Fuzzy goal programming for multiobjective transportation problems

Several fuzzy approaches can be considered for solving multiobjective transportation problem. This paper presents a fuzzy goal programming approach to determine an optimal compromise solution for the multiobjective transportation problem. We assume that each objective function has a fuzzy goal. Also we assign a special type of nonlinear (hyperbolic) membership function to each objective function to describe each fuzzy goal. The approach focuses on minimizing the negative deviation variables from 1 to obtain a compromise solution of the multiobjective transportation problem. We show that the proposed method and the fuzzy programming method are equivalent. In addition, the proposed approach can be applied to solve other multiobjective mathematical programming problems. A numerical example is given to illustrate the efficiency of the proposed approach.     

Inverse problems of reconstructing parameters of the Navier-Stokes system

An inverse problem of reconstructing parameters not known a priori of the dynamical system described by the boundary-value problem for the Navier-Stokes system is considered. The reconstruction is based on one piece of admissible information or another about the motion of the dynamical system (solution of the corresponding boundary-value problem). In particular, one of the problems considered is the inverse problem consisting of reconstruction of the a priori unknown right-hand side of the Navier-Stokes system. The right-hand side characterizes the density of exterior mass forces acting on the system. This problem, as well as many other similar problems, is ill-posed. Two methods are proposed for its solution: the statistical method and the dynamical method. These methods use different initial information. In solving the problem by using the statistical method, initial information for the solution is the results of approximate measurement (in one sense or another) of the motion of the dynamical system on a given interval of time. Here, the reconstruction is performed after the corresponding interval of time. For solution of the problem by this method, the concepts and constructions of open-loop control theory are used. In solving the problem by using the dynamical method, initial information for its solution is the results of approximate (in one sense or another) measurements of the current states of the system, which are dynamically obtained by the observer. Here, the reconstruction is dynamically performed during the process. For solution of the problem by the dynamical method, the concepts and constructions of the dynamical regularization method based on positional control theory are used. Also, the author considers various modifications and regularizations of the methods for solution of problems proposed that are based on one piece of a priori information or another about the desired solution and solvability conditions of the problem. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 26, Nonlinear Dynamics, 2005.     

Fuzzy Linear Programming Approach for Solving Fuzzy Transportation Problems with Transshipment

To find the fuzzy optimal solution of fuzzy transportation problems it is assumed that the direct route between a source and a destination is a minimum-cost route. However, in actual application, the minimum-cost route is not known a priori. In fact, the minimum-cost route from one source to another destination may well pass through another source first. In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy transportation problems with the following transshipment: (1) From a source to any another source, (2) from a destination to another destination, and (3) from a destination to any source. In the proposed method all the parameters are represented by trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem with transshipment is solved. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems with transshipment occurring in real life situations.     

Optimal fleet composition and periodic routing of offshore supply vessels

The supply vessel planning problem is a maritime transportation problem faced by amongst others the energy company Statoil. A set of offshore installations requires supplies from an onshore supply depot on a regular basis, a service performed by a fleet of offshore supply vessels. The problem consists of determining the optimal fleet composition of offshore supply vessels and their corresponding weekly voyages and schedules. We present a voyage-based solution method for the supply vessel planning problem. A computational study shows how the solution method can be used to solve real-life problems. Statoil has implemented a planning tool based on the voyage-based solution method and reports significant savings.     

Cross decomposition applied to the stochastic transportation problem

In this paper we give a solution method for the stochastic transportation problem based on Cross Decomposition developed by Van Roy (1980). Solution methods to the derived sub and master problems are discussed and computational results are given for a number of large scale test problems. We also compare the efficiency of the method with other methods suggested for the stochastic transportation problem: The Frank-Wolfe algorithm and separable programming.     

Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems

To the best of our knowledge till now there is no method in the literature to find the exact fuzzy optimal solution of unbalanced fully fuzzy transportation problems. In this paper, the shortcomings and limitations of some of the existing methods for solving the problems are pointed out and to overcome these shortcomings and limitations, two new methods are proposed to find the exact fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as LR flat fuzzy numbers. To show the advantages of the proposed methods over existing methods, a fully fuzzy transportation problem which may not be solved by using any of the existing methods, is solved by using the proposed methods and by comparing the results, obtained by using the existing methods and proposed methods. It is shown that it is better to use proposed methods as compared to existing methods.     

Decision Networks

Decision Networks is a technique for solving problems which involve a sequence of decisions. It is similar in style to critical path analysis in that it consists of arrow diagrams which give a visual representation of the problem and are used as a basis for a simple calculation procedure. The technique can deal with deterministic and stochastic problems and in the latter case is more general than decision trees. The decision network approach meets the need for a method of solution for multi-stage decision problems which is easily understood, helps the user to visualize the nature of the problem and is routine in application.     

A repeated matching heuristic for the single-source capacitated facility location problem

Facility location models form an important class of integer programming problems, with application in many areas such as the distribution and transportation industries. An important class of solution methods for these problems are so-called Lagrangean heuristics which have been shown to produce high quality solutions and which are at the same time robust. The general facility location problem can be divided into a number of special problems depending on the properties assumed. In the capacitated location problem each facility has a specific capacity on the service it provides. We describe a new solution approach for the capacitated facility location problem when each customer is served by a single facility. The approach is based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied. The method generates feasible solutions in each iteration in contrast to Lagrangean heuristics where problem dependent heuristics must be used to construct a feasible solution. Numerical results show that the approach produces solutions which are of similar and often better than those produced using the best Lagrangean heuristics.     

满意度优化运输问题

传统运输问题只考虑配送方案的效率, 而不考虑参与者对配送方案的满意度. 通过引入参与者对配送方案的满意度这一概念, 提出了满意度优化运输问题, 构建了以最大化相对公平为目标的满意度优化运输模型, 并证明了: (1) 当运输问题的可行域不空时, 新模型的解集非空; (2) 从满意度的角度来看, 新模型的解是唯一的. 另外, 还给出了新模型的求解方法. 研究结果进一步丰富了运输问题的类型, 可为解决其他类型运输问题提供借鉴.     

Transportation Problems with Inadmissible Routes

Transportation problems with inadmissible routes (routes that cannot be used) need not have a feasible solution, even if the total supply exceeds the total demand. A method for adjusting the demands equitably to obtain a feasible solution is presented. The algorithm used generates a feasible minimum cost solution in roughly twice the amount of time that it would take to solve a transportation problem of the same size. It is shown how the solution time is reduced by aggregating the adjustment of demands and decomposing the cost minimization.     

A truck scheduling problem arising in intermodal container transportation

We address a truck scheduling problem that arises in intermodal container transportation, where containers need to be transported between customers (shippers or receivers) and container terminals (rail or maritime) and vice versa. The transportation requests are handled by a trucking company which operates several depots and a fleet of homogeneous trucks that must be routed and scheduled to minimize the total truck operating time under hard time window constraints imposed by the customers and terminals. Empty containers are considered as transportation resources and are provided by the trucking company for freight transportation. The truck scheduling problem at hand is formulated as Full-Truckload Pickup and Delivery Problem with Time Windows (FTPDPTW) and is solved by a 2-stage heuristic solution approach. This solution method was specially designed for the truck scheduling problem but can be applied to other problems as well. We assess the quality of our solution approach on several computational experiments.     

A limited-feedback approximation scheme for optimal switching problems with execution delays

We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a probabilistic method. The main contribution is, however, a scheme for approximating the optimal control by limiting the information in the state-feedback. In a numerical example the approximation routine gives a considerable computational performance enhancement when compared to a conventional algorithm.     

A Note on Resolution of Degeneracy in Transportation Problems

Degeneracy in transportation problems is a frequent phenomenon. In this paper, a method of obtaining optimal solutions to degenerate transportation problems has been suggested. The method is a modification of the already-known Modified Distribution (MODI) method and consists in proceeding with the non-zero cells of the basis and a dual solution corresponding to these cells—without attempting to complete the basis. It appears that the method proposed here would be more effective than the well-known perturbation method, especially when the problem is highly degenerate.     

多约束水平运输问题的时间费用均衡

基于为顾客提供最佳服务的现代营销理念,剖析了从一定产地到一定销地所发生的运输问题,构建了时间用均衡的目标模式及多目标约束水平MC^2运输问题的数学模型,本文在建立一系列定义,定理的基础上,提出了认明时间费用均衡解空间的优化决策方法,并结合示例展现了这一方法在解决客观实际问题中的有效性。     

A biased random-key genetic algorithm for road congestion minimization

One of the main goals in transportation planning is to achieve solutions for two classical problems, the traffic assignment and toll pricing problems. The traffic assignment problem aims to minimize total travel delay among all travelers. Based on data derived from the first problem, the toll pricing problem determines the set of tolls and corresponding tariffs that would collectively benefit all travelers and would lead to a user equilibrium solution. Obtaining high-quality solutions for this framework is a challenge for large networks. In this paper, we propose an approach to solve the two problems jointly, making use of a biased random-key genetic algorithm for the optimization of transportation network performance by strategically allocating tolls on some of the links of the road network. Since a transportation network may have thousands of intersections and hundreds of road segments, our algorithm takes advantage of mechanisms for speeding up shortest-path algorithms.     

Constrained two-dimensional cutting: an improvement of Christofides and Whitlock's exact algorithm

Christofides and Whitlock have developed a top-down algorithm which combines in a nice tree search procedure Gilmore and Gomory's algorithm and a transportation routine called at each node of the tree for solving exactly the constrained two-dimensional cutting problem. Recently, another bottom-up algorithm has been developed and reported as being more efficient. In this paper, we propose a modification to the branching strategy and we introduce the one-dimensional bounded knapsack in the original Christofides and Whitlock algorithm. Then, by exploiting dynamic programming properties we obtain good lower and upper bounds which lead to significant branching cuts, resulting in a drastic reduction of calls of the transportation routine. Finally, we propose an incremental solution of the numerous generated transportation problems. The resulting algorithm reveals superior performance to other known algorithms.     

Exact solution methods for uncapacitated location problems with convex transportation costs

In this paper we study exact solution methods for uncapacitated facility location problems where the transportation costs are nonlinear and convex. An exact linearization of the costs is made, enabling the formulation of the problem as an extended, linear pure zero–one location model. A branch-and-bound method based on a dual ascent and adjustment procedure is developed, and compared to application of a modified Benders decomposition method. The specific application studied is the simple plant location problem (SPLP) with spatial interaction, which is a model suitable for location of public facilities. Previously approximate solution methods have been used for this problem, while we in this paper investigate exact solution methods. Computational results are presented.     

A new method for solving linear multi-objective transportation problems with fuzzy parameters

There are several methods in the literature for solving transportation problems by representing the parameters as normal fuzzy numbers. Chiang [J. Chiang, The optimal solution of the transportation problem with fuzzy demand and fuzzy product, J. Inform. Sci. Eng. 21 (2005) 439-451] pointed out that it is better to represent the parameters as (λ, ρ) interval-valued fuzzy numbers instead of normal fuzzy numbers and proposed a method to find the optimal solution of single objective transportation problems by representing the availability and demand as (λ, ρ) interval-valued fuzzy numbers. In this paper, the shortcomings of the existing method are pointed out and to overcome these shortcomings, a new method is proposed to find solution of a linear multi-objective transportation problem by representing all the parameters as (λ, ρ) interval-valued fuzzy numbers. To illustrate the proposed method a numerical example is solved. The advantages of the proposed method over existing method are also discussed.     

An Algorithm for Solving Capacitated Multicommodity <Emphasis Type="Italic">p</Emphasis>-median Transportation Problems

An algorithm for solving a special capacitated multicommodity p-median transportation problem (CMPMTP), which arises in container terminal management, is presented. There are some algorithms to solve similar kinds of problems. The formulation here is different from the existing modelling of the p-median or some related location problems. We extend the existing work by applying a Lagrangean relaxation to the CMPMTP. In order to obtain a satisfactory solution, a heuristic branch-and-bound algorithm is designed to search for a better solution, if one is possible. A comparison is also made with different algorithms.     

平衡和不平衡运输问题与分配问题的通用迭代算法

将不平衡运输问题转化成网络最短路问题,利用Floyd算法规则,给出了一种既可以解平衡和不平衡运输问题,又可以解平衡和不平衡分配问题的通用迭代算法。与专门用于解运输问题的闭合回路法和专门用于解分配问题的匈牙利法相比,这种算法不但具有通用的优点,而且更便于在计算机上运行。