Network Design Problem Research Articles

A two-stage robust optimization model for emergency service facilities location-allocation problem under demand uncertainty and sustainable development

Under the backdrop of frequent emergencies, the rational layout of emergency service facilities (ESF) and the effective allocation of emergency supplies have emerged as crucial in determining the timeliness of post-disaster response. By adequately accounting for potential uncertainties and carrying out comprehensive pre-planning, the robustness of location-allocation decisions can be significantly improved. This paper delves into the ESF network design problem under demand uncertainty and formulates this problem as a two-stage robust optimization model. The presented model defines a generalized budget uncertainty set to capture victims’ uncertain demand and minimizes the sum of the costs involved in the two stages. The objective function integrates the input cost in the preparedness phase, the deprivation cost from the victims’ perspective and the environmental impact cost responding to sustainable development in the response phase, which respectively correspond to the comprehensive optimization of the deployment of ESF, the distribution of emergency supplies and the implementation of sustainable measures. Subsequently, we employ the column and constraint generation (C&CG) algorithm to solve the proposed model and take the COVID-19 epidemic in Wuhan as a case to verify the effectiveness of the model and algorithm. Finally, we examine the influence of demand uncertainty and environmental impact cost on the optimal solution, yielding valuable managerial insights.

Designing the Liner Shipping Network of Tomorrow Powered by Alternative Fuels

The liner shipping industry is undergoing an extensive decarbonization process to reduce its 275 million tons of CO2 emissions as of 2018. In this process, the long-term solution is the introduction of new alternative maritime fuels. The introduction of alternative fuels presents a great set of unknowns. Among these are the strategic concerns regarding sourcing of alternative fuels and, operationally, how the new fuels might affect the network of shipping routes. We propose a problem formulation that integrates fuel supply/demand into the liner shipping network design problem. Here, we present a model to determine the production sites and distribution of new alternative fuels—we consider methanol and ammonia. For the network design problem, we apply an adaptive large neighborhood search combined with a delayed column generation process. In addition, we wish to test the effect of designing a robust network under uncertain demand conditions because of the problem’s strategic nature and importance. Therefore, our proposed solution method will have a deterministic and stochastic setup when we apply it to the second-largest multihub instance, WorldSmall, known from LINER-LIB. In the deterministic setting, our proposed solution method finds a new best solution to three instances from LINER-LIB. For the main considered WorldSmall instance, we even noticed a new best solution in all our tested fuel settings. In addition, we note a profit drop of 7.2% between a bunker-powered and pure alternative fuel–powered network. The selected alternative fuel production sites favor a proximity to European ports and have a heavy reliance on wind turbines. The stochastic results clearly showed that the found networks were much more resilient to the demand changes. Neglecting the perspective of uncertain demand leads to highly fluctuating profits. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0143 .

Complexity Framework for Forbidden Subgraphs I: The Framework

AbstractFor a set of graphs $${\mathcal {H}}$$ H , a graph G is $${\mathcal {H}}$$ H -subgraph-free if G does not contain any graph from $${{{\mathcal {H}}}}$$ H as a subgraph. We propose general and easy-to-state conditions on graph problems that explain a large set of results for $${\mathcal {H}}$$ H -subgraph-free graphs. Namely, a graph problem must be efficiently solvable on graphs of bounded treewidth, computationally hard on subcubic graphs, and computational hardness must be preserved under edge subdivision of subcubic graphs. Our meta-classification says that if a graph problem $$\Pi $$ Π satisfies all three conditions, then for every finite set $${{{\mathcal {H}}}}$$ H , it is “efficiently solvable” on $${{{\mathcal {H}}}}$$ H -subgraph-free graphs if $${\mathcal {H}}$$ H contains a disjoint union of one or more paths and subdivided claws, and $$\Pi $$ Π is “computationally hard” otherwise. We apply our meta-classification on many well-known partitioning, covering and packing problems, network design problems and width parameter problems to obtain a dichotomy between polynomial-time solvability and -completeness. For distance-metric problems, we obtain a dichotomy between almost-linear-time solvability and having no subquadratic-time algorithm (conditioned on some hardness hypotheses). Apart from capturing a large number of explicitly and implicitly known results in the literature, we also prove a number of new results. Moreover, we perform an extensive comparison between the subgraph framework and the existing frameworks for the minor and topological minor relations, and pose several new open problems and research directions.

Relax-and-Fix and Fix-and-Optimise algorithms to solve an integrated network design problem for closing a supply chain with hybrid retailers/collection centres

Relax-and-Fix and Fix-and-Optimise algorithms to solve an integrated network design problem for closing a supply chain with hybrid retailers/collection centres

AutoLDT: a lightweight spatio-temporal decoupling transformer framework with AutoML method for time series classification

Time series classification finds widespread applications in civil, industrial, and military fields, while the classification performance of time series models has been improving with the recent development of deep learning. However, the issues of feature extraction effectiveness, model complexity, and model design uncertainty constrain the further development of time series classification. To address the above issues, we propose a Lightweight Spatio-Temporal Decoupling Transformer framework based on Automated Machine Learning technique (AutoLDT). The framework proposes a novel lightweight Transformer with fuzzy position encoding, TS-separable linear self-attention mechanism, and convolutional feedforward network, which mine the temporal and spatial features, as well as the local and global relationship of time series. Fuzzy positional encoding integrates fuzzy ideas to enhance the generalization performance of model information mining. TS-separable linear self-attention mechanism and convolutional feedforward network achieve feature extraction in a lightweight way by decoupling temporal and spatial features of time series. Notably, we adopt the Covariance Matrix Adaptation Evolution Strategy and global adaptive pruning technique to realize automated network structure design, which further improves the model training efficiency and automation, and avoids the uncertainty problem of network design. Finally, we validate the effectiveness of the proposed framework on publicly available UCR and UEA time series datasets. The experimental results show that the proposed framework not only improves the model classification performance in a lightweight way but also dramatically improves the model training efficiency.

Asia‒Europe liner shipping network design model considering Arctic route and black carbon tax

The recent improvement in navigational conditions along the Northern Sea Route (NSR) has attracted the attention of academia and industrial circles. For liner companies, the NSR offers a considerably shorter voyage distance than the Suez Canal Route does, making it a viable option to increase their profits. However, the overexploitation and utilization of the NSR may produce large amounts of black carbon, thus damaging the Arctic ecosystem. In light of the aforementioned background, we examine the challenges in designing liner shipping networks while considering the navigability and transit cost of the NSR and the environmental costs (i.e., black carbon pollution taxes) associated with black carbon. To this end, we establish a bi-level optimization model. Specifically, the upper-level model selects a network design scheme that maximizes the liner company's profit, whereas the lower-level model optimizes the slot allocation scheme to evaluate the derived network design scheme from the upper-level model. To solve this bi-level model, we develop a meta-heuristic algorithm embedded with a linear programming model and perform numerical experiments via a practical Asia‒Europe shipping route. Sensitivity analyses are conducted under various navigational conditions and black carbon taxes. The findings demonstrate that the proposed model and algorithm can effectively address the network design problem, offering practical managerial insights for the liner company's daily operations and the policy formulation of green sustainable transportation policies by governments of countries along the NSR. This paper provides a valuable contribution to advancing green shipping practices in the Arctic region.

Code and Data Repository for A Quantum-Inspired Bilevel Optimization Algorithm for the First Responder Network Design Problem

The software in this repository is developed to solve the First Responder Network Design Problem (FRNDP) using Graver Augmentation Multi-seeded Algorithm (GAMA) and Branch-and-Bound.

A Quantum-Inspired Bilevel Optimization Algorithm for the First Responder Network Design Problem

A Quantum-Inspired Bilevel Optimization Algorithm for the First Responder Network Design Problem

Economic Justice in the Design of a Sugarcane-Derived Biofuel Supply Chain: A Fair Profit Distribution Approach

Background: In agricultural supply chains, unequal bargaining power often leads to economic inequality, particularly for farmers. The fair profit distribution (FPD) approach offers a solution by optimizing supply chain flows (materials, information, and money) to promote economic equity among members. However, our literature review highlights a gap in applying the FPD approach to the facility location-allocation problem in supply chain network design (SCND), particularly in sugarcane-derived biofuel supply chains. Methods: Consequently, we propose a multi-period optimization model based on FPD to design a sugarcane biofuel supply chain. The methodology involves four steps: constructing a conceptual model, developing a mathematical model, designing a solution strategy, and generating insights. This model considers both investment (crop development, biorefinery construction) and operational phases over a long-term planning horizon, focusing on farm location and crop allocation. Results: By comparing the FPD model to a traditional centralized planning supply chain (CSC) approach, we examine the impact of the planning horizon, number of farms, and sugarcane prices paid by biorefineries on financial performance. While the FPD model results in lower overall system profits, it fosters a fairer economic scenario for farmers. Conclusions: This study contributes to economic justice in supply chains and offers insights to promote fair trade among stakeholders.

The parameterized complexity of the survivable network design problem

In the well-known Survivable Network Design Problem (SNDP), we are given an undirected graph G with edge costs, a set R of terminal vertices, and an integer demand ds,t for every terminal pair s,t∈R. The task is to compute a subgraph H of G of minimum cost, such that for every terminal pair s,t∈R there are at least ds,t disjoint paths between s and t in H. Depending on the type of disjointness, we obtain several variants of SNDP that have been widely studied in the literature: if the paths are required to be edge-disjoint we obtain EC-SNDP, while if they must be internally vertex-disjoint we obtain VC-SNDP. Another important case is the element-connectivity variant (LC-SNDP), where the paths must be disjoint on edges and non-terminals, i.e., they may only share terminals. In this work we shed light on the parameterized complexity of the above problems. We consider several natural parameters, which include the solution size ℓ, the sum of demands D, the number of terminals k, and the maximum demand dmax.

Collaborative supply chain network design under demand uncertainty: A robust optimization approach

This paper studies a collaborative robust supply chain network design (CRSCND) problem aimed at maximizing economic and social benefits by enabling enterprises to jointly address demand uncertainties. Through strategies including joint inventory replenishment, shared distribution centers (DCs), and pooled transportation resources, the CRSCND problem seeks to optimize plant and DC locations and the allocation of DCs to customers under a collaborative framework. To address this, we develop two robust optimization models incorporating a budget uncertainty set, each model representing a distinct risk-pooling policy. These models are then reformulated into solvable linear programming structures. Results from numerical experiments confirm the cost-reduction benefits of collaboration and robust optimization. Sensitivity analysis reveals that factors like violated probability and high demand volatility minimally impact cost savings enabled by collaboration and robustness. Moreover, each robust model shows distinct suitability depending on specific scenario parameters. Finally, we test three cost-saving allocation mechanisms, finding that only the Shapley value method yields best allocations in cases involving overlapping demand.

An Iterative Exact Algorithm over a Time-Expanded Network for the Transportation of Biomedical Samples

In this article we propose an iterative algorithm to address the optimization problem of distributing a set of multiple highly perishable commodities in a healthcare network. In the biomedical sample transportation problem, numerous commodities with short lifespans presume multiple transportation requests at the same facility in a day and restrict the maximum time to reach their destination. These two characteristics create an interdependency between the routing and the pickup decisions in time that is highly complex. To address these timing issues, we model this problem as a service network design problem over a time-expanded network. Our solution method aggregates the network at two levels. First, the commodities are aggregated and artificially consolidated, reducing the symmetry arising when multiple transportation requests are solicited within a short period of time. Second, the space-time nodes in the network are constructed dynamically, thus reducing the size of the mathematical model to be solved at each iteration. Moreover, the method creates auxiliary networks to calculate good-quality primal bounds to the problem. Our algorithm proves to be efficient to solve a set of real-life instances from the Quebec laboratory network under the management of the Ministère de la Santé et des Services sociaux (Ministry of Health and Social Services) with a detailed network of up to 2,377 periods and 277 transportation requests. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grants 2018-04609, 2020-06311]. 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.2023.0061 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0061 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Two-stage robust multimodal hub network design under budgeted demand uncertainty: A Benders decomposition approach and a case study

The widening use of hub networks in urban agglomeration freight systems requires several actual extensions in conventional hub network design problems. For this purpose, we introduce a two-stage robust multimodal hub network design problem for the urban agglomeration freight system by considering incomplete hub network topology, multiple transportation modes, travel time limit and discuss the uncertainty in the constructed network from the demand point of view. Particularly, we model the demand uncertainty for the considered problem in two different ways. The basic model supposes that interval-budgeted uncertainty set is adopted to characterize uncertain demand, while the expanded model additionally considers possible states of the uncertain demand and weights summation of performances over multiple uncertainty sets, namely state-wise budgeted uncertainty set. By using a min–max criterion, we develop the path-based mixed-integer programming formulations for the proposed problem, which can significantly decrease the number of required integer variables and constraints. To handle large-sized problems, we propose an improved Benders decomposition algorithm, in which the master problem is implemented in a branch-and-bound framework and the subproblem is optimality solved by a customized two-step strategy. In addition to evaluating on the standard CAB, TR and AP datasets, we conduct a real-world case study of the Beijing–Tianjin–Hebei urban agglomeration freight system to explore the effect of incorporating uncertainty and showcase the superior performance of the proposed methods.

Joint deployment of exclusive bus lanes and limited access bus lanes in a transportation network

Providing exclusive right-of-way to buses is considered an effective measure to enhance the transit system’s performance. However, the conversion of a General-Purpose Lane (GPL), which is shared by all transportation modes, to an Exclusive Bus Lane (EBL), reduces the available capacity for auto users and may result in an underutilized lane known as the empty syndrome lane. To address this deficiency, it is suggested that a special class of vehicles, such as High Occupancy Vehicles (HOVs) be permitted to drive in EBLs, but they may be required to pay tolls. This type of lane is called a Limited Access Bus Lane (LABL) and is designed to prioritize public transportation and restrict the entry of HOVs in bus lanes. The goal is to ensure transit passengers do not experience a decrease in the quality of service. This paper compares the results of four bi-level optimization models used to determine the optimal location of different combinations of special-use lanes in the network, namely: 1) only EBLs; 2) joint deployment of EBLs and HOV lanes; 3) joint deployment of EBLs and tolled HOV lanes; and 4) joint deployment of EBLs and LABLs. A base optimization problem is developed for the last proposed scheme (i.e., joint deployment of EBLs and LABLs), and the formulation is modified to solve three other network design problems. The proposed model is solved by applying a genetic algorithm. To analyze the suggested framework, a numerical test is conducted on the Sioux Falls network as a medium-sized network and the network of Zanjan as a real-sized network. Furthermore, by analyzing the numerical results of the four optimization problems, this study highlights that the joint deployment of EBLs and LABLs outperforms the other three schemes in terms of transit users’ travel time and the average volume capacity of bus routes.

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 .

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.

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.

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.

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.