.

Pre-disaster evacuation network design with uncertain demand and behavioural choices: A bi-criteria generalized cost perspective

Pre-disaster evacuation network design is critical to improving evacuation efficiency and reducing the loss of life and property caused by disasters. However, evacuation network design is complicated by the uncertainty of pre-disaster evacuation demand and the heterogeneity of evacuees’ route choices when faced with a disaster scenario. Therefore, how to design efficient evacuation networks considering these uncertainties has become an important research topic. In this paper, we study the pre-disaster flood evacuation network design problem, define a bi-criteria generalized cost metric based on Evacuation Travel Time (ETT) and Evacuation Network Congestion Degree (ENCD), and develop a model that considers uncertain demand and evacuation behavioural choices to minimize the generalized cost in the evacuation network. For the uncertain behavioural choice, we propose an Expanded Stochastic User Equilibrium (ESUE) model based on the Random Regret Minimization (RRM) principle and Boundedly Rational User Equilibrium (BRUE) conditions to describe it. For the uncertain demand, we design a Distributionally Robust Optimization (DRO) method based on Mean Absolute Deviation (MAD) to deal with this uncertain model. This paper designs an Improved Method of Successive Averages Combined with Genetic Algorithm (IMSA-GA) to solve the model and uses the Nguyen-Dupuis test network to verify the applicability and feasibility of the model and algorithm. In addition, we also conduct an evacuation network design in the Hawkesbury-Nepean region of Australia. The larger the threshold value based on the regret utility ratio, the smaller the generalized cost value, which indicates the behavioural choices of the evacuees have an impact on the evacuation network design, and the generalized cost decreases by 6.12% when the threshold value is increased from 0.1 to 0.9. In addition, the generalized cost value obtained by IMSA-GA will be 0.0025 lower than Improved Method of Successive Averages Combined with Simulated Annealing (IMSA-SA) and 0.0005 lower than Improved Method of Successive Averages Combined with Taboo Search (IMSA-TS). The theoretical contribution of this paper is to find an approach to the uncertain evacuation network design problem, especially to improve the practicality of the model by fully considering evacuation behaviour. The practical contribution is that our findings can provide insights for government authorities to design efficient and reliable evacuation networks that balance evacuation travel time and evacuation network congestion. In the future, if evacuation behavioural choices can be analysed based on actual surveys, the estimation of behavioural parameters based on survey data will be more instructive for the evacuation process.

Developing a Bi-Level Optimization Model for the Coupled Street Network and Land Subdivision Design Problem with Various Lot Areas in Irregular Blocks

Street design and land subdivision are significant tasks in the development and redevelopment planning process. Optimizing street and land subdivision layouts within a unified framework to achieve solutions that meet a set of objectives and constraints (e.g., minimizing parcel area deviation from standard values, minimizing land consumption for street construction, etc.) is a critical concern for planners, particularly in complex contexts such as blocks with irregular shapes and parcels of varying sizes and requirements. To address this challenge, a mathematical formulation is presented for the bi-level street network and land subdivision optimization problem. Subsequently, the solution procedure is outlined, which utilizes a genetic-based algorithm for street design and a memetic–genetic-based algorithm for land subdivision. Finally, two cases are presented, solved, and discussed to analyze and verify the proposed mathematical model and solution procedures. The results suggest that the formulated problem is suitable for addressing the coupled street network and land subdivision design problem, and it can be adapted and extended to other case studies. Additionally, the introduced ideas and algorithms satisfactorily solved the stated problem.

Travel bubble policies for low‐risk air transport recovery during pandemics

AbstractGlobal pandemics restrict long‐haul mobility and international trade. To restore air traffic, a policy named “travel bubble” was implemented during the recent COVID‐19 pandemic, which seeks to re‐establish air connections among specific countries by permitting unrestricted passenger travel without mandatory quarantine upon arrival. However, travel bubbles are prone to bursting for safety reasons, and how to develop an effective restoration plan through travel bubbles is under‐explored. Thus, it is vital to learn from COVID‐19 and develop a formal framework for implementing travel bubble therapy for future public health emergencies. This article conducts an analytical investigation of the air travel bubble problem from a network design standpoint. First, a link‐based network design problem is established with the goal of minimizing the total infection risk during air travel. Then, based on the relationship between origin‐destination pairs and international candidate links, the model is reformulated into a path‐based one. A Lagrangian relaxation‐based solution framework is proposed to determine the optimal restored international air routes and assign the traffic flow. Finally, computational experiments on both hypothetical data and real‐world cases are conducted to examine the algorithm's performance. The results demonstrate the effectiveness and efficiency of the proposed model and algorithm. In addition, compared to a benchmark strategy, it is found that the infection risk under the proposed travel bubble strategy can be reduced by up to 45.2%. More importantly, this work provides practical insights into developing pandemic‐induced air transport recovery schemes for both policymakers and aviation operations regulators.

Resilient and sustainable semiconductor supply chain network design under trade credit and uncertainty of supply and demand

Supply Chain (SC) performance appraisal extends beyond economic evaluation to encompass environmental and social impacts, as well as resilience to supply and demand disruptions. Thus, SC network design decisions should simultaneously optimize all these performance metrics as a primary objective. However, existing studies optimized these objectives independently or in a limited scope, failing to comprehensively address the interconnected nature of these performance metrics. Therefore, this study proposes a mixed integer linear programming (MILP) model with four objectives to address a multi-tier resilient and sustainable semiconductor SC network design problem under trade credit, supply, and demand uncertainties. The model aims to determine the optimal number and location of various facilities, the amount to order from suppliers, economic production quantities, quantity allocation between SC entities, and ideal supplier selections. The proposed supply chain network contributes to the global effort to reduce carbon emissions and enhance the circular economy by considering carbon trading, recycling, and the proper disposal of end-of life products. Uncertainties in input parameters are addressed using a fuzzy programming approach, while lexicographic optimization and the ɛ-constraint method are used to solve the proposed model. This paper presents a numerical example to illustrate the applicability of the proposed model and provide managerial insights. The numerical analysis results show that provided an appropriate confidence level for the uncertain parameters, the sets of Pareto optimal solutions can be generated. And it also shows that the total SC cost increases with decreasing carbon emissions level and increasing job opportunities created. This research advances sustainable and resilient supply chain management practices while offering practical guidance for decision-makers in real-world contexts.