A generalized linear exchange model

The linear exchange model is studied in which alongside the consumers there are firms minimizing expenses to guarantee some minimal level of the total cost of production. Some finite algorithm for finding an equilibrium is proposed and justified in the case of the fixed budgets of consumers. This algorithm develops the original approach of polyhedral complementarity which was proposed by the author for the classical exchange model.     

Minimizing greenhouse gas emissions in intermodal freight transport: an application to rail service design

Freight transport has undesirable effects on the environment. The most prominent of these is greenhouse gas emissions. Intermodal freight transport, where freight is shipped from origin to destination by a sequence of at least two transportation modes, offers the possibility of shifting freight (either partially or in full) from one mode to another in the hope of reducing the greenhouse emissions by appropriately scheduling the services and routing the freight. Traditional planning methods for scheduling services in an intermodal transportation network usually focus on minimizing travel or time-related costs of transport. This article breaks away from such an approach by addressing the issue of incorporating environment-related costs (greenhouse gases, to be specific) into freight transportation planning and proposes an integer program in the form of a linear cost, multicommodity, capacitated network design formulation that minimizes the amount of greenhouse gas emissions of transportation activities. Computational results based on an application of the proposed approach on a real-life rail freight transportation network are presented.     

Capacitated location model with online demand pooling in a multi-channel supply chain

This paper presents a location model that assigns online demands to the capacitated regional warehouses currently serving in-store demands in a multi-channel supply chain. The model explicitly considers the trade-off between the risk pooling effect and the transportation cost in a two-echelon inventory/logistics system. Keeping the delivery network of the in-store demands unchanged, the model aims to minimize the transportation cost, inventory cost, and fixed handling cost in the system when assigning the online demands. We formulate the assignment problem as a non-linear integer programming model. Lagrangian relaxation based procedures are proposed to solve the model, both the general case and an important special case. Numerical experiments show the efficiency of our algorithms. Furthermore, we find that because of the pooling effect the variance of in-store demands currently served by a warehouse is an important parameter of the warehouse when it is considered as a candidate for supplying online demands. Highly uncertain in-store demands, as well as low transportation cost per unit, can make a warehouse appealing. We illustrate with numerical examples the trade-off between the pooling effect and the transportation cost in the assignment problem. We also evaluate the cost savings between the policy derived from the model, which integrates the transportation cost with the pooling effect, and the commonly used policy, which is based only on the transportation cost. Results show that the derived policy can reduce 1.5–7.5% cost in average and in many instances the percentage of cost savings is more than 10%.     

基于线路“异质性”假设的轴辐式公共交通网络优化研究

特大城市公共交通局部静态拥堵问题日益成为制约公共交通网络运行效率提高的关键。针对这一问题改变线路“同质性”假设,在线路“异质性”假设的基础上,提出了将轴辐式网络设计运用到公共交通领域中来,综合考虑居民采用公共交通方式出行的单位运输可变成本、不变成本、枢纽换乘成本等要素,将枢纽间大型客车干线运输所带来的规模经济效应进行量化,构建了基于单分配、多枢纽、混合式网络结构特征的轴辐式公共交通网络优化模型,旨在多重约束下通过枢纽布局降低网络运输成本,提高公共交通网络站点的可达性。最后根据模拟退火算法对模型进行求解,并通过算例分析与讨论的方式验证了模型的有效性。     

碳税政策下生产和销售的选址问题

本文考虑碳税政策下一个生产型企业生产和销售的选址问题。消费者分布在一条直线上,运输成本是线性的,企业除承担自身产品的运输费用外还承担消费者的运输成本。本文建立了利润最大化模型,分析了利润函数的性质,给出了求解方法。通过数值实验证明了求解方法的有效性,同时得出,即使消费者分布是中心对称的,最优的选址也不一定中心对称,这纠正了人们的错觉。增加碳税可使销售点靠近自己的消费者,增加企业的费用,但不一定起到减排的作用,只有通过灵活的碳税政策才有可能达到减排的目的。     

运输问题的合作对策求解方法

产地间或销地间往往存在竞争,在这种情况下,使用运输问题最优化方法是不合理的。因此,从个体理性的视角提出运输问题的合作对策求解方法,方法将运输问题看作是一个博弈问题,各个产地或销地是博弈的局中人,求解其纳什均衡与纳什讨价还价解。在此基础上,说明了运输问题的非合作形式是一个指派问题,并证明指派问题的最优解是一个纳什均衡点。接着,通过实验验证运输问题的最优解是一个纳什讨价还价解,满足产地或销地的自身利益。在此基础上,针对纳什讨价还价解不唯一的问题,从决策者的视角给出最大可能激励成本的计算方法。最后,为弥补纳什讨价还价解不唯一及纳什讨价还价解不允许出现子联盟的缺陷,给出运输收益分配或成本分摊的Shapely值计算方法。     

Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost

In this paper, we study a solid transportation problem with interval cost using fractional goal programming approach (FGP). In real life applications of the FGP problem with multiple objectives, it is difficult for the decision-maker(s) to determine the goal value of each objective precisely as the goal values are imprecise, vague, or uncertain. Therefore, a fuzzy goal programming model is developed for this purpose. The proposed model presents an application of fuzzy goal programming to the solid transportation problem. Also, we use a special type of non-linear (hyperbolic) membership functions to solve multi-objective transportation problem. It gives an optimal compromise solution. The proposed model is illustrated by using an example.     

General transport problems with branched minimizers as functionals of 1-currents with prescribed boundary

A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a given final distribution. The cost of the scheme encodes a higher transport efficiency the more mass is moved together, which automatically leads to optimal transportation networks with a hierarchical branching structure. The two major existing model formulations use either mass fluxes (vector-valued measures, Eulerian formulation) or patterns (probabilities on the space of particle paths, Lagrangian formulation). In the branched transport problem the transportation cost is a fractional power of the transported mass. In this paper we instead analyse the much more general class of transport problems in which the transportation cost is merely a nonnegative increasing and subadditive function (in a certain sense this is the broadest possible generalization of branched transport). In particular, we address the problem of the equivalence of the above-mentioned formulations in this wider context. However, the newly-introduced class of transportation costs lacks strict concavity which complicates the analysis considerably. New ideas are required, in particular, it turns out convenient to state the problem via 1-currents. Our analysis also includes the well-posedness, some network properties, as well as a metrization and a length space property of the model cost, which were previously only known for branched transport. Some already existing arguments in that field are given a more concise and simpler form.     

多阶段生产系统最优生产批量和原材料订购决策模型

Sarker和Parija(1996)建立了生产系统最优生产批量和原材料订购决策模型。然而他们的模型仅局限于单阶段生产系统,本文将他们的模型扩展到多阶段生产系统,我们首先建立了使整个多阶段生产系统总成本最小的各阶段最优生产批量、原材料订购批量及阶段之间的运输批量模型,然后分析了原材料订购费、半成品运费及设备安装费的敏感性。最后,我们结合实例综合分析了原材料订购费、半成品运输费和设备安装费的变化及最小值点取整后对原材料订购决策、最优生产批量和总成本的影响。     

Sugar cane transportation in Cuba,a case study

In this study the authors present a mixed integer linear programming model to solve the problem of cost minimization of sugar cane removal and its transport from the fields to the sugar mill at operational level. The complexity of the problem is basically determined by the system approach which results in the generation of a great number of variables and constraints that refer to the following operational dimensions: (a) need for continuous supply to the sugar mill; (b) cutting means used in cane harvesting; (c) transportation vehicles and (d) providing routes, which are characterized by the existence of storage facilities at the beginning of the railroads. The results demonstrate the model is not only useful to minimize transportation cost, but also for scheduling daily cane road transport and harvesting quotas of cutting means.     

Enumeration and Search Procedures for a Hub Location Problem with Economies of Scale

Within a communications or transportation network, in which a number of locations exchange material or information, hubs can be used as intermediate switching points. In this way, traffic can be consolidated on inter-hub links and, thus, achieve economies of scale in transport costs. Recently, O'Kelly and Brian in 1998 proposed a model (termed the FLOWLOC model) that treats these economies of scale by means of piecewise-linear concave cost functions on the interhub arcs. We show that, for a fixed set of hubs, the FLOWLOC model can be solved using the classic Uncapacitated Facility Location Problem (UFLP). This observation then motivates an optimal enumeration procedure for the FLOWLOC model, as well as some search heuristics that are based upon tabu search and greedy random adaptive search procedures (GRASP). These search procedures would be especially applicable for large-sized problems. Some computational experience is described.     

Integrating link-based discrete credit charging scheme into discrete network design problem

In this paper, we present an optimization model for integrating link-based discrete credit charging scheme into the discrete network design problem, to improve the transport performance from the perspectives of both transport network planning and travel demand management. The proposed model is a mixed-integer nonlinear bilevel programming problem, which includes an upper level problem for the transport authority and a lower level problem for the network users. The lower level sub-model is the traffic network user equilibrium (UE) formulation for a given network design strategy determined by the upper level problem. The network user at the lower level tries to minimize his/her own generalized travel cost (including both the travel time and the value of the credit charged for using the link) by choosing his/her route. While the transport authority at the upper level tries to find the optimal number of lanes and credit charging level with their locations to minimize the total system travel time (or maximize the transportation system performance). A genetic algorithm is used to solve the proposed mixed-integer nonlinear bilevel programming problem. Numerical experiments show the efficiency of the proposed model for traffic congestion mitigation, reveal that interaction effects across the tradable credit scheme and the discrete network design problem which amplify their individual effects. Moreover, the integrated model can achieve better performance than the sequential decision problems.     

Bicriterion Weight Varying Spatial Price Networks

We consider a spatial price equilibrium problem in which the consumers take their decisions according to the transportation cost and transportation time necessary for obtaining a given commodity. In particular, each consumer market can give a different weight to each component of a generalized cost, and we suppose that this weight can depend on time. Thus, we are faced with a time-dependent equilibrium problem which we cast within the framework of variational inequalities. We give existence results and, by using the example of a linear operator, we propose also a discretization procedure for equilibrium problems which can be modeled by the same type of variational inequality.     

循环取货模式下的多车场协同运输问题研究

分析循环取货模式和协同运输问题的关联性,提出了供需节点分离下的多车场一体化协同运输路线优化问题,考虑运输价值和运输成本,引入节点-弧流量的概念,通过比较流量大小确定节点集合,构建了问题的多供应点、多需求点运输模型.考虑取货的单向性和送货的闭合性,构造了求解模型的两阶段算法,运用动态规划的递推解法确定取货最优路线,然后基于余弦定理的几何法求解出发点和返回点不相同的送货路径优化问题,最后通过算例分析,说明了模型的合理性和算法的有效性.     

区间数型多目标联运路线优化问题的模型与算法

联运路线优化问题直接关系到货物运输的费用、时间和运输质量.首先分析了联运路线优化问题的数学模型及虚拟运输网络图;其次,将区间数排序的思想及属性值为区间数的多属性决策方法引入适应度函数的设计中,提出了一种求解区间数型联合运输路线优化问题的混合型遗传算法,给出了染色体编码、遗传算子设计、适应度函数定义及群体多样性控制的方法;最后用示例对算法的有效性进行了验证.     

Reliability based assignment in stochastic-flow freight network

Based on the reliability of transportation time, a transportation assignment model of stochastic-flow freight network is designed in this paper. This transportation assignment model is built by mean of stochastic chance-constraint programming and solved with a hybrid intelligent algorithm (HIA) which integrates genetic algorithm (GA), stochastic simulation (SS) and neural network (NN). GA is employed to report the optimal solution as well as the optimal objective function values of the proposed model. SS is used to simulate the value of uncertain system reliability function. The uncertain function approximated via NN is embedded into GA to check the feasibility and to compute the fitness of the chromosomes. These conclusions have been drawn after a test of numerical case using the proposed formulations. System reliability, total system cost and flow on each path would finally reach at their own convergence points. Increase of the system reliability causes increase of the total time cost. The system reliability and the total time cost converge at a possible Nash Equilibrium point.     

On optimal partitions,individual values and cooperative games: Does a wiser agent always produce a higher value?

We consider an optimal partition of resources (e.g. consumers) between several agents, given utility functions (“wisdoms”) for the agents and their capacities. This problem is a variant of optimal transport (Monge–Kantorovich) between two measure spaces where one of the measures is discrete (capacities) and the costs of transport are the wisdoms of the agents. We concentrate on the individual value for each agent under optimal partition and show that, counter-intuitively, this value may decrease if the agent’s wisdom is increased. Sufficient and necessary conditions for the monotonicity with respect to the wisdom functions of the individual values will be given, independently of the other agents. The sharpness of these conditions is also discussed. Motivated by the above we define a cooperative game based on optimal partition and investigate conditions for stability of the grand coalition.     

Joint Vendor-buyer Policy in JIT Manufacturing

In this study, we show that a co-operative batching policy, based on cost information exchange between the vendor and the buyer, can reduce total cost significantly in the just-in-time (JIT) environment. We examine the impact of such co-operation on total costs, including ordering, set-up, transportation and inventory holding costs for a long-term supply relationship. The study shows that joint optimization of both the vendor and the buyer's operations does not necessarily result in a common lot size. We further examine the sensitivity of the resulting cost savings due to the exchange of cost information to changes in the relevant operating parameters.     

面向远海岛礁群的双向物流网络规划

针对若干远海岛礁群系统封闭性的分布特点,将中心岛礁选址、各岛礁建设泊位数量和规模、仓库储存量、运输船型和数量以及航线设置、班期组织等作为规划内容,以整个运输网络系统总成本最低为原则,综合考虑了仓库存储理论,建立了兼顾“选址-库存-路径”的规划模型。结合所建模型特点,提出了双层并行搜索遗传算法,构建了以海上运输为基本交通方式的双向物流系统。最后,以我国南海为例进行建模并求解,采用不同算法并通过多组不同规模的算例进行演算比较,验证了所建模型和算法的有效性与合理性。     

Cost allocation in inventory transportation systems

In this paper, we deal with the cost allocation problem arising in an inventory transportation system with a single item and multiple agents that place joint orders using an EOQ policy. In our problem, the fixed-order cost of each agent is the sum of a first component (common to all agents) plus a second component which depends on the distance from the agent to the supplier. We assume that agents are located on a line route, in the sense that if any subgroup of agents places a joint order, its fixed cost is the sum of the first component plus the second component of the agent in the group at maximal distance from the supplier. For these inventory transportation systems, we introduce and characterize a rule which allows us to allocate the costs generated by the joint order. This rule has the same flavor as the Shapley value, but requires less computational effort. We show that our rule has good properties from the point of view of stability.