An extended shortest path problem: A data envelopment analysis approach

A special and important network structured linear programming problem is the shortest path problem. Classical shortest path problems assume that there are unit of shipping cost or profit along an arc. In many real occasions, various attributes (various costs and profits) are usually considered in a shortest path problem. Because of the frequent occurrence of such network structured problems, there is a need to develop an efficient procedure for handling these problems. This paper studies the shortest path problem in the case that multiple attributes are considered along the arcs. The concept of relative efficiency is defined for each path from initial node to final node. Then, an efficient path with the maximum efficiency is determined.     

求解物流运输网络SUM-MIN双目标路径问题的扩展标号法

研究了物流运输网络SUM-MIN双目标路径问题. 基于模糊规划方法提出了一种求解SUM-MIN双目标路径问题的目标函数集成方法,以及集成后目标函数的扩展标号法. 在将双目标转化为单目标时,综合考虑了每个目标的边缘评价和两个目标的整体评价因素,通过对每个目标分配的权重将决策者的偏好充分体现到决策过程中,采用广义的模糊目标集成算子形成了相应的折衷规划模型. 最后,通过实例对所提方法进行了说明.     

An alternate approach to solve two-level hierarchical time minimization transportation problem

This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers (Sharma et al. in Eur J Oper Res 246:700–707, 2015; Sonia and Puri in TOP 12(2):301–330, 2004; Xie et al. in Comput Oper Res 86:124–139, 2017) and therefore, a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem, of different sizes validates the efficiency of the proposed algorithm.

     

An optimization approach for winner determination problem considering transportation cost discounts

Journal of Global Optimization - This study proposes a mixed-integer nonconvex programming (MINP) model for the winner determination problem (WDP) considering two discount functions in a...     

An approach for solving a modification of the extended rapid transit network design problem

In this paper we deal with a slight modification of the extended rapid transit network design problem to allow circular lines. A two-stage approach is proposed for solving this problem. In the first stage, an integer model is solved for selecting the stations to be constructed and the links between them. It drastically reduces the dimension of a modification of a 0–1 model given in the literature to adapt it to our problem. In the second stage, the line design problem is solved by means of a procedure that assigns each selected link to exactly one line under certain constraints. We report some computational experiments that show that our approach also produces a drastic reduction on the computational effort required for solving the modification of the 0–1 model given in the literature.     

A fuzzy approach to the transportation problem

The transportation problem with fuzzy supply values of the deliverers and with fuzzy demand values of the receivers is analysed. For the solution of the problem the technique of parametric programming is used. This makes it possible to obtain not only the maximizing solution (according to the Bellman-Zadeh criterion) but also other alternatives close to the optimal solution.     

An equitable DEA-based approach for assigning fixed resources along with targets

A typical problem in organization management is how to divide a fixed resource along with a target among decision making units (DMUs) of an organization equitably. By using the data envelopment analysis technique, this paper concerns the problem from the perspective of efficiency analysis and proposes a new sharing model. In the proposed method, the fixed resource and target are divided among DMUs such that the efficiencies of DMUs remain unchanged after assigning the fixed cost and target. The proposed method is unit-invariant; it eliminates resource waste and target insufficiency brought by slacks. Also, every DMU is assigned a positive resource and a positive target under this method. Two corresponding algorithms are designed to yield a unique allocation. The proposed approach can be developed under both constant returns to scale and variable returns to scale. Two examples are presented to illustrate the validity and superiorities of our method.     

Completing extended metric spaces: An alternative approach

This paper proves the completion of extended metric spaces using the concept of $\epsilon$-approach nearness spaces, in terms of clusters that are a generalization of Cauchy sequences.     

A heuristic approach to a single stage assembly problem with transportation allocation

Determining assembly scheduling and transportation allocation are two practical problems that industries face, such as the electronics and health products industries. Problems associated with assembly scheduling mainly focus on how to determine the orders’ processing sequence on the assembly line in order to minimize the waiting times before they are flown to their destinations. Problems associated with transportation allocation arise in the system of assigning processed orders to transport modes with the purpose of minimizing penalties from earliness and tardiness. To minimize overall delivery costs, businesses should decide on assembly scheduling and transportation allocation decision simultaneously. However, since simultaneously making these two decisions is not an easy task, most of the works done on them usually deal with these two problems separately. Apart from previous works, this paper establishes a mixed integer programming model that deals with these problems simultaneously. Due to the computational complexity of the problem, this paper develops a hybrid heuristic algorithm to solve this problem, and we evaluate the performance of the presented heuristic algorithm with the well-known GAMS/BARON and Lingo commercial software, which tests the heuristic algorithm on randomly-generated problems. The presented heuristic algorithm is shown to perform well compared with well-known commercial software.     

A decentralized two-level transportation problem in a housing material manufacturer: Interactive fuzzy programming approach

In this paper, we deal with a transportation problem in a housing material manufacturer and derive a satisfactory solution to the problem by taking into account not only the degree of satisfaction with respect to objectives of the housing material manufacturer but also those of two forwarding agents to which the housing material manufacturer entrusts transportation of products. The two forwarding agents handle the regular transportation and the small lot transportation, and each of them assigns work force, the transformation tasks properly. There are two objectives in the housing material manufacturer: one is to minimize the transportation cost and the other is to minimize the opportunity loss with respect to transportation time. The objectives of the two forwarding agents are to maximize their profits. We formulate the transportation planning and work force assignment problem as a decentralized two-level integer programming problem, and derive a satisfactory solution by applying an interactive fuzzy programming method.     

A heuristic approach to the multi-period multi-commodity transportation problem

This paper describes an approach to solving a real-world problem which involves the transportation of multiple types of commodities from a number of sources to a number of destinations in discrete time periods, using a capacitated heterogeneous fleet of vehicles. The preliminary objective is to minimize the total number of discrete periods needed to complete the entire operation. The problem is first formulated as a mixed integer programme and its tractability is then greatly improved by reformulating it through backward decomposition into two separate models and solved iteratively. A heuristic approach harnessing specific features of the second approach is developed for solving large size problems to obtain near-optimal solutions within reasonable time. The design of the heuristic also takes into consideration the secondary objectives of minimizing the total vehicle capacity used and minimizing the total capacity of sources needed to satisfy the demands at the destinations. Computational results are provided for a variety of randomly generated problems as well as problems from the literature. The approach described here may be applied to the multi-period transportation of personnel and goods from multiple starting points to multiple destinations in both military and civilian applications.     

An extended controllability problem with minimum energy

The aim of this paper is to consider an output controllability problem. It consists in driving the state of a distributed parabolic system toward a state between two prescribed functions on a boundary subregion of the system evolution domain with minimum energy control. Two necessary conditions are given. The first is formulated in terms of the subdifferential associated with a minimized functional. The second is formulated as a system of equations for arguments of the Lagrange systems. Numerical illustrations show the efficiency of the second approach and lead to open questions. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.     

An approach for analysing transportation costs and a case study

One of the important parameters in the determination of optimal transportation system is economy. Therefore, a realistic method based on the technical, economical and operational parameters of various transportation modes, namely, road, railway, and sea routes is required in the analysis of costs. This method will take into consideration the probable price escalations during the lifetime of a certain transportation system. The cost of a unit of cargo or passenger per route length should be considered since it is an indicator of economics. In this paper, an approach for transportation cost analysis based on the economic analysis of the alternative modes of cargo or passenger transportation, is presented.     

An approach for solving a class of transportation scheduling problems

An algorithm is developed for solving a class of transportation scheduling problems. It applies for a variety of problems such as: the Combining Truck Trip problem, the Delivery problem, the School Bus problem, the Assignment of Buses to Schedules, and the Travelling Salesman problem. The objective functions of the above problems differ from each other. Yet, by using the “savings method” proposed by Clarke and Wright, and extended by Gaskell, we are able to define each one of the above problems as a series of assignment problems. The cost matrix entries of each one of the assignment problems are a function of the constraints of the particular routing or scheduling problem. The solution to the assignment problem determines an upper bound of the optimal solution to the original problem. By combining the above procedure with a Branch and Bound procedure, it is possible to obtain the optimal solution in a finite number of steps. In some cases the Branch and Bound process can be eliminated due to the nature of the problem and in those cases the algorithm is efficient.     

An extended and tractable approach on the convergence problem of the mixed push-pull manpower model

In this paper, the asymptotic behavior of the time-homogeneous mixed push-pull manpower model is studied under the assumption that the desired stock vector and the recruitment policy are fixed over time. In the mixed push-pull manpower model, the internal mobility of a personnel system can be regulated by both pull and push transitions. Based on those characteristics, we express and examine the dynamics of the personnel system by formulating the mixed push-pull manpower model by means of particular transition matrices, which we demonstrate to have interesting properties. We show that under certain conditions the stock vector converges. An explicit analytical form for this limiting personnel stock vector is found.     

An extended class of orthogonal polynomials defined by a Sturm-Liouville problem

We present two infinite sequences of polynomial eigenfunctions of a Sturm-Liouville problem. As opposed to the classical orthogonal polynomial systems, these sequences start with a polynomial of degree one. We denote these polynomials as X₁-Jacobi and X₁-Laguerre and we prove that they are orthogonal with respect to a positive definite inner product defined over the compact interval [−1,1] or the half-line [0,∞), respectively, and they are a basis of the corresponding L² Hilbert spaces. Moreover, we prove a converse statement similar to Bochner's theorem for the classical orthogonal polynomial systems: if a self-adjoint second-order operator has a complete set of polynomial eigenfunctions , then it must be either the X₁-Jacobi or the X₁-Laguerre Sturm-Liouville problem. A Rodrigues-type formula can be derived for both of the X₁ polynomial sequences.     

Risk-control approach for bottleneck transportation problem with randomness and fuzziness

Solving transportation problems is essential in engineering and supply chain management, where profitability depends on optimal traffic flow. This study proposes risk-control approaches for two bottleneck transportation problems with random variables and preference levels to objective functions with risk parameters. Each proposed model is formulated as a multiobjective programming problem using robust-based optimization derived from stochastic chance constraints. Since it is impossible to obtain a transportation pattern that optimizes all objective functions, our proposed models are numerically solved by introducing an aggregation function for the multiobjective problem. An exact algorithm that performs deterministic equivalent transformations and introduces auxiliary problems is also developed.