In continuation of a set of types of problems in fleet management science, Rail and inter-modal transportation have several noteworthy approaches to solutions.

Several interesting algorithms have been proposed for the Rail and Intermodal problem space. This is a complex system composed by different transport networks, infrastructures, different transport means and operators, such as dryage operators, terminal operators, network operators and others. Intermodal means there are lots of decision makers who must work in a coordinated manner for the system to run smoothly. If intermodal transport is to be developed, it will require more decision-making support tools to assist the decision-makers and stakeholders.

When train operations are perturbed, a new conflict free timetable must be recomputed such that the deviation from the original must be minimized. This scheduling problem is modeled with an alternative graph formulation and a branch and bound algorithm is developed. Some approaches use an integrated framework which deals with signal layout optimization, train scheduling optimization at microscopic level, and others.

Heuristic approaches include a look-ahead greedy heuristic and a global neighborhood search algorithm, in terms of railway total train delay. Scheduling additional train services to be integrated into the current timetables is a problem that is modeled as a hybrid job shop scheduling techniques that operate upon a disjunctive graph model of trains.

One approach presented a two phased train set routing algorithm to cover a weekly train timetable with minimal working days of a minimal number of train sets. The first step involves relaxing maintenance requirements and obtaining minimum cost routes by solving the polynomial relaxation. Then maintenance-feasible routes are generated from the crossovers of the minimum cost routes. This pragmatic approach seems particularly effective for the high-speed railways system which is simpler, with fewer end stations and higher frequency of trains.

Corman et al addressed the problem of train conflict detection and resolution that became quite popular among traffic controllers. This approach proposed a family of techniques referred to as the Railway Optimization by Means of Alternative graphs and it involved effective rescheduling algorithms and local rerouting strategies in a tabu search scheme. A fast heuristic and a truncated branch and bound algorithm are alternate for computing train schedules within a short computation time. The effectiveness of using different neighborhood structures can be investigated for train rerouting. Tabu search is known to be faster than ROMA. Another approach proposed a train slot selection model based on multicommodity network flow concepts for determining freight train timetables for scheduling rail services along multiple interconnected routes. The model seeks to minimize operating costs incurred by carriers and delays incurred by shippers while ensuring that the schedules and demands are mutually consistent.

 

Another problem space that defines fleet management in its own way is Rail and intermodal transport. This is a complex system composed by different transport networks, infrastructures, different transport means and operators, such as dryage operators, terminal operators, network operators and others. Intermodal means there are lots of decision makers who must work in a coordinated manner for the system to run smoothly. If intermodal transport is to be developed, it will require more decision-making support tools to assist the decision-makers and stakeholders.

For example, the operational level involves the day-to-day management decisions about the load order of trains and barges, redistribution of railcars or push barges and load units. The fleet comprises of load units. The assignment of a set of trailers and containers to the available flatcars that can move the equipment is a classic problem in this space. Routing involves a lot  more than that. While the minimum cost path algorithm was common to road network, in this case, the routing decision is a mere modal choice problem for specific trajectories between beginning and end points and involving specific freight volumes and specific time constraints.

Container transportation is a major component of intermodal transportation carried out by a combination of truck, rail and ocean shipping. Fleet management covers  the whole range of planning and management issues from procurement of power units and vehicles to vehicle dispatch and scheduling of crews and maintenance operations. But rail transport is characterized by different kinds of trains travelling on the network and the subdivision of resources between passenger and freight trains. The train scheduling and routing must consider their timetables.

When train operations are perturbed, a new conflict free timetable must be recomputed such that the deviation from the original must be minimized. This scheduling problem is modeled with an alternative graph formulation and a branch and bound algorithm is developed. Some approaches use an integrated framework which deals with signal layout optimization, train scheduling optimization at microscopic level, and others.

 

Another problem space that defines fleet management in its own way is Maritime support. This is not restricted to sea borne transportation and includes water-borne transportation as well. Ships and ports, their logistics and containers management and interconnections among vessels characterize this field.

There are three modes of transportation in maritime – liner, industrial and tramp. Adjustments to fleet size and mix, fleet deployment, ship routing and scheduling are some of the tactical problems. As with the airline transportation discussed earlier, the issue of robustness needs to be addressed here as well as disruptions are common. Therefore, robustness is factored into the optimization models used for planning.

Methodologies used towards solutions include input parameters, deterministic models that incorporate penalties and stochastic optimization models. One of the established techniques uses fleet composition and mix routing while another uses decision support methodology for strategic planning in tramp and industrial shipping. This involves simulation and optimization, where a Monte-Carlo simulation framework is built around an optimization-based decision support system and short term routing and scheduling using a rolling horizon principle where information is revealed as time goes by. This helps with a wide range of strategic planning problems.

When it comes to ferry scheduling, the analogy from public transit system discussed earlier hold true. The common objective is the minimization of costs and maximization of customer satisfaction. Decreasing the operational costs and reducing the travel time and waiting time for passengers requires reevaluation and improvements to the ferry schedule. There is a ‘logit’ model that determines’ the passengers’ service choices. This is used by the formulation to determine the best mixed-fleet operating strategy, including interlining schemes, so as to minimize the objective function that combines both the operator and passengers’ performance measures.

 Another class of problems in fleet management aside from those discussed, is the one concerning air transport. This is characterized by network design and schedule construction, fleet assignment, aircraft routing, crew scheduling, revenue management, irregular operations, air traffic control and ground delay programs, gate assignment, fuel management, short term fleet assignment swapping. They were mostly solved by operation research techniques and the majority of applications utilized network-based models. 

The airline scheduling process is carried out sequentially so that flight, aircraft and schedules are created one after another over several months prior to the day of the operations. A detailed flight schedule might be based on marketing decisions. The first step in operational scheduling is the assignment of an aircraft fleet type to each flight and is based on the demand forecasts, the capacity and the availability of the aircrafts. After fleet assignment, an aircraft is assigned to each flight with respect to maintenance constraints such as aircraft routing. Crew scheduling can be broken down into two steps. The first phase is called crew pairing and it involves anonymous crew itineraries subject to constraints such as maximum allowed working time or flying time per duty. The second phase is crew rostering, and it involves assigning individual crew members to the itineraries. The goal of this scheduling process is to reduce costs. 

Fleet routing and fleet scheduling also affect costs but it determines the airline’s level of service and its competitive capability in the market. Network flow techniques are adopted for modeling and solving such complex mathematical problems. The full optimization problem can be hard so they are solved in parts sequentially. The output of one is input to the next. 

The limitations of the sequential approach were subsequently solved with an integrated approach that reduces costs even more. 

The fleet assignment problem deals with assigning aircraft types, each having a different capacity to the scheduled flights, based on equipment capabilities and availability, operational costs and potential revenues. When there are many flights each day, this problem becomes difficult. Some remediations include: 1) integrating the FAP with other decision processes such as schedule design, aircraft maintenance routing, and crew scheduling, 2) proposing solution techniques that introduces additional parameters and constraints into the traditional fleeting models, such as itinerary based demand forecasts and the recapture effect and 3) studying dynamic fleeting mechanisms that update the initial fleeting solution as departures approach and more information is gathered on demand patterns. In a few models, a non-linear integer multi-commodity network flow is formulated, and new branch-and-bound strategies are developed. 

Traffic disruptions are one characteristic of this problem space. This might lead to an infeasible aircraft and crew schedules on the day of the operations and the recovery to reasonable schedule must be attempted. The short-term recovery actions might increase operational costs, sometimes even higher than the planned costs. Recovery options could be factored into the scheduling at the design time and this approach is generally called robust scheduling. Sometimes this is articulated as a measure. For example, a non-robustness measure is used to penalize restricted aircraft changes according to the slack time during an aircraft change. 

Global stochastic models have been attempted to be solved with an iterative approach. The iterative approach yields a set of different solutions regarding the trade-offs between the costs and robustness whereas an integrated approach returns mostly one near-optimal solution for a given robustness penalty. Iterative approach is more favorable to a decision maker. When multiple airlines must coordinate, the models are formulated as multiple commodity network flow problems which can be solved by programs based on mathematical formulations. 

 

 Another class of problems in fleet management aside from those discussed, is the one concerning air transport. This is characterized by network design and schedule construction, fleet assignment, aircraft routing, crew scheduling, revenue management, irregular operations, air traffic control and ground delay programs, gate assignment, fuel management, short term fleet assignment swapping. They were mostly solved by operation research techniques and the majority of applications utilized network-based models.

The airline scheduling process is carried out sequentially so that flight, aircraft and schedules are created one after another over several months prior to the day of the operations. A detailed flight schedule might be based on marketing decisions. The first step in operational scheduling is the assignment of an aircraft fleet type to each flight and is based on the demand forecasts, the capacity and the availability of the aircrafts. After fleet assignment, an aircraft is assigned to each flight with respect to maintenance constraints such as aircraft routing. Crew scheduling can be broken down into two steps. The first phase is called crew pairing and it involves anonymous crew itineraries subject to constraints such as maximum allowed working time or flying time per duty. The second phase is crew rostering, and it involves assigning individual crew members to the itineraries. The goal of this scheduling process is to reduce costs.

Fleet routing and fleet scheduling also affect costs but it determines the airline’s level of service and its competitive capability in the market. Network flow techniques are adopted for modeling and solving such complex mathematical problems. The full optimization problem can be hard so they are solved in parts sequentially. The output of one is input to the next.

The limitations of the sequential approach were subsequently solved with an integrated approach that reduces costs even more.

The fleet assignment problem deals with assigning aircraft types, each having a different capacity to the scheduled flights, based on equipment capabilities and availability, operational costs and potential revenues. When there are many flights each day, this problem becomes difficult. Some remediations include: 1) integrating the FAP with other decision processes such as schedule design, aircraft maintenance routing, and crew scheduling, 2) proposing solution techniques that introduces additional parameters and constraints into the traditional fleeting models, such as itinerary based demand forecasts and the recapture effect and 3) studying dynamic fleeting mechanisms that update the initial fleeting solution as departures approach and more information is gathered on demand patterns. In a few models, a non-linear integer multi-commodity network flow is formulated, and new branch-and-bound strategies are developed.

Traffic disruptions are one characteristic of this problem space. This might lead to an infeasible aircraft and crew schedules on the day of the operations and the recovery to reasonable schedule must be attempted. The short-term recovery actions might increase operational costs, sometimes even higher than the planned costs. Recovery options could be factored into the scheduling at the design time and this approach is generally called robust scheduling. Sometimes this is articulated as a measure. For example, a non-robustness measure is used to penalize restricted aircraft changes according to the slack time during an aircraft change.

Global stochastic models have been attempted to be solved with an iterative approach. The iterative approach yields a set of different solutions regarding the trade-offs between the costs and robustness whereas an integrated approach returns mostly one near-optimal solution for a given robustness penalty. Iterative approach is more favorable to a decision maker. When multiple airlines must coordinate, the models are formulated as multiple commodity network flow problems which can be solved by programs based on mathematical formulations.

 

 

In continuation of a set of types of problems in fleet management area, Urban public transport and dial-a-ride are more recent.

Urban public transport deserves to be called a class of problems by itself. It consists of determining ways to provide good quality of service to passengers with finite resources and operating costs. Their planning process often involves 1. Network route design, 2. Frequency setting and timetable development, 3. Vehicle scheduling and 4. Crew scheduling and rostering. Some state-of-the-art models involve tuning the routing and scheduling with minimization of passenger cost functions. Metaheuristics schemes that combine simulated annealing, tabu, and greedy search methods serve this purpose. One of the distinguishing features of this problem space is that customers often formulate two requests per day, specifying an outbound request from pick-up to drop-off and an inbound request for the round trip. Another feature is that the quality of service needs to be maximized while minimizing operating costs incurred to satisfy all the requests.

Dial-a-ride transport is a move toward more economical and greater flexibility of transport services. Demand responsive transportation systems require the planning of routes and customer pick-up and drop-off scheduling on the basis of received requests. It must deal with multiple vehicles with limited capacity and time-windows. The problem of working out optimal routes and times is referred to as the Dial-a-ride problem. As with many problem spaces in fleet management, this can be treated as NP-hard combinatorial optimization problem. Attempts to develop an optimal solution has been limited to simple and small-size problems.

Such a service may operate in a static or dynamic mode. In the static settings, all the customer requests are known beforehand, nd the system solves a tour each vehicle must make within the constraints of the pick-up and drop-off time window and minimizing the solution cost. In the dynamic mode, the customer requests arrive over time to a control station and the solution may change over time. Processing must also keep up with the incoming rate without interfering with the optimization cycle at the end of the service. The goal is two-fold: reduce overall costs and improve quality of service to customers. Several algorithms have been tried for this purpose. They include tabu search heuristics, dynamic programming, branch and cut, a heuristic two phase solution method, genetic algorithms and variable neighborhood search.

Even the users can be differentiated as well as the transportation modes. Some meta-heuristics such as vehicle waiting time with passenger onboard can also be used with branch-cut algorithms for this purpose.

Studying quality of service in this context has evolved into models which use various measurement scales. The quality of service provided by organizations also depend on the type of organization and the operational rules used.

 Fleet Management continued...

The need for fleet management arose from the requirements of passengers and freight transportation services. Usually, their fleet is considered heterogeneous because it includes a variety of vehicles. Some of the fleets must perform tasks that may be known beforehand or are done repetitively. Most of them respond to demand. The scale and size of the fleet can be massive.

Vehicle routing and scheduling is one such class of problems. A fleet of vehicles with limited capacity based at one or several depots must be routed serving a certain number of customers to minimize the number of routes, total traveling time and the distance traveled. Additional restrictions can specialize this class of problems with time windows where each customer is served in a specified time interval. This class of problems is central to the field of transportation, distribution, and logistics.

Dynamic fleet management is another class of problems. While classical fleet management problems address routing and scheduling plans, unforeseen events might force additional requirements. When communication is leveraged to get this additional information, real-time usage of fleet resources can be improved. The changes in vehicle location, travel time and customer orders can be used with an efficient re-optimization procedure for updating the route plan as dynamic information arrives. When reacting to real-time events leaves no time, it can be worked around by finding ways to anticipate future events in an effective way. Data processing and forecasting methods, optimization-simulation models, and decision heuristics can be included to improve comprehensive decision-support systems.

Another field of increasing interest is the urban freight transportation and the development of new organizational models for management of freight. As for any complex systems, city logistics transportation systems require planning at strategic, tactical, and operational levels. While wide area road networks require routing based on distances, that within the city logistics network demands time-dependent travel times estimates for every route section. While static approaches are well studied, time-dependent vehicle routing still appears to be unexplored. One of the ways to bridge this gap has been to use an integration framework that brings dedicated systems together for a holistic simulation that performs something like a dynamic router and scheduler.

Urban public transport deserves to be called a class of problems by itself. It consists of determining ways to provide good quality of service to passengers with finite resources and operating costs. Their planning process often involves 1. Network route design, 2. Frequency setting and timetable development, 3. Vehicle scheduling and 4. Crew scheduling and rostering. Some state-of-the-art models involve tuning the routing and scheduling with minimization of passenger cost functions. Metaheuristics schemes that combine simulated annealing, tabu, and greedy search methods serve this purpose. One of the distinguishing features of this problem space is that customers often formulate two requests per day, specifying an outbound request from pick-up to drop-off and an inbound request for the round trip. Another feature is that the quality of service needs to be maximized while minimizing operating costs incurred to satisfy all the requests.