Location of hubs in a competitive environment

We offer a formulation that locates hubs on a network in a competitive environment; that is, customer capture is sought, which happens whenever the location of a new hub results in a reduction of the current cost (time, distance) needed by the traffic that goes from the specified origin to the specified destination. The formulation presented here reduces the number of variables and constraints as compared to existing covering models. This model is suited for both air passenger and cargo transportation. In this model, each origin–destination flow can go through either one or two hubs, and each demand point can be assigned to more than a hub, depending on the different destinations of its traffic. Links (“spokes”) have no capacity limit. Computational experience is provided.     

双模式网络停车限制交通需求管理模型与方法研究

在轨道网和公路网并存的双模式交通网络, 合理设计出行终点的停车容量可优化汽车出行需求, 改善路网交通环境。本文通过分析私家车与城市轨道两种交通模式的出行需求, 并考虑私家车模式的终点停车收费服务, 建立了一种带路段环境容量和终点停车需求容量共同约束的交通需求管理模型。模型中路网使用者的出行模式采用二元Logit模型来计算, 而私家车的路线选择行为服从Logit随机用户均衡, 因此该模型是一个带不动点约束的数学规划问题。针对模型求解困难, 文中采用灵敏度分析来获取各路段流量和需求量关于终点容量波动的梯度信息, 进而设计了一种新的灵敏度分析求解算法.最后通过数值仿真实验, 验证了算法的有效性, 同时分析了不同停车收费参数对模型各指标变化趋势的影响。     

Robust solutions for network design under transportation cost and demand uncertainty

In many applications, the network design problem (NDP) faces significant uncertainty in transportation costs and demand, as it can be difficult to estimate current (and future values) of these quantities. In this paper, we present a robust optimization-based formulation for the NDP under transportation cost and demand uncertainty. We show that solving an approximation to this robust formulation of the NDP can be done efficiently for a network with single origin and destination per commodity and general uncertainty in transportation costs and demand that are independent of each other. For a network with path constraints, we propose an efficient column generation procedure to solve the linear programming relaxation. We also present computational results that show that the approximate robust solution found provides significant savings in the worst case while incurring only minor sub-optimality for specific instances of the uncertainty.     

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.     

Transportation policies for single and multi-objective transportation problem using fuzzy logic

In this paper, single and multi-objective transportation models are formulated with fuzzy relations under the fuzzy logic. In the single-objective model, objective is to minimize the transportation cost. In this case, the amount of quantities transported from an origin to a destination depends on the corresponding transportation cost and this relation is verbally expressed in an imprecise sense i.e., by the words ‘low’, ‘medium’, ‘high’. For the multi-objective model, objectives are minimization of (i) total transportation cost and (ii) total time for transportation required for the system. Here, also the transported quantity from a source to a destination is determined on the basis of minimum total transportation cost as well as minimum transportation time. These relations are imprecise and stated by verbal words such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’. Both single objective and multi-objective problems using Real coded Genetic Algorithms (GA and MOGA) are developed and used to solve the single level and bi-level logical relations respectively. The models are illustrated with numerical data and optimum results are presented.     

Improved rounding procedures for the discrete version of the capacitated EOQ problem

We consider a transportation problem where different products have to be shipped from an origin to a destination by means of vehicles with given capacity. The production rate at the origin and the demand rate at the destination are constant over time and identical for each product. The problem consists in deciding when to make the shipments and how to fill the vehicles, with the objective of minimizing the sum of the average transportation and inventory costs at the origin and at the destination over an infinite horizon. This problem is the well known capacitated EOQ (economic order quantity) problem and has an optimal solution in closed form. In this paper we study a discrete version of this problem in which shipments are performed only at multiples of a given minimum time. It is known that rounding-off the optimal solution of the capacitated EOQ problem to the closest lower or upper integer value gives a tight worst-case ratio of 2, while the best among the possible single frequency policies has a performance ratio of 5/3. We show that the 5/3 bound can be obtained by a single frequency policy based on a rounding procedure which considers classes of instances and, for each class, identifies a shipping frequency by rounding-off in a different way the optimal solution of the capacitated EOQ problem. Moreover, we show that the bound can be reduced to 3/2 by using two shipping frequencies, obtained by a rounding procedure, in one class of instances only.     

The effect of information on commuters' behavior: A comparative micro-simulation approach

This paper presents a micro simulation model for studying the effect of information on commuters' behavior during morning peak congestion, and its impact is examined here in relation to network performance. The model is fed by survey data of perceived behavior in two cities in two different countries: Israel and Sweden. The model considers parameters such as: home-to-work trips, constraints with respect to the arrival time at the destination, exposure to various levels of information, flexibility of the mode of transportation, pre-trip information and en-route information.     

Analysis of the Best Double Frequency Policy in the Single Link Problem with Discrete Shipping Times

We study an inventory–transportation problem where one product has to be shipped from an origin to a destination by vehicles of given capacity over an infinite time horizon. The product is made available at the origin and consumed at the destination at the same constant rate. The intershipment time must be not lower than a given minimum value. The problem is to decide when to make the shipments and how to load the vehicles to minimize the sum of the transportation and the inventory costs at the origin and at the destination per time unit. We study the case in which the intershipment time is a multiple of the minimum value, i.e., the problem with discrete shipping times. We show that, in this case, the best double frequency policy has a tight performance bound of about 1.1603 with respect to the optimal periodic policy and of about 1.1538 with respect to the best frequency-based policy. Moreover, we show that, from the worst-case point of view, the best double frequency policy is the optimal frequency-based policy.     

Two-echelon vehicle routing problem with satellite bi-synchronization

In considering route optimization at a series of express stages from pickup to delivery via the intercity linehaul, we introduce the two-echelon vehicle routing problem with satellite bi-synchronization (2E-VRP-SBS) from the perspective of modeling the routing problems of two-echelon networks. The 2E-VRP-SBS involves the inter-satellite linehaul on the first echelon, and the pickups from senders to origin satellites (i.e., satellites for cargo collection) and deliveries from destination satellites (i.e., satellites for cargo deliveries) to receivers on the second echelon. The 2E-VRP-SBS integrates satellite bi-synchronization constraints, multiple vehicles, and time window constraints on the two-echelon network and aims to find cost-minimizing routes for various types of trucks. Satellite bi-synchronization constraints, which synchronously guarantee the synchronization at origin satellites and the synchronization at destination satellites, provide an innovative method to formulate the two-echelon routing problem. In this study, we develop a mixed-integer programming model for the 2E-VRP-SBS. An exact method using CPLEX solver is presented and a modified adaptive large neighborhood search is conducted. Furthermore, the effectiveness of the 2E-VRP-SBS formulation and the applicability of the heuristic for various instances are experimentally evaluated.     

On trade-off solution pairs in a special type of transportation problem

In this paper, we have developed an algorithm to determine the trade-off solution pairs in a special type of transportation problem considering two objectives,viz., cost and time. It is assumed that the time of transportation from an origin to a destination depends on the quantity transported. This results in a time objective, which is a piecewise constant increasing function. The cost objective function is taken to be linear. A potential physical situation of this model is given and a numerical example is worked out to illustrate the algorithm.     

Optimal control of polling models for transportation applications

We formulate and analyze a dynamic scheduling problem for a class of transportation systems in a Markov Decision Process (MDP) framework. A transportation system is represented by a polling model consisting of a number of stations and a server with switch-over costs and constraints on its movement (the model we have analyzed is intended to emulate key features of an elevator system). Customers request service in order to be transported by the server from various arrival stations to a common destination station. The objective is to minimize a cost criterion that incorporates waiting costs at the arrival stations. Two versions of the basic problem are considered and structural properties of the optimal policy in each case are derived. It is shown that optimal scheduling policies are characterized by switching functions dependent on state information consisting of queue lengths formed at the arrival stations.     

Dynamic capacitated user-optimal departure time/route choice problem with time-window

A discrete-time predictive dynamic user-optimal departure time/route choice problem has been formulated and solved with the nested diagonalization method by Chen, H.K., Hsueh, C.F. (1998a. A discrete-time dynamic user-optimal departure time/route choice model. Transportation Engineering, ASCE 124 (3), 246–254). That model did not impose constraints on either departure times at origin or arrival times at destination, which are typically required for regular work trips. However, for better representing practical situations, the time-window constraints associated with both the departure times and arrival times, along with link capacity side constraints, need to be incorporated into the aforementioned model. The resulting dynamic capacitated user-optimal departure time/route choice model with time-window can appropriately model the queuing delay associated with each capacitated time–space link and also can properly differentiate off-peak and peak phenomena within the analysis period. A numerical example is provided for demonstration.     

The capacitated p-hub median problem with integral constraints: An application to a Chinese air cargo network

Consolidation at hubs in a pure hub-and-spoke network eliminates partial center-to-center direct loads, resulting in savings in transportation costs. In this research, we propose a general capacitated p-hub median model, with economies of scale and integral constraints on the paths. This model requires the selection of a specific p among a set of candidate hubs so that the total cost on the resulting pure capacitated hub-and-spoke network is minimized while simultaneously meeting origin–destination demands, operational capacity and singular path constraints. We explored the problem structure and developed a genetic algorithm using the path for encoding. This algorithm is capable of determining local optimality within less than 0.1% of the Lagrangian relaxation lower bounds on our Chinese air cargo network testing case and has reasonable computational times. The study showed that designating airports with high pickups or deliveries as hubs resulted in a high percentage of origin–destination pairs (ODs) in direct deliveries. Furthermore, the more hubs there are, the higher the direct share and the less likely for double rehandles. Sensitivity analysis on the discount rate showed that the economies of scale on trunk lines of hub-and-spoke networks may have a substantial impact on both the operating costs and the route patterns.     

Uncertain solid transportation problems

The solid transportation problem arises when bounds are given on three item properties. Usually, these properties are source, destination and type of product or mode of transport, and often are given in a uncertain way. This paper deals with two of the ways in which uncertainty can appear in the problem: Interval solid transportation problem and fuzzy solid transportation problem. The first arises when data problem are expressed as intervals instead of point values, and the second when the nature of the information is vague. Both models are treated in the case in which the uncertainty affects only the constraint set. For interval case, an auxiliary problem is obtained in order to find a solution. This auxiliary problem is a standard solid transportation problem which can be solved with the efficient methods existing. For fuzzy case, a parametric approach which makes it possible to find a fuzzy solution to the former problem is used.     

沿海港口集装箱空箱调运策略优化模型

我国沿海港口进出口箱分布非常不均衡,由此产生了集装箱空箱调运现象,合理的空箱调运策略能够有效地降低航运成本。本文研究了沿海港口间的空箱调运问题。在传统确定目的港策略的基础上,提出了一种新的空箱调运策略,不确定目的港策略。针对两种不同调运策略分别建立了以总调运费用最小为目标的规划模型。并以中国沿海港口空箱调运为例,运用遗传算法,在不同的空箱供需情况下,对两种调运策略费用进行了优化求解。结果表明,供需平衡模式下,固定目的港策略略有优势;在供需不平衡模式中,不确定目的港策略优势更加明显。此研究能够为港口间空箱调运提供辅助决策。     

A modified Physarum-inspired model for the user equilibrium traffic assignment problem

The user equilibrium traffic assignment principle is very important in the traffic assignment problem. Mathematical programming models are designed to solve the user equilibrium problem in traditional algorithms. Recently, the Physarum shows the ability to address the user equilibrium and system optimization traffic assignment problems. However, the Physarum model are not efficient in real traffic networks with two-way traffic characteristics and multiple origin–destination pairs. In this article, a modified Physarum-inspired model for the user equilibrium problem is proposed. By decomposing traffic flux based on origin nodes, the traffic flux from different origin–destination pairs can be distinguished in the proposed model. The Physarum can obtain the equilibrium traffic flux when no shorter path can be discovered between each origin–destination pair. Finally, numerical examples demonstrate the rationality and convergence properties of the proposed model.     

Solving the transportation problem with mixed constraints

Summary Variants of the standard transportation problem in which availability or requirement constraints are specified as inequalities can be solved by means of related standard transportation problems. In this paper we show that to each transportation problem with mixed constraints a standard transportation problem with two additional constraints can be related. The method of solution proposed also applies to the case that a lexicographic optimization is to be performed.

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Zusammenfassung Gegenstand dieses Beitrags sind unkapazitierte einstufige Transportprobleme, deren Nebenbedingungen nicht ausschließlich in Gleichungsform vorliegen. Einem einstufigen Transportproblem mit gemischten Restriktionen läßt sich ein erweitertes klassisches Transport-problem zuordnen, aus dessen optimaler Lösung eine optimale Lösung des Ausgangsproblems ermittelt werden kann. In diesem Beitrag soll gezeigt werden, daß zur Generierung eines erweiterten klassischen Transportproblems die Einführung einer Zeilenrestriktion und einer Spaltenrestriktion ausreichen. Die hier vorgestellte Vorgehensweise bietet sich auch im Falle einer lexikographischen Optimierung an.

     

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.     

Buyer’s response to a temporary price reduction incorporating freight costs

In this paper, we characterize the buyer’s response to a temporary price reduction. Although there have been many studies that have considered the above problem, most of those studies assume that the buyer orders FOB (free on board) destination and that the freight charges are included in the supplier’s unit price. Our model thus becomes applicable for a buyer whose strategy is to include transportation costs in their purchase decisions. The buyer may want direct control on his inbound logistics costs. The company may have outsourced its logistics function and as a result is charged for freight as invoiced by the public motor carrier. In some cases, the supplier may only allow for orders that are FOB origin. Our model allows for less-than-truckload as well as truckload rates. Freight cost for a LTL shipment is modeled using tariffs set by public carriers in practice. These tariffs generally involve 6–7 breakpoints in terms of the weight of the shipment. Another complication in practice is that the shipper/buyer has an option to over-declare the weight of the shipment.