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Optimization transportation cargo and passengers between ports and regions are very important, because industrial regions are located some distance from ports. The demand for energy request for the movement of transport is a necessity in the modern world. Transport and activity called transportation are used daily, everywhere, and a lot of energy is needed to power the various transport modes. Today different transport modes are being used to transport passengers and cargo. It is quite common to use road transport, which can transport passengers and cargo from door to door. Considering alternative possibilities (road, railway and/or inland waterway transport), it is important, based on theoretical and experimentation, to identify optimal solutions. In finding transport modes that are either most technically or economically effective, we could unearth possible solutions which would require minimal energy use. Unfortunately, with increased transportation, this often leads to traffic congestion on the roads, which requires additional energy (fuel). This situation generates requirements from many stakeholders in terms of finding ways to decrease the transportation time and energy (fuel) consumed by transport modes. A theoretical method evaluation is conducted on the optimal transportation possibility that minimizes transportation time and energy (fuel) use by employing graph theory, which is presented in this paper. The scientific contribution is the development of a transport modes comparative index, which is then used for evaluations. This paper presents possible alternative transportation conditions based on a multi-criteria evaluation system, proposes a theoretical basis for the optimal solutions from an eco-economic perspective that considers energy, and provides for experimental testing during a specific case study. The final results from the case study provide recommendations and conclusions.

This paper describes an exact algorithm capable of solving large-scale instances of the well-known uncapacitated hub location problem with multiple assignments . The algorithm applies Benders decomposition to a strong path-based formulation of the problem. The standard decomposition algorithm is enhanced through the inclusion of several features such as the use of a multicut reformulation, the generation of strong optimality cuts, the integration of reduction tests, and the execution of a heuristic procedure. Extensive computational experiments were performed to evaluate the efficiency and robustness of the algorithm. Computational results obtained on classical benchmark instances (with up to 200 nodes) and on a new and more difficult set of instances (with up to 500 nodes) confirm the efficiency of the algorithm.

In most urban public transit rail systems, passengers may need to make several interchanges between different lines to reach their destination. The design of coordinated timetables that enable smooth interchanges with minimal delay for all passengers is a very difficult task. This paper presents a mixed-integer-programming optimization model for this schedule synchronization problem for nonperiodic timetables that minimizes the interchange waiting times of all passengers. A novelty in our formulation is the use of binary variables that enable the correct representation of the waiting times to the \"next available\" train at the interchange stations. By adjusting trains' run times and station dwell times during their trips and their dispatch times, turnaround times at the terminals, and headways at the stations, our model can construct high-quality timetables that minimize transfer waiting times. We also discuss an optimization-based heuristic for the model. We have tested our algorithm for the Mass Transit Railway (MTR) system in Hong Kong, which runs six railway lines with many cross-platform interchange stations. Preliminary numerical results indicate that our approach improves the synchronization significantly compared with the current practice of using fixed headways and trip times. We also explore the trade-offs among different operational parameters and flexibility and their impact on overall passenger waiting times.

This paper presents an extension of the classical capacitated hub location problem with multiple assignments in which the amount of capacity installed at the hubs is part of the decision process. An exact algorithm based on a Benders decomposition of a strong path-based formulation is proposed to solve large-scale instances of two variants of the problem: the splittable and nonsplittable commodities cases. The standard decomposition algorithm is enhanced through the inclusion of features such as the generation of strong optimality cuts and the integration of reduction tests. Given that in the nonsplittable case the resulting subproblem is an integer program, we develop an efficient enumeration algorithm. Extensive computational experiments are performed to evaluate the efficiency and robustness of the proposed algorithms. Computational results obtained on benchmark instances with up to 300 nodes and five capacity levels confirm their efficiency.

In this paper, we describe an effective exact method for solving both the capacitated vehicle routing problem ( cvrp ) and the vehicle routing problem with time windows ( vrptw ) that improves the method proposed by Baldacci et al. [Baldacci, R., N. Christofides, A. Mingozzi. 2008. An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Math. Programming 115 (2) 351-385] for the cvrp . The proposed algorithm is based on the set partitioning (SP) formulation of the problem. We introduce a new route relaxation called ng -route, used by different dual ascent heuristics to find near-optimal dual solutions of the LP-relaxation of the SP model. We describe a column-and-cut generation algorithm strengthened by valid inequalities that uses a new strategy for solving the pricing problem. The new ng -route relaxation and the different dual solutions achieved allow us to generate a reduced SP problem containing all routes of any optimal solution that is finally solved by an integer programming solver. The proposed method solves four of the five open Solomon's vrptw instances and significantly improves the running times of state-of-the-art algorithms for both vrptw and cvrp .

This research mainly focuses on presenting an innovative study of a multi-stage multi-objective fixed-charge solid transportation problem (MMFSTP) with a green supply chain network system under an intuitionistic fuzzy environment. The most controversial issue in recent years is that greenhouse gas emissions such as carbon dioxide, methane, etc. induce air pollution and global warming, thus motivating us to formulate the proposed research. In real-world situations the parameters of MMFSTP via a green supply chain network system usually have unknown quantities, and thus we assume trapezoidal intuitionistic fuzzy numbers to accommodate them and then employ the expected value operator to convert intuitionistic fuzzy MMFSTP into deterministic MMFSTP. Next, the methodologies are constructed to solve the deterministic MMFSTP by weighted Tchebycheff metrics programming and min-max goal programming, which provide Pareto-optimal solutions. A comparison is then drawn between the Pareto-optimal solutions that are extracted from the programming, and thereafter a procedure is performed to analyze the sensitivity analysis of the target values in the min–max goal programming. Finally, we incorporate an application example connected with a real-life industrial problem to display the feasibility and potentiality of the proposed model. Conclusions about the findings and future study directions are also offered.

Bi-objective optimization seeks to obtain Pareto optimal solutions that balance two trade-off objectives, providing guidance for decision making in various fields, particularly in the field of transportation. The novelty of this study lies in two aspects. On the one hand, considering that Pareto optimal solutions are often numerous, finding the full set of Pareto optimal solutions is often computationally challenging and unnecessary for practical purposes. Therefore, we shift the focus of bi-objective optimization to finding a subset of Pareto optimal solutions whose resulting set of nondominated objective vectors is the same as, or at least a good approximation of, the full set of nondominated objective vectors for the problem. In particular, we elaborate three methods for generating a near-optimal subset of Pareto optimal solutions, including the revised ϵ-constraint method, the improved revised ϵ-constraint method, and the augmented ϵ-constraint method. More importantly, the near-optimality of the Pareto optimal solution subset obtained by these methods is rigorously analyzed and proved from a mathematical point of view. This study helps to offer theoretical support for future studies to find the subset of Pareto optimal solutions, which reduces the unnecessary workload and improves the efficiency of solving bi-objective optimization problems while guaranteeing a pre-specified tolerance level.

During past few decades, fuzzy decision is an important attention in the areas of science, engineering, economic system, business, etc. To solve day-to-day problem, researchers use fuzzy data in transportation problem for presenting the uncontrollable factors; and most of multi-objective transportation problems are solved using goal programming. However, when the problem contains interval-valued data, then the obtained solution was provided by goal programming may not satisfy by all decision-makers. In such condition, we consider a fixed-charge solid transportation problem in multi-objective environment where all the data are intuitionistic fuzzy numbers with membership and non-membership function. The intuitionistic fuzzy transportation problem transforms into interval-valued problem using ( α , β ) -cut, and thereafter, it reduces into a deterministic problem using accuracy function. Also the optimum value of alternative corresponds to the optimum value of accuracy function. A numerical example is included to illustrate the usefulness of our proposed model. Finally, conclusions and future works with the study are described.

In the two-echelon capacitated vehicle routing problem (2E-CVRP), the delivery to customers from a depot uses intermediate depots, called satellites . The 2E-CVRP involves two levels of routing problems. The first level requires a design of the routes for a vehicle fleet located at the depot to transport the customer demands to a subset of the satellites. The second level concerns the routing of a vehicle fleet located at the satellites to serve all customers from the satellites supplied from the depot. The objective is to minimize the sum of routing and handling costs. This paper describes a new mathematical formulation of the 2E-CVRP used to derive valid lower bounds and an exact method that decomposes the 2E-CVRP into a limited set of multidepot capacitated vehicle routing problems with side constraints. Computational results on benchmark instances show that the new exact algorithm outperforms the state-of-the-art exact methods.

Classical facility location models like the P -median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that, once constructed, the facilities chosen will always operate as planned. In reality, however, facilities \"fail\" from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost, while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable . This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a trade-off curve between the day-to-day operating cost and the expected cost, taking failures into account, and we use these trade-off curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.