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The functionality of infrastructures, particularly in densely populated areas, is greatly impacted by natural disasters, resulting in uncertain networks. Thus, it is important for crisis management professionals and computer-based systems for transportation networks (such as expert systems) to utilize trustworthy data and robust computational methodologies when addressing convoluted decision-making predicaments concerning the design of transportation networks and optimal routes. This study aims to evaluate the vulnerability of paths in post-disaster transportation networks, with the aim of facilitating rescue operations and ensuring the safe delivery of supplies to affected regions. To investigate the problem of links' tolerances in uncertain networks and the resiliency and reliability of paths, an uncertainty theory-based model that employs minmax optimization with a bottleneck objective function is used. The model addresses the uncertain maximum reliable paths problem, which takes into account uncertain risk variables associated with links. Rather than using conventional methods for calculating the deterministic tolerances of a single element in combinatorial optimization, this study introduces a generalization of stability analysis based on tolerances while the perturbations in a group of links are involved. The analysis defines set tolerances that specify the minimum and maximum values that a designated group of links could simultaneously fluctuate while maintaining the optimality of the max-type reliable paths. The study shows that set tolerances can be considered as well-defined and proposes computational methods to calculate or bound such quantities - which were previously unresearched and difficult to measure. The model and methods are demonstrated to be both theoretically and numerically efficient by applying them to four subnetworks from our case study. In conclusion, this study provides a comprehensive approach to addressing uncertainty in reliability problems in networks, with potential applications in various fields.

Designing an optimal machine trail network is a complex locational problem that requires an understanding of different machines’ operations and terrain features as well as the trade-offs between various objectives. With the overall goal to minimize the operational costs of the logging operation, this paper proposes a mathematical optimization model for the trail network design problem and a greedy heuristic method based on different randomized search scenarios aiming to find the optimal location of machine trails —with potential to reduce negative environmental impact. The network is designed so that all trees can be reached and adapted to how the machines can maneuver while considering the terrain elevation's influence. To examine the effectiveness and practical performance of the heuristic and the optimization model, it was applied in a case study on four harvest units with different topologies and shapes. The computational experiments show that the heuristic can generate solutions that outperform the solutions corresponding to conventional, manual designs within practical time limits for operational planning. Moreover, to highlight certain features of the heuristic and the parameter settings’ effect on its performance, we present an extensive computational sensitivity analysis.

The foundations of efficient management are laid on transport networks in various scientific and industrial fields. Nonetheless, establishing an optimum transport network design (TND) is complicated due to uncertainty in the operating environment. As a result, an uncertain network may be a more realistic representation of an actual transport network. The present study deals with an uncertain TND problem in which uncertain programming and the greedy randomized adaptive search procedure (GRASP) are used to develop an original optimization framework and propose a solution technique for obtaining cost-efficient designs. To this end, we originally develop the concept of α-shortest cycle (α-SC) employing the pessimistic value criterion, given a user-defined predesignated confidence level α. Employing this concept and the operational law of uncertain programming, a new auxiliary chance-constrained programming model is established for the uncertain TND problem, and we prove the existence of an equivalence relation between TNDs in an uncertain network and those in an auxiliary deterministic network. Specifically, we articulate how to obtain the uncertainty distribution of the overall optimal uncertain network's design cost. After all, the effectiveness and practical performance of the heuristic and optimization model is illustrated by adopting samples with different topology from a case study to show how our approach work in realistic networks and to highlight some of the heuristic's features.

The study of complex networks is a new powerful tool that can provide a profitable skeleton to better elucidate technology-related phenomena and interactions between components of real-world networks However, it is not easy to predict the communal behavior of such systems from their elements and on the other hand, the failure of one or few elements can trigger the failure of other elements throughout the network, resulting in network breakdown and catastrophic events at large scales. Therefore, developing predictive mathematical techniques to examine complex networks is one of the biggest challenges of the present time. Knowing that link failure prediction is less studied in the OR literature, the present study articulates a method to predict link failures in complex networks, which is primarily based on Bayesian Belief Networks (BBN) and TOPSIS. The method aims to predict failures based on the affective factors of failures in networks. To this end, effective factors of failures are first detected, and then the graph of the relationship of factors along with their weight is determined. After all, the method provides the prediction for future damaged components. The functionality of the method is validated by an extensive computational analysis employing simulation in scale-free, random, and actual international aviation networks and its performance is compared with other benchmark algorithms. The results and sensitivity analysis experiments arrive at prominent managerial insights and efficacious implications and show that our method can generate high-quality solutions in many networks.

Ground-based mechanized forestry requires the traversal of terrain by heavy machines. The routes they take are often called machine trails, and are created by removing trees from the trail and placing the logs outside it. Designing an optimal machine trail network is a complex locational problem that requires understanding how forestry machines can operate on the terrain as well as the trade-offs between various economic and ecological aspects. Machine trail designs are currently created manually based on intuitive decisions about the importance, correlations, and effects of many potentially conflicting aspects. Badly designed machine trail networks could result in costly operations and adverse environmental impacts. Therefore, this study was conducted to develop a holistic optimization framework for machine trail network design. Key economic and ecological objectives involved in designing machine trail networks for mechanized cut-to-length operations are presented, along with strategies for simultaneously addressing multiple objectives while accounting for the physical capabilities of forestry machines, the impact of slope, and operating costs. Ways of quantitatively formulating and combining these different aspects are demonstrated, together with examples showing how the optimal network design changes in response to various inputs.

In transportation via containers, unbalanced movement of loaded containers forces shipping companies to reposition empty containers. This study addresses the problem of empty container repositioning (ECR) in the distribution network of a European logistics company, where some restrictions impose decision making in an uncertain environment. The problem involves dispatching empty containers of multiple types and various conditions (dirty and clean) to meet the on-time delivery requirements and repositioning the other containers to terminals, depots, and cleaning stations. A multi-period optimization model is developed to help make tactical decisions under uncertainty and data shortage for flow management of empty containers over a predetermined planning horizon. Employing the operational law of uncertainty programming, a new auxiliary chance-constrained programming is established for the ECR problem, and we prove the existence of an equivalence relation between the ECR plans in the uncertain network and those in an auxiliary deterministic network. Exploiting this new problem, we give the uncertainty distribution of the overall optimal ECR operational cost. The computational experiments show that the model generates good-quality repositioning plans and demonstrate that cost and modality improvement can be achieved in the network.

Multi-period multi-product distribution planning problems are depicted as multi-commodity network flow problems where parameters may change over time. The corresponding mathematical formulation is presented for a discrete time setting, and it can also be used as an approximation for a continuous time setting. A penalty-based method which employs a cost-scaling approach is developed to solve some auxiliary penalty problems aiming to obtain an optimal solution for the original problem. The experiments on both random instances and case study problems show that the algorithm finds good-quality solutions with reasonable computational effort.