Network Design Problem Research Articles

Integrated supply chain network design and superstructure optimization problem: A case study of microalgae biofuel supply chain

In recent years, several strategies have been developed and adopted in a bid to manage the biofuel supply chain. In this paper, a two-stage optimization model is proposed for integrated microalgae biofuel supply chain network design and superstructure optimization problems. In the first stage, the design of the carbon capture, utilization, and storage (CCUS) network is taken into account. A robust mixed integer linear programming (RMILP) model is proposed to optimize the strategic CCUS decisions, including the simultaneous selection of emission sources, capture facilitates, Carbon Dioxide (CO2) pipelines, intermediate transportation sites and storage sites, or microalgae cultivation sites. The second stage is dedicated to biorefinery superstructure optimization in order to determine the optimal/promising biorefinery configurations. The presented model is able to handle the inherent uncertainty of critical input parameters. Moreover, the results show that biodiesel production cost cannot compete with current diesel price, but it can be reduced significantly by improving biomass productivity.

Regulating hazardous material transportation: a scenario-based network design approach with integrated risk-mitigation mechanisms

Integrating both proactive and reactive risk-mitigation mechanisms, this research constructs a bi-level network design problem for hazardous materials (hazmats) to regulate the carriers' use of roads, such that the environmental impact is minimized. In more detail, by embedding the emergency response time into the risk assessment, the locations of hazmat response teams are determined along with toll schemes, road closures, and new road constructions. The uncertainties of demand, including differences in the number of shipments, origin/destination changes, and amount variations, are also taken into account by applying a scenario-based approach. The proposed bi-level model is first solved optimally by a single-level reformulation, and then by a three-stage heuristic method for larger instances. Through numerical experiments on a real-world road network in Nanchang, a city in China, a set of management insights are derived to facilitate policy-making in regulating hazmat transportation.

The complexity of the timetable‐based railway network design problem

AbstractBecause of the long planning periods and their long life cycle, railway infrastructure has to be outlined long ahead. At the present, the infrastructure is designed while only little about the intended operation is known. Hence, the timetable and the operation are adjusted to the infrastructure. Since space, time and money for extension measures of railway infrastructure are limited, each modification has to be done carefully and long lasting and should be appropriate for the future unknown demand. To take this into account, we present the robust network design problem for railway infrastructure under capacity constraints and uncertain timetables. Here, we plan the required expansion measures for an uncertain long‐term timetable. We show that this problem is NP‐hard even when restricted to bipartite graphs and very simple timetables and present easier solvable special cases. This problem corresponds to the fixed‐charge network design problem where the expansion costs are minimized such that the timetable is conductible. We model this problem by an integer linear program using time expanded networks. To incorporate the uncertainty of the future timetable, we use a scenario‐based approach. We define scenarios with individual departure and arrival times and optional trains. The network is then optimized such that a given percentage of the scenarios can be operated while minimizing the expansion costs and potential penalty costs for not scheduled optional trains.

Designing a two-stage model for the resilient agri-food supply chain network under dynamic competition

PurposeSupply chain risk management can effectively reduce the loss of retailers. In this regard, retailers need to consider the competition risks of competitors in addition to the disruption risks. This paper designs a resilient retail supply chain network for perishable foods under the dynamic competition to maximize retailer's profits.Design/methodology/approachA two-stage mixed-integer non-linear model is presented for designing the supply chain network. In the first stage, an equilibrium model that considers the characteristics of perishable foods is developed. In the second stage, a mixed integer non-linear programming model is presented to deal with the strategic decisions. Finally, an efficient memetic algorithm is designed to deal with large-scale problems.FindingsThe optimal the selection of suppliers, distribution centers and the order allocation are found among the supply chain entities. Considering the perishability of agri-food products, the equilibrium retail price and selling quantity are determined. Through a numerical example, the optimal inventory period under different maximum shelf life and the impact of three resilient strategies on retailer's profit, selling price and selling quantity are analyzed.Research limitations/implicationsAs for future research, the research can be extended in a number of directions. First, this paper studies the retail supply chain network design problem under competition among retailers. It can be an interesting direction to consider retailers competing with suppliers. Second, the authors can try to linearize the non-linear model and solve the large-scale integer programming problem by exact algorithm. Finally, the freshness of perishable foods gradually declines linearly to zero as the maximum shelf life approaches, and it would be a meaningful attempt to consider the freshness of perishable foods declines exponentially.Originality/valueThis paper innovatively designs the resilient supply chain network for perishable foods under dynamic competition. The retailer's dynamic competition and resilient strategies are considered simultaneously when designing supply chain network for perishable foods. In addition, this paper gives insights into how to obtain the optimal inventory period and compare the retailer's resilient strategies.

Restorable Shortest Path Tiebreaking for Edge-Faulty Graphs

The restoration lemma by Afek et al. [ 3 ] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as the concatenation of two original shortest paths. However, the lemma is tiebreaking-sensitive : if one selects a particular canonical shortest path for each node pair, it is no longer guaranteed that one can build replacement paths by concatenating two selected shortest paths. They left as an open problem whether a method of shortest path tiebreaking with this desirable property is generally possible. We settle this question affirmatively with the first general construction of restorable tiebreaking schemes . We then show applications to various problems in fault-tolerant network design. These include a faster algorithm for subset replacement paths, more efficient fault-tolerant (exact) distance labeling schemes, fault-tolerant subset distance preservers and + 4 additive spanners with improved sparsity, and fast distributed algorithms that construct these objects. For example, an almost immediate corollary of our restorable tiebreaking scheme is the first nontrivial distributed construction of sparse fault-tolerant distance preservers resilient to three faults.

A multi-product and multi-period supply chain network design problem with price-sensitive demand and incremental quantity discount

Demand is an important factor in supply chain network design (SCND). Among the many factors that affect demand, the impact of price cannot be underestimated. This study, for the first time, provides enterprises with direct multi-period pricing and demand decision solutions in SCND by simultaneously considering the impact of price-sensitive demand and incremental quantity discounts on the network. In this way, a mixed-integer nonlinear programming model is established based on the relationships between price and demand functions to maximize the overall profit of the supply chain. Due to the nonlinear characteristics of the model, this study proves the existence of the optimal solution of the problem and the feasibility of implementing the following two algorithms by analyzing the nature of the problem. The first algorithm is based on the second-order cone programming (SOCP) method, and the second algorithm is based on the outer-approximation method. The results of numerical experiments at different scales show that the SOCP method can obtain the optimal solution for small and medium-scale experiments. In contrast, the outer-approximation method can find approximate optimal solutions within a reasonable time for large-scale experiments. The results confirm that considering incremental quantity discount can significantly enhance the profitability of supply chain networks in long-term planning. Finally, some future research directions in the field of SCND are discussed.

A two-stage stochastic model for a multi-objective blood platelet supply chain network design problem incorporating frozen platelets

Platelet supply chain (PLT SC) management is always a challenging task for healthcare systems due to the nature of platelets (PLTs). PLTs have an extremely short shelf life and their demand is highly uncertain, which may lead to a high percentage of wastage and shortage in the corresponding PLT SC. This paper proposes a two-stage stochastic programming (2SSP) model to investigate the opportunity of incorporating frozen PLTs (FPLTs) into the PLT SC to see how it can improve the performance of the PLT SC in which the PLTs are used only in liquid form with respect to the platelet shortage, wastage and substitution penalties in transfusions. To investigate a more realistic situation when clear targets of blood shortage, wastage and substitution penalties are available, an extended goal programming model is built based on the proposed 2SSP model. Furthermore, we generate scenarios based on the real data provided by healthcare practitioners using the combination of a top-down forecasting approach and a Monte Carlo based scenario generation method. From the experimental results we note that, when comparing the model that incorporates FPLTs with the one that doesn't, the average reduction rates for platelet shortages, wastage, and substitution penalties in transfusions are 0.55, 0.55, and 0.23, respectively, when 40% of the overall demand is from patients who can receive both liquid PLTs and thawed PLTs sourced from FPLTs (Patient Type I). These rates can be further improved to 0.64, 0.55 and 0.23 or 0.65, 0.55 and 0.23 when 50% or 60% of the total demand is from Patient Type I. Furthermore, in contrast to real-world performance, the output of the 2SSP model, when not incorporating FPLTs, results in notable reductions in platelet shortage, wastage, and substitution penalties by 95%, 56% and 18%, respectively.

Vaccine supply chain network design by considering viability, robustness and risk

This study aims to develop a solution for the Viable Vaccine Supply Chain Network Design (VVSCND) problem, which concurrently addresses multiple factors such as sustainability, resiliency, agility, risk, and robustness. To achieve this, the researchers propose a Mixed-Integer Linear Programming (MILP) model based on a Robust Stochastic Programming (RSP) approach, which minimizes the weighted expected and max cost function. Furthermore, the research considers factors such as limiting CO2 emissions, introducing flexible capacity, and ensuring the reliability and redundancy of facilities to establish a more agile and environmentally sustainable supply chain. The key decisions in the proposed methodology involve determining facility location and product flow within an efficient healthcare system. According to the findings, the cost function of the VVSCND problem was only marginally higher, by 0.04%, than its counterpart in a VSCND that did not consider any risks or worst-case scenarios. However, increasing the conservatism coefficient or agility coefficient by 50% and 10%, respectively, leads to similar increases in the cost function. Similarly, the resiliency coefficient has a direct relationship with the cost function. Overall, the study demonstrates that an optimal VSCND can be achieved by considering multiple factors through RSP-based MILP modeling.

Machine Learning for Robust Network Design: A New Perspective

With the rapid growth of backbone networks and data center networks, ensuring network robustness under various failure scenarios has become a key challenge in network design. The combinatorial nature of failure scenarios in data plane, control plane, and management plane seriously challenges existing practice on robust network design, which often requires verifying the designed network's performance by enumerating all possible failure combinations. Meanwhile, machine learning (ML) has been applied to many networking problems and has shown tremendous success. In this article, we show a general approach to leveraging machine learning to support robust network design. First, we give a selective overview of current work on robust network design and show that failure evaluation provides a common kernel to improve the tractability and scalability of existing solutions. Then we propose a function approximation of the common kernel based on graph attention network (GAT) to efficiently evaluate the impact of various potential failure scenarios and identify critical failures that may have significant consequences. The function approximation allows us to obtain new models of three important robust network design problems and to solve them efficiently by evaluating the solutions against a pruned set of critical failures. We evaluate our approach in the three use cases and demonstrate significant reduction in time-tosolution with minimum performance gap. Finally, we discuss how the proposed framework can be applied to many other robust network design problems.

Multi-objective optimisation of sustainable closed-loop supply chain networks in the tire industry

As environmental concerns and social legislation continue to gain importance, supply chain decision-makers are increasingly required to consider economic and ecological objectives. A potential strategy for mitigating sustainability issues entails the utilisation of discarded tyres through the process of recycling. Nevertheless, the establishment of a closed-loop supply chain that is both sustainable and profitable presents a noteworthy challenge. This study proposes a novel multi-objective mixed-integer linear programming model to design a sustainable closed-loop supply chain network in the tire industry. The objective of the model is to optimize the overall cost of the network, taking into account the environmental consequences related to the establishment of facilities, tire processing, and transportation. While metaheuristic algorithms have been extensively employed to solve network design problems, they are not very effective in handling large-scale networks. To overcome this limitation, our study introduces six new multi-objective evolutionary algorithms based on decomposition (MOEA/D) variants. The present study introduces a prospective methodology for devising supply chain networks that are sustainable in nature, while simultaneously ensuring a harmonious equilibrium between economic and environmental considerations. The efficacy of the proposed multi-objective mixed-integer linear programming model and its MOEA/D variants in addressing large-scale networks has been demonstrated through the obtained results. As such, this study contributes to sustainable supply chain management, which is becoming increasingly important in the current environment.

Better-than-43\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{4}{3}$$\\end{document}-approximations for leaf-to-leaf tree and connectivity augmentation

The Connectivity Augmentation Problem (CAP) together with a well-known special case thereof known as the Tree Augmentation Problem (TAP) are among the most basic Network Design problems. There has been a surge of interest recently to find approximation algorithms with guarantees below 2 for both TAP and CAP, culminating in the currently best approximation factor for both problems of 1.393 through quite sophisticated techniques. We present a new and arguably simple matching-based method for the well-known special case of leaf-to-leaf instances. Combining our work with prior techniques, we readily obtain a (4/3+ε)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(4/3+\\varepsilon )$$\\end{document}-approximation for Leaf-to-Leaf CAP by returning the better of our solution and one of an existing method. Prior to our work, a 4/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4/3$$\\end{document}-guarantee was only known for Leaf-to-Leaf TAP instances on trees of height 2. Moreover, when combining our technique with a recently introduced stack analysis approach, which is part of the above-mentioned 1.393-approximation, we can further improve the approximation factor to 1.29, obtaining for the first time a factor below 43\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{4}{3}$$\\end{document} for a nontrivial class of TAP/CAP instances.

An uncertain multi-objective model for simultaneous design of supply chain and assemblers considering sustainable development: a case study

Supply chain network design (SCND) problems are used to formulate and make strategic decisions on the number of facilities, network facility location and plant capacity, to ensure the optimal delivery of products from manufacturers to end consumers. On the other hand, assembly line balancing (ALB) problems provide details on operational decisions which encompass production levels and inventories and therefore should be flexible enough to react when changes in resource availability and product demands occur. Integration of the SCND and ALB problems has thus been explored to develop a more holistic model and to further improve the efficiency of the supply chain. This study develops a novel SCND-ALB optimization model which considers economic, environmental, and social objectives in determining the optimal design and operational conditions of the supply chain under flexible cycle time of the assembly lines. Furthermore, for the first time a zigzag type belief degree model is integrated to address system uncertainties of the SCND-ALB problem. Two multi-objective solution approaches are then considered to simultaneously account for the three sustainability objectives. A case study on the production of a nozzle is explored to demonstrate the capabilities of the model.

Robust Design Problem for Multi-Source Multi-Sink Flow Networks Based on Genetic Algorithm Approach

Robust design problems in flow networks involve determining the optimal capacity assignments that enable the network to operate effectively even in the case of events’ occurrence such as arcs or nodes’ failures. Multi-source multi-sink flow networks (MMSFNs) are frequent in many real-life systems such as computer and telecommunication, logistics and supply-chain, and urban traffic. Although numerous studies on the design of MMSFNs have been conducted, the robust design problem for multi-source multi-sink stochastic-flow networks (MMSFNs) remains unexplored. To contribute to this field, this study addresses the robust design problem for MMSFNs using an approach of two steps. First, the problem is mathematically formulated as an optimization problem and second, a sub-optimal solution is proposed based on a genetic algorithm (GA) involving two components. The first component, an outer genetic algorithm, is employed to search the optimal capacity assigned to the network components with minimum sum. The second component, an inner genetic algorithm, is used to find the optimal flow vectors that maximize the system’s reliability. Through extensive experimentation on three different networks with different topologies, the proposed solution has been found to be efficient.

A case-oriented computational study for sustainable fleet planning in a battery closed-loop supply chain network under uncertainty

PurposeThe purpose of this study is to develop a holistic optimization model for an integrated sustainable fleet planning and closed-loop supply chain (CLSC) network design problem under uncertainty.Design/methodology/approachA novel mixed-integer programming model that is able to consider interactions between vehicle fleet planning and CLSC network design problems is first developed. Uncertainties of the product demand and return fractions of the end-of-life products are handled by a chance-constrained stochastic program. Several Pareto optimal solutions are generated for the conflicting sustainability objectives via compromise and fuzzy goal programming (FGP) approaches.FindingsThe proposed model is tested on a real-life lead/acid battery recovery system. By using the proposed model, sustainable fleet plans that provide a smaller fleet size, fewer empty vehicle repositions, minimal CO2 emissions, maximal vehicle safety ratings and minimal injury/illness incidence rate of transport accidents are generated. Furthermore, an environmentally and socially conscious CLSC network with maximal job creation in the less developed regions, minimal lost days resulting from the work's damages during manufacturing/recycling operations and maximal collection/recovery of end-of-life products is also designed.Originality/valueUnlike the classical network design models, vehicle fleet planning decisions such as fleet sizing/composition, fleet assignment, vehicle inventory control, empty repositioning, etc. are also considered while designing a sustainable CLSC network. In addition to sustainability indicators in the network design, sustainability factors in fleet management are also handled. To the best of the authors' knowledge, there is no similar paper in the literature that proposes such a holistic optimization model for integrated sustainable fleet planning and CLSC network design.

Investigating the Optimality of Existing Hubs in Terms of Coverage Capacity and Locating New Hubs for the Green Supply Chain of Medical and Pharmaceutical Equipment

The problem of locating the hub is one of the most important and widely used problems in network design. The deployed hubs can fail over time for various reasons, including disruptions in the processes, in which case excessive costs are imposed on the operating companies. Therefore, proper planning is needed to reduce the harmful effects of environmental disorders. In this regard, we seek to examine the optimization of existing hubs in terms of the capacity of the new hubs and location of the hubs, with the aim of reducing the cost of coverage to reduce the cost and maximizing the level of green hubs. To this end, the economic benefits of the measures were carried out: the establishment of a new hub, the removal of the previous or current hub, the increase and decrease of the capacity of the hubs. Eventually a new structure of hubs was introduced where the location and capacity of some hubs have changed, but in contrast, the amount of demand coverage has increased.

A blockchain-based system for a network design problem considering pricing decisions and sustainability

The emergence of cryptocurrency and blockchain technology revolutionizes supply chains. In addition, blockchain technology can result in novel models ensuring supply chain transparency, originality, and traceability. This research is aimed to develop a blockchain-based system ascertaining supply chain transparency and originality. To this aim, a joint pricing and sustainable network design model is developed for a closed-loop supply chain. Labeling products with internet-of-thing (IoT) and radio frequency identification (RFID) technology strengthens originality and traceability in this supply chain. Afterward, smart contracts deal with transparency concerns while pricing the used products in reverse flow and controlling CO2 emissions. By triggering smart contracts in disorder time, each facility's optimal price and demand can be optimized in an iterative process until the final solution is yielded. Then, the optimization phase of the blockchain-based system starts using data from a distributed ledger form. Then, a fuzzy satisfying approach is used to find the optimal solution across the Pareto regions. Finally, the model is evaluated using real data from the Hamedan glass industry, and sensitivity analyses are done to derive managerial insights, conducting further practitioners and managers of food, agriculture, health, and other supply chains.

Solving a real-life multi-period trailer-truck waste collection problem with time windows

By introducing local recovery networks, regional and local environmental authorities can play an important role in facilitating the circular economy. This paper studies a network design problem that encompasses the recovery of separately collected household waste streams, which are collected in containers at civic amenity sites. We formulate a generic tactical-operational container collection problem that will be solved using a mixed integer linear programming approach. This paper makes both a theoretical and practical contribution. We are the first to study a two container vehicle capacity restriction combined with collection site inventory capacities, time windows, shift break time, and shift duration constraints. The model is applied to a number of real-life test instances and scenarios. The results provide insight in how different combinations of scenarios exactly affect the fleet requirements. This not only includes the number of trucks or information under which circumstances an additional truck would (not) be needed, but also the 12-day collection schedule for the collection crews.

Humanitarian transportation network design via two-stage distributionally robust optimization

Natural disasters are highly unpredictable, with varying degrees of magnitude, and thus require a reliable and robust humanitarian relief network. Faced with the adverse effects of disasters, we advocate taking pre-disaster preventive actions, e.g., road link strengthening, to mitigate post-disaster disruptions to road networks. In this paper, we study a highly integrated humanitarian relief network design problem, in which the network strengthening plan and inventory pre-positioning scheme are optimized cooperatively. The proposed problem is formulated as a two-stage distributionally robust optimization (DRO) model, in which the first and second stages correspond to pre- and post-disaster relief operations, respectively. By leveraging prior data and the Wasserstein metric, a tailored ambiguity set is constructed to capture both node- and link-wise uncertainties. We demonstrate that the two-stage DRO model over the Wasserstein ambiguity set has an equivalent reformulation that can be solved via the L-shaped method with bilinear subproblems. Based on observations of the problem structure and the spirit of separation optimization, both exact and heuristic approaches are proposed to address the bilinear subproblems. Via the case study of the Yushu earthquake, we highlight the value of jointly optimizing network strengthening and inventory pre-positioning decisions. Specifically, with the same investment budget, integrating network strengthening into inventory pre-positioning can easily achieve an approximately 60% reduction in shortage penalties. Furthermore, our method can produce reliable solutions, based on which we explore several managerial implications.

Transmission line planning using global best artificial bee colony method

Introduction. Network expansion, substation planning, generating expansion planning, and load forecasting are all aspects of modern power system planning. The aim of this work is to solve network planning considering both future demand and all equality and inequality constraints. The transmission network design problem for the 6-bus system is considered and addressed using the Global Best Artificial Bee Colony (GABC) method in this research. The program is written in the Matrix Laboratory in MATLAB environment using the proposed methodology. Novelty of the work consist in considering the behavior of bees to find food source in most optimized way in nature with feature of user based accuracy selection and speed of execution selection on any scale of the system to solve Transmission Lines Expansion Problem (TLEP). The proposed method is implemented on nonlinear mathematical function and TLEP function. When demand grows, the program output optimally distributes new links between new generation buses and old buses, determines the overall minimum cost of those links, and determines if those linkages should meet power system limits. Originality of the proposed method is that it eliminated the need of load shedding while planning the future demand with GABC method. Results are validated using load flow analysis in electrical transient analyzer program, demonstrating that artificial intelligence approaches are accurate and particularly effective in non-linear transmission network planning challenges. Practical value of the program is that it can use to execute cost oriented complex transmission planning decision.

Survivable Network Design with Constrained h-Subgraph Flows

In this paper, we propose a variant of the survivable network design problem, where subgraphs are given flow constraints, which represent upper bounds on weights of outgoing edges with endpoints that belong to vertex subsets of these subgraphs. The general problem of verifying whether the weights of outgoing edges of any vertex subset (i.e. a graph cut) of an arbitrary subgraph meets a certain upper bound is a computationally hard problem. However, our proposed problem considers special types of subgraphs (termed h-subgraphs) which possess a tree structure. In particular, a h-subgraph consists of a trunk whose vertices are connected by a unique path and which are termed as trunk vertices. Each trunk vertex is connected to a branch which also has a tree structure. This special graph structure of h-subgraphs - along with conditions over the flow constraint function and additional constraints on the optimization problem allow for the construction of a polynomial-time algorithm to solve our proposed problem - using efficient separation oracles under the ellipsoid method of linear programming. Our proposed algorithm provides (2pl,2z(S)+3)-performance where p is the maximum length of any path that connects the root and leaves of a branch of any h-subgraph, l is the maximum number of leaves of any branch of a h-subgraph, and S is a vertex subset of a branch of a h-subgraph.