Liner shipping network design with emission control areas: A genetic algorithm-based approach

To curb emissions, containerized shipping lines face the traditional trade-off between cost and emissions (CO₂ and SO_x) reduction. This paper considers this element in the context of liner service design and proposes a mixed integer linear programming (MILP) model based on a multi-commodity pickup and delivery arc-flow formulation. The objective is to maximize the profit by selecting the ports to be visited, the sequence of port visit, the cargo flows between ports, as well as the number/operating speeds of vessels on each arc of the selected route. The problem also considers that Emission Control Areas (ECAs) exist in the liner network and accounts for the vessel carrying capacity. In addition to using the MILP solver of CPLEX, we develop in the paper a specific genetic algorithm (GA) based heuristic and show that it gives the possibility to reach an optimal solution when solving large size instances.     

Intermodal Transit System Coordination

In urban areas where transit demand is widely spread, passengers may be served by an intermodal transit system, consisting of a rail transit line (or a bus rapid transit route) and a number of feeder routes connecting at different transfer stations. In such a system, passengers may need one or more transfers to complete their journey. Therefore, scheduling vehicles operating in the system with special attention to reduce transfer time can contribute significantly to service quality improvements. Schedule synchronization may significantly reduce transfer delays at transfer stations where various routes interconnect. Since vehicle arrivals are stochastic, slack time allowances in vehicle schedules may be desirable to reduce the probability of missed connections. An objective total cost function, including supplier and user costs, is formulated for optimizing the coordination of a general intermodal transit network. A four-stage procedure is developed for determining the optimal coordination status among routes at every transfer station. Considering stochastic feeder vehicle arrivals at transfer stations, the slack times of coordinated routes are optimized, by balancing the savings from transfer delays and additional cost from slack delays and operating costs. The model thus developed is used to optimize the coordination of an intermodal transit network, while the impact of a range of factors on coordination (e.g., demand, standard deviation of vehicle arrival times, etc) is examined.     

Green supply chain network design to reduce carbon emissions

We consider a supply chain network design problem that takes CO₂ emissions into account. Emission costs are considered alongside fixed and variable location and production costs. The relationship between CO₂ emissions and vehicle weight is modeled using a concave function leading to a concave minimization problem. As the direct solution of the resulting model is not possible, Lagrangian relaxation is used to decompose the problem into a capacitated facility location problem with single sourcing and a concave knapsack problem that can be solved easily. A Lagrangian heuristic based on the solution of the subproblem is proposed. When evaluated on a number of problems with varying capacity and cost characteristics, the proposed algorithm achieves solutions within 1% of the optimal. The test results indicate that considering emission costs can change the optimal configuration of the supply chain, confirming that emission costs should be considered when designing supply chains in jurisdictions with carbon costs.     

Segment-based alteration for container liner shipping network design

Container liner shipping companies only partially alter their shipping networks to cope with the changing demand, rather than entirely redesign and change the network. In view of the practice, this paper proposes an optimal container liner shipping network alteration problem based on an interesting idea of segment, which is a sequence of legs from a head port to a tail port that are visited by the same type of ship more than once in the existing shipping network. In segment-based network alteration, the segments are intact and each port is visited by the same type of ship and from the same previous ports. As a result, the designed network needs minimum modification before implementation. A mixed-integer linear programming model with a polynomial number of variables is developed for the proposed segmented-based liner shipping network alternation problem. The developed model is applied to an Asia–Europe–Oceania liner shipping network with a total of 46 ports and 11 ship routes. Results demonstrate that the problem could be solved efficiently and the optimized network reduces the total cost of the initial network considerably.     

A segregated urban busway system

A transport system has been proposed using buses operating over ordinary roads and over special reserved tracks (busways) on which they might be automatically guided. Using cost and performance data resulting from an earlier technical study (not reported here), a hypothetical network of routes and services in the West Midlands conurbation is studied. Estimates of patronage diverted from public and private transport enable the profitability of the system and its costs and benefits to be assessed. It is concluded that the system could be attractive both in commercial and in cost/benefit terms, providing acceptable means could be found for handling the buses around and through the inner central areas of cities. The net environmental changes, which would result from additional fixed plant permitting more efficient use of mobile plant, have not been quantified.     

The design of capacitated intermodal hub networks with different vehicle types

In this study, we allow using alternative transportation modes and different types of vehicles in the hub networks to be designed. The aim of the problem is to determine the locations and capacities of hubs, which transportation modes to serve at hubs, allocation of non-hub nodes to hubs, and the number of vehicles of each type to operate on the hub network to route the demand between origin-destination pairs with minimum total cost. Total cost includes fixed costs of establishing hubs with different capacities, purchasing and operational costs of vehicles, transportation costs, and material handling costs. A mixed-integer programming model is developed and a variable neighborhood search algorithm is proposed for the solution of this problem. The heuristic algorithm is tested on instances from the Turkish network and CAB data set. Extensive computational analyzes are conducted in order to observe the effects of changes in various problem parameters on the resulting hub networks.     

Cargo Container Loading Plan Model and Solution Method for International Air Express Carriers

Abstract

In this article, a cargo container loading plan model is developed based on the operations of FedEx, the international air express carrier. The objective is to minimize total container handling cost, subject to related operating constraints. The model is expected to be a useful planning tool whereby international air express carriers such as FedEx can decide on container loading plans that will lead to lower operating costs, thus enhancing profits and market competitiveness. The model is formulated as a non-linear mixed integer program that is characterized as NP-hard. A solution method is then developed, with the use of the mathematical programming solver, CPLEX, to solve the problem efficiently. To evaluate the model and the solution method, we perform a case study using data from FedEx. The preliminary results indicate that the model and the solution method are both efficient and effective.     

Optimal recharging strategies for electric vehicle fleets with duration constraints

Electrical vehicles (EVs) have become a popular green transportation means recently because they have lower energy consumption costs and produce less pollution. The success of EVs relies on technologies to extend their driving range, which can be achieved by the good deployment of EV recharging stations. This paper considers a special EV network composed of fixed routes for an EV fleet, where each EV moves along its own cyclic tour of depots. By setting up a recharging station on a depot, an EV can recharge its battery for no longer than a pre-specified duration constraint. We seek an optimal deployment of recharging stations and an optimal recharging schedule for each EV such that all EVs can continue their tours in the planning horizon with minimum total costs. To solve this difficult location problem, we first propose a mixed integer program (MIP) formulation and then derive four new valid inequalities to shorten the solution time. Eight MIP models, which were created by adding different combinations of the four valid inequalities to the basic model, have been implemented to test their individual effectiveness and synergy over twelve randomly generated EV networks. Valuable managerial insights into the usage of valid inequalities and the relations between the battery capacity and the total costs, number of recharging facilities to be installed, and running time are analyzed.     

A planning model for multiple‐mode transportation system operations

The problem of generating a set of “good” transportation alternatives during the early and intermediate stages of transportation planning is addressed in this paper. A linear programming model of a multi‐modal transportation system is developed. The model is run interactively to determine optimal operating levels for all modes for various transport policy decisions. The model described is a component of a composite network generation model incorporating dynamic changes. The linear programming component determines optimal operating policies for given points in time. The composite model incorporates these in a dynamic programming framework to determine optimal staged investment policies over several time periods.     

Interurban road network planning model with accessibility and robustness objectives

Abstract

Road network planning (or design) problems consist of determining the best investment decisions to be made with regard to the improvement of a road network. In this paper, we propose an optimization model for long-term interurban road network planning where accessibility and robustness objectives are simultaneously taken into account. Three network robustness measures were defined to assess different robustness concerns: network spare capacity; city evacuation capacity; and network vulnerability. The results that may be obtained from the application of the model are illustrated for three random networks. Special attention is given to the implications of adopting each one of the robustness measures upon the optimum solution provided by the model.     

Towards a general microeconomic model for the operation of public transport

After Vickrey's view, Mohring constructed a microeconomic model to determine the optimal frequency of buses serving a corridor with fixed demand. The main result was that frequency should be proportional to the square root of demand. The role of users' costs was shown to be crucial. This approach has evolved over the past decades, improving our understanding of public transport operations. This paper describes and analyses the evolution of microeconomic models for the analysis of public transport services with parametric demand, leading towards a more comprehensive one. An in-depth review of all the contributions in the academic literature is presented, emphasizing both the treatment of variables and the form of the results mostly in terms of frequency and fleet size. A series of partial new elements is also identified. An extension of Jansson's model for a single period is developed analytically, including the effect of vehicle size on operating costs and the influence of crowding on the value of time. Numerical simulations are used for comparison and analysis. A general model is then proposed where bus operations are optimized accounting for a number of simultaneous relations. Finally, the different models are discussed and compared.     

Optimal feeder bus routes on irregular street networks

The methodology presented here seeks to optimize bus routes feeding a major intermodal transit transfer station while considering intersection delays and realistic street networks. A model is developed for finding the optimal bus route location and its operating headway in a heterogeneous service area. The criterion for optimality is the minimum total cost, including supplier and user costs. Irregular and discrete demand distributions, which realistically represent geographic variations in demand, are considered in the proposed model. The optimal headway is derived analytically for an irregularly shaped service area without demand elasticity, with non‐uniformly distributed demand density, and with a many‐to‐one travel pattern. Computer programs are designed to analyze numerical examples, which show that the combinatory type routing problem can be globally optimized. The improved computational efficiency of the near‐optimal algorithm is demonstrated through numerical comparisons to an optimal solution obtained by the exhaustive search (ES) algorithm. The CPU time spent by each algorithm is also compared to demonstrate that the near‐optimal algorithm converges to an acceptable solution significantly faster than the ES algorithm.     

Fuel burn and environmental implications of airline hub networks

Hubs act as switching points for interactions and so are places through which flows are concentrated. This research uses the interactions between a system of cities as an experimental context for understanding selected environmental costs and benefits of concentrated flow. Whether hub based networks create additional environmental costs has been debated in the literature. In this paper, fuel burn is used as an indicator of environmental cost. The essential ideas are: (1) to examine fuel costs associated with larger aircraft; (2) to determine implications of higher loads on dense routes; and (3) to model the resulting implications for hub and gateway location. Variants of these questions apply to passenger and freight flows, and the paper will initially concentrate on passenger models.The paper shows that by modeling fuel burn and introducing a fixed charge (like a set up cost), a multiple allocation hub and spoke model can be adjusted to direct more or less flow onto the inter-facility connector. In other words, usage of multiple connections and direct links can be controlled and modeled as a function of the fixed charge. The resulting networks are characterized by quite different levels of passenger miles, aggregate fuel burn and fixed charges. The preferred network in terms of minimal fuel burn is found by subtracting the fixed set up charge, thereby focusing attention on the modeled fuel burn. The lowest cost set up is a network with a high degree of connectivity, and a pure single assignment hub network has the highest fuel cost (as a result of larger passenger miles needed by connecting paths). The data also allow a tabulation of total passenger miles, which, not surprisingly, track very closely with the fuel burn. In an interesting application of the ideas, it is shown that a fuel efficient network may require a large number of smaller regional jets, and in the interests of avoiding noise and congestion from so many extra airport operations, the carriers may choose to substitute a smaller number of larger planes, thereby slightly increasing fuel needs. This paper also provides a key ingredient for models of an international network where it is impossible to serve many long distance market pairs without consolidation.     

Flexible feeder transit route design to enhance service accessibility in urban area

To improve the accessibility of transit system in urban areas, this paper presents a flexible feeder transit routing model that can serve irregular‐shaped networks. By integrating the cost efficiency of fixed‐route transit system and the flexibility of demand responsive transit system, the proposed model is capable of letting operating feeder busses temporarily deviate from their current route so as to serve the reported demand locations. With an objective of minimizing total bus travel time, a new operational mode is then proposed to allow busses to serve passengers on both street sides. In addition, when multiple feeder busses are operating in the target service area, the proposed model can provide an optimal plan to locate the nearest one to response to the demands. A three‐stage solution algorithm is also developed to yield meta‐optimal solutions to the problem in a reasonable amount of time by transforming the problem into a traveling salesman problem. Numerical studies have demonstrated the effectiveness of the proposed model as well as the heuristic solution approach. Copyright © 2015 John Wiley & Sons, Ltd.     

“Comparing guideway transit implementation plans,including the impact on road traffic”

A methodology for comparing phased implementation plans for a new fixed guideway transit system in an urban area is presented. Four assumptions are made: (1) the guideway system replaces existing or planned bus service, (2) superior service on the new system results in increased ridership when compared to buses; (3) presence of the guideway facility redirects outward urban growth resulting in additional ridership, and (4) conversely, the absence of any action on the new guideway facility reinforces a diffuse urban growth pattern that creates an irreversible loss of transit ridership. The economic comparision of alternative plans includes total as well as “relative” inflation of principal cost components. A key feature of the proposed methodology is including in the comparisons the costs of private automobile mileage that could have been replaced by transit. These costs are expressed as “fuel” and “all other” automobile costs; favorable transit system implementation schedules can then be identified as a function of parametrically assumed values for these two unit costs. A hypothetical example demonstrates the proposed method.     

Weather impact on containership routing in closed seas: A chance-constraint optimization approach

Weather conditions have a strong effect on the operation of vessels and unavoidably influence total time at sea and associated transportation costs. The velocity and direction of the wind in particular may considerably affect travel speed of vessels and therefore the reliability of scheduled maritime services. This paper considers weather effects in containership routing; a stochastic model is developed for determining optimal routes for a homogeneous fleet performing pick-ups and deliveries of containers between a hub and several spoke ports, while incorporating travel time uncertainties attributed to the weather. The problem is originally formulated as a chance-constrained variant of the vehicle routing problem with simultaneous pick-ups and deliveries and time constraints and solved using a genetic algorithm. The model is implemented to a network of island ports of the Aegean Sea. Results on the application of algorithm reveal that a small fleet is sufficient enough to serve network’s islands, under the influence of minor delays. A sensitivity analysis based on alternative scenarios in the problem’s parameters, leads to encouraging conclusions with respect to the efficiency and robustness of the algorithm.     

Optimization of Fare Structure and Service Frequency for Maximum Profitability of Transit Systems

Abstract

Providing efficient public transportation has been recognized as a potential way of alleviating congestion, improving mobility, mitigating air pollution, and reducing energy consumption. Many people use public transportation systems for their daily commute, while others use different transportation modes (e.g. cars, taxis, carpools, etc.). Inexpensive fares with good transit service encourages ridership, and the resulting revenue may be used to provide better service. Optimization of transit service frequency and its associated fare structure is desirable in order to increase revenue at reasonable transit operating expenditure. The objective of the study reported here is to maximize profit subject to service capacity constraint, while elastic demand is considered. The solution methodology is developed and applied to solve the profit maximization problem in a case study based on Newark, NJ, USA. Numerical results, including optimal solutions and sensitivity analyses, are presented. It is found that an optimal temporal headway and differential fare structure that maximizes total profit for the studied subway system can be efficiently solved.     

An epsilon-optimal algorithm considering greenhouse gas emissions for the management of a ship’s bunker fuel

This paper provides an algorithm to minimize the fixed ordering, purchase, and inventory-carrying costs associated with bunker fuel together with ship time costs; and environmental costs associated with greenhouse gas emissions. It determines the optimum ship speed, bunkering ports, and amounts of bunker fuel for a given ship’s route. To solve the problem, we use an epsilon-optimal algorithm by deriving a property. The algorithm is illustrated by applying it to typical sample data obtained and the effects of bunker prices, carbon taxes, and ship time costs on the ship speed are analyzed. The results indicate that the ship speed and CO₂ emissions are highly sensitive to the factors considered.     

High-Speed Rail Operations on an Existing Network: An Assessment Model for China

High-speed rail operations have the potential to reduce the long-term decline in rail passenger travel demand for the medium to long distance inter-urban markets. Such decline has been evident through most of the industrialized countries where air and road transport tend to be the dominant modes. In China, the operations of long distance high-speed rail on fully dedicated track is not very easy to implement, due to the high proportion of passengers who travel between high-speed and conventional railways. An alternative approach would be to allow for mixed operations with trains of various speeds on the same track. This article puts forward a simulation model designed to allow an evaluation of the most efficient distance for high-speed rail operations under mixed train speed scenarios. The model takes into account the main operating parameters such as passenger volumes, train speeds, capital and maintenance costs, train operating costs and energy consumption. The distance of high-speed train running on conventional rail that will yield the most economic benefit can be estimated using the model. The article includes the results of using the model for a specific example. It is concluded that large-scale high-speed trains have the potential to be successfully operated on conventional rail networks.     

Algorithms for logit-based stochastic user equilibrium assignment

The paper proposes an efficient algorithm for determining the stochastic user equilibrium solution for logit-based loading. The commonly used Method of Successive Averages typically has a very slow convergence rate. The new algorithm described here uses Williams’ result [ Williams, (1977) On the formation of travel demand models and economic evaluation measures of user benefit. Environment and Planning 9A(3), 285–344] which enables the expected value of the perceived travel costs S_rs to be readily calculated for any flow vector x. This enables the value of the Sheffi and Powell, 1982 objective function [Sheffi, Y. and Powell, W. B. (1982) An algorithm for the equilibrium assignment problem with random link times. Networks 12(2), 191–207], and its gradient in any specified search direction, to be calculated. It is then shown how, at each iteration, an optimal step length along the search direction can be easily estimated, rather than using the pre-set step lengths, thus giving much faster convergence. The basic algorithm uses the standard search direction (towards the auxiliary solution). In addition the performance of two further versions of the algorithm are investigated, both of which use an optimal step length but alternative search directions, based on the Davidon–Fletcher–Powell function minimisation method. The first is an unconstrained and the second a constrained version. Comparisons are made of all three versions of the algorithm, using a number of test networks ranging from a simple three-link network to one with almost 3000 links. It is found that for all but the smallest network the version using the standard search direction gives the fastest rate of convergence. Extensions to allow for multiple user classes and elastic demand are also possible.