A note on asymptotic formulae for one-dimensional network flow problems

This note develops asymptotic formulae for single-commodity network flow problems with random inputs. The transportation linear programming problem (TLP) where N points lie in a region of R¹ is one example. It is found that the average distance traveled by an item in the TLP increases with N^1/2; i.e., the unit cost is unbounded when N and the length of the region are increased in a fixed ratio. Further, the optimum distance does not converge in probability to the average value. These one-dimensional results are a useful stepping stone toward a network theory for two and higher dimensions. Research supported in part by the University of California Transportation Center.     

A robust optimization model for a cross-border logistics problem with fleet composition in an uncertain environment

Since the implementation of the open-door policy in China, many Hong Kong-based manufacturers' production lines have moved to China to take advantage of the lower production cost, lower wages, and lower rental costs, and thus, the finished products must be transported from China to Hong Kong. It has been discovered that logistics management often encounters uncertainty and noisy data. In this paper, a robust optimization model is proposed to solve a cross-border logistics problem in an environment of uncertainty. By adjusting penalty parameters, decision-makers can determine an optimal long-term transportation strategy, including the optimal delivery routes and the optimal vehicle fleet composition to minimize total expenditure under different economic growth scenarios. We demonstrate the robustness and effectiveness of our model using the example of a Hong Kong-based manufacturing company. The analysis of the trade-off between model robustness and solution robustness is also presented.     

The stochastic transportation problem with single sourcing

We propose a branch-and-price algorithm for solving a class of stochastic transportation problems with single-sourcing constraints. Our approach allows for general demand distributions, nonlinear cost structures, and capacity expansion opportunities. The pricing problem is a knapsack problem with variable item sizes and concave costs that is interesting in its own right. We perform an extensive set of computational experiments illustrating the efficacy of our approach. In addition, we study the cost of the single-sourcing constraints.     

带学习效应和资源依赖的单机排序模型

在工业生产中,随着员工操作技能的熟练程度的增加,对于相同的任务越往后加工,所花的时间将会减少。 同时,为了尽早完工,管理者也会考虑给加工工件分配一定量的额外资源来缩短工件加工时间。 本文基于以上实例,讨论了工件的实际加工时间既具有学习效应又依赖所分配资源的单机排序问题。 在问题中,假设工件的学习效应是之前已加工工件正常加工时间和的指数函数。 同时随着分配给工件资源量的增加,工件的实际加工时间呈线性减少,所需费用呈线性增加。对这一排序模型,主要探讨以下五个目标函数:最小化最大完工时间与资源消耗量总费用的和;最小化总完工时间与资源消耗量总费用的和;最小化加权总完工时间与资源消耗量总费用的和;最小化总提前、总延误、总共同交货期与资源消耗量总费用的和以及最小化总提前、总延误、总松弛交货期与资源消耗量总费用的和。 本文对前三个目标函数相应的排序问题给出了多项式时间可求解的算法。 对后两个目标函数所涉及的排序问题借助于指派问题分别给出了时间复杂性为O(n³)的算法。     

Optimizing production and transportation in a commit-to-delivery business mode

In problems involving the simultaneous optimization of production and transportation, the requirement that an order can only be shipped once its production has been completed is a natural one. One example is a problem of optimizing shipping costs subject to a production capacity constraint studied recently by Stecke and Zhao. Here we present an integer programming formulation for the case in which only completed orders can be shipped that leads to very tight dual bounds and enables one to solve instances of significant size to optimality.     

Quasi-linear stochastic programming model based on expectation and variance and its application in transportation problem

The stochastic transportation problem involves in many areas such as production scheduling, facility location, resource allocation, logistics management. Constructing an operable solving method has important theoretical and practical value. In this paper, we first analyze the characteristic and deficiencies of the existing stochastic programming methods, such as higher computation complexity. We then give the concept of reliability coefficient and a quasi-linear processing pattern based on expectation and variance. We further analyze the relationship between reliability coefficient and reliability degree, also give the selecting strategy of reliability coefficient. Based on that, we establish a quasi-linear programming model for stochastic transportation problem, and we analyze its performance by a case-based example. The results indicate that this model has good interpretability and operability. It can effectively solve the transportation problem under complex stochastic environment or with incomplete information.     

Asymptotic Properties of Random Multidimensional Assignment Problems

The multidimensional assignment problem (MAP) is a NP-hard combinatorial optimization problem, occurring in many applications, such as data association. In this paper, we prove two conjectures made in Ref. 1 and based on data from computational experiments on MAPs. We show that the mean optimal objective function cost of random instances of the MAP goes to zero as the problem size increases, when assignment costs are independent exponentially or uniformly distributed random variables. We prove also that the mean optimal solution goes to negative infinity when assignment costs are independent normally distributed random variables.     

Operational scheduling of refined product pipeline with dual purpose depots

Pipelines are one of the most economic and safe ways to transport oil derivatives to depots near the local markets. This is so, especially when there is a need for carrying a huge amount of petroleum products to long distance points. A pipeline may connect several refineries and depots where the connected points are able to inject products or receive them, or both (dual purpose depots). The main point of pipeline scheduling is to identify an optimal sequence of batches that satisfy demand with minimum costs. This paper presents an MILP continuous formulation for pipeline scheduling. The proposed model results in the reduction of problem size with respect to available models, and increases the accuracy. Computational results and data are reported.     

Dynamic journeying under uncertainty

We introduce a journey planning problem in multi-modal transportation networks under uncertainty. The goal is to find a journey, possibly involving transfers between different transport services, from a given origin to a given destination within a specified time horizon. Due to uncertainty in travel times, the arrival times of transport services at public transport stops are modeled as random variables. If a transfer between two services is rendered unsuccessful, the commuter has to reconsider the remaining path to the destination. The problem is modeled as a Markov decision process in which states are defined as paths in the transport network. The main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time. By assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem. Analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination, the proposed approximations may be useful for practical purposes due to their computational simplicity. In addition to on-time arrival probability, we show how travel and overdue costs can be taken into account, making the model applicable to freight transportation problems.     

Capacitated transportation problem with bounds on RIM conditions

Motivated by dead-mileage problem assessed in terms of running empty buses from various depots to starting points, we consider a class of the capacitated transportation problems with bounds on total availabilities at sources and total destination requirements. It is often difficult to solve such problems and the present paper establishes their equivalence with a balanced capacitated transportation problem which can be easily solved by existing methods. Sometimes, total flow in transportation problem is also specified by some external decision maker because of budget/political consideration and optimal solution of such problem is of practical interest to the decision maker and has motivated us to discuss such problem. Various situations arising in unbalanced capacitated transportation problems have been discussed in the present paper as a particular case of original problem. In addition, we have discussed paradoxical situation in a balanced capacitated transportation problem and have obtained the paradoxical solution by solving one of the unbalanced problems. Numerical illustrations are included in support of theory.     

A truncated projected SVD method for linear discrete ill-posed problems

Truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. However, since the singular value decomposition of the matrix is independent of the right-hand side, there are linear discrete ill-posed problems for which this method fails to yield an accurate approximate solution. This paper describes a new approach to incorporating knowledge about properties of the desired solution into the solution process through an initial projection of the linear discrete ill-posed problem. The projected problem is solved by truncated singular value decomposition. Computed examples illustrate that suitably chosen projections can enhance the accuracy of the computed solution.     

Replenishment decisions under an all-units discount schedule and stepwise freight costs

In this study, we analyze the replenishment decisions under a general replenishment cost structure that includes stepwise freight costs and all-units quantity discounts. We first formulate a general model that accounts for a larger class of problems and prove several useful properties of the expected profit function. We later utilize these properties to develop a computational solution approach to find the optimal order quantity. As an application of the general results, we study the replenishment decisions in the single-period, i.e., the Newsboy, problem considering several scenarios that model the cost considerations either for the buyer or for both the buyer and the vendor.     

Operations Research for green logistics – An overview of aspects,issues, contributions and challenges

The worldwide economic growth of the last century has given rise to a vast consumption of goods while globalization has led to large streams of goods all over the world. The production, transportation, storage and consumption of all these goods, however, have created large environmental problems. Today, global warming, created by large scale emissions of greenhouse gasses, is a top environmental concern. Governments, action groups and companies are asking for measures to counter this threat. Operations Research has a long tradition in improving operations and especially in reducing costs. In this paper, we present a review that highlights the contribution of Operations Research to green logistics, which involves the integration of environmental aspects in logistics. We give a sketch of the present and possible developments, focussing on design, planning and control in a supply chain for transportation, inventory of products and facility decisions. While doing this, we also indicate several areas where environmental aspects could be included in OR models for logistics.     

Zaremba's problem for elliptic equations in the neighborhood of a singular point or in the infinity

In the present paper the behavior of solutions of the mixed Zaremba's problem in the neighborhood of a boundary point and at infinity is studied. In part I of this paper[4] the concept of Wiener's generalized solution of Zaremba's problem was introduced and the so called Growth Lemma for the class of domains, satisfying isoperimetric condition, was proven. In part II regularity criterion for joining points of Neumann's and Dirichlet's boundary conditions is formulated. Generalized solution in unlimited domains as a limit of Zaremba's problem's solutions in a sequence of limited domains is introduced and a regularity condition allowed to obtain an analogue of Phragmen-Lindeloeff theorem for the solutions of Zaremba's problem. Main results of the present paper are formulated in terms of divergence of Wiener's type series.     

基于仿真优化的炼钢生产批调度求解方法

论文针对钢铁企业炼钢工序具有高温、高能耗、复杂工况的实际特征,从中提炼出生产批调度问题,其工件根据其实际工艺属性可分为多个簇,基于给定的工件簇,决策工件的分批和调度情况,综合考虑工件之间的切换费用,以及工件提前、拖期所导致的惩罚,使得总的生产成本期望最小化,从而降低生产成本;针对该问题,考虑工件的处理时间、工件的加工属性具有不确定性,基于仿真优化思想,建立数学模型,并基于大数定理,对模型目标函数进行近似;提出基于样本近似方法的求解框架,通过随机抽样的方法获得不同规模的样本,针对不同规模的样本,提出Filter & Fan算法对问题进行求解;最后,通过基于实际数据的计算实验验证所提算法的有效性。     

Hub location–allocation in intermodal logistic networks

Within the context of intermodal logistics, the design of transportation networks becomes more complex than it is for single mode logistics. In an intermodal network, the respective modes are characterized by the transportation cost structure, modal connectivity, availability of transfer points and service time performance. These characteristics suggest the level of complexity involved in designing intermodal logistics networks. This research develops a mathematical model using the multiple-allocation p-hub median approach. The model encompasses the dynamics of individual modes of transportation through transportation costs, modal connectivity costs, and fixed location costs under service time requirements. A tabu search meta-heuristic is used to solve large size (100 node) problems. The solutions obtained using this meta-heuristic are compared with tight lower bounds developed using a Lagrangian relaxation approach. An experimental study evaluates the performance of the intermodal logistics networks and explores the effects and interactions of several factors on the design of intermodal hub networks subject to service time requirements.     

On solution strategies to Saint-Venant problem

Different solution strategies to the relaxed Saint-Venant problem are presented and comparatively discussed from a mechanical and computational point of view. Three approaches are considered; namely, the displacement approach, the mixed approach, and the modified potential stress approach. The different solution strategies lead to the formulation of two-dimensional Neumann and Dirichlet boundary-value problems. Several solution strategies are discussed in general, namely, the series approach, the reformulation of the boundary-value problems for the Laplace's equations as integral boundary equations, and the finite-element approach. In particular, the signatures of the finite-element weak solutions—the computational costs, the convergence, the accuracy—are discussed considering elastic cylinders whose cross sections are represented by piece-wise smooth domains.     

The Three-Dimensional Problem of Statics of the Elastic Mixture Theory with Displacements Given on the Boundary

The first three-dimensional boundary value problem is considered for the basic equations of statics of the elastic mixture theory in the finite and infinite domains bounded by the closed surfaces. It is proved that this problem splits into two problems whose investigation is reduced to the first boundary value problem for an elliptic equation which structurally coincides with an equation of statics of an isotropic elastic body. Using the potential method and the theory of Fredholm integral equations of second kind, the existence and uniqueness of the solution of the first boundary value problem is proved for the split equation.     

A production-transportation problem with stochastic demand and concave production costs

Well known extensions of the classical transportation problem are obtained by including fixed costs for the production of goods at the supply points (facility location) and/or by introducing stochastic demand, modeled by convex nonlinear costs, at the demand points (the stochastic transportation problem, [STP]). However, the simultaneous use of concave and convex costs is not very well treated in the literature. Economies of scale often yield concave cost functions other than fixed charges, so in this paper we consider a problem with general concave costs at the supply points, as well as convex costs at the demand points. The objective function can then be represented as the difference of two convex functions, and is therefore called a d.c. function. We propose a solution method which reduces the problem to a d.c. optimization problem in a much smaller space, then solves the latter by a branch and bound procedure in which bounding is based on solving subproblems of the form of [STP]. We prove convergence of the method and report computational tests that indicate that quite large problems can be solved efficiently. Problems up to the size of 100 supply points and 500 demand points are solved. Received October 11, 1993 / Revised version received July 31, 1995 Published online November 24, 1998     

Mixed boundary value problems with a shift for a pair of metaanalytic and analytic functions

In this article, we reconsider the mixed boundary value problem on the unit circle for a pair of metaanalytic and analytic functions as in Du and Wang (2008) [9]. By adopting appropriate transformations, we convert the problem into two independent boundary value problems for analytic functions. We then obtain expressions of solution and condition of solvability for the mixed boundary value problem. The forms of the solutions and the condition of solvability here are rather dissimilar to those in Du and Wang (2008) [9]. But the equivalence is established at the end of this article.