Taïeb Mellouli

A time–space network based exact optimization model for multi-depot bus scheduling

Abstract The vehicle scheduling problem, arising in public transport bus companies, addresses the task of assigning buses to cover a given set of timetabled trips with consideration of practical requirements, such as multiple depots and vehicle types as well as depot capacities. An optimal schedule is characterized by minimal fleet size and minimal operational costs including costs for unloaded trips and waiting time. This paper discusses the multi-depot, multi-vehicle-type bus scheduling problem (MDVSP), involving multiple depots for vehicles and different vehicle types for timetabled trips. We use time–space-based instead of connection-based networks for MDVSP modeling. This leads to a crucial size reduction of the corresponding mathematical models compared to well-known connection-based network flow or set partitioning models. The proposed modeling approach enables us to solve real-world problem instances with thousands of scheduled trips by direct application of standard optimization software. To our knowledge, the largest problems that we solved to optimality could not be solved by any existing exact approach. The presented research results have been developed in co-operation with the provider of transportation planning software PTV AG. A software component to support planners in public transport was designed and implemented in context of this co-operation as well.

A partially integrated airline crew scheduling approach with time-dependent crew capacities and multiple home bases

Abstract Crew scheduling for airlines requires an optimally scheduled coverage of flights with regard to given timetables. We consider the crew scheduling and assignment process for airlines, where crew members are stationed unevenly among home bases. In addition, their availability changes dynamically during the planning period due to pre-scheduled activities, such as office and simulator duties, vacancy, or requested off-duty days. We propose a partially integrated approach based on two tightly coupled components: the first constructs chains of crew pairings spaced by weekly rests, where crew capacities at different domiciles and time-dependent availabilities are considered. The second component rearranges parts of these pairing chains into individual crew schedules with, e.g., even distribution of flight time. Computational results with real-life data from an European airline are presented.

Managing and Preventing Delays in Railway Traffic by Simulation and Optimization

When a disturbance occurs within a railway network, a dispatcher has to decide ‘online’ about changes in the schedule in order to reduce induced delays and disadvantages for passengers. Computer assistance for dispatchers is needed. In an earlier work, a system architecture for a decision support system for operations control is proposed. This paper concerns the simulation part of this system, needed to manage and prevent delays. Besides operations control, we stress the usefulness of simulation already in the planning phase to prevent delays at operations. Analyzing (types of) disturbances, suitable distributions of delays are generated, and simulation is used to test the robustness of the timetable against disturbances. As a test vehicle, a computer-based environment configured for German Rail’s network has been developed. Robustness depends on dimensions of conflicts and of passengers involved. Conflicts and their causes directly depend on the ‘waiting time rules’ in use. By a simulation study, the quality of these rules can be evaluated and corrected. Preventing delays may be achieved by a better planning, too. Special optimization models can be used to increase buffer times without need of extra resources.

Rotation planning of locomotive and carriage groups with shared capacities

In a large railway passenger traffic network, a given set of trips or service blocks are to be serviced by equipment consisting of several groups of locomotives/carriages. The allowed groups per service block are predefined as patterns or multisets of locomotives and carriages. A given type of locomotive/carriage may occur with varying numbers in several groups. We search for a cost-minimal assignment of locomotive/ carriage groups to rotations taking special restrictions into account, especially, we shall find the optimal mix of groups obeying given capacities on the level of locomotive and carriage units for each type. Our solution approach is based on a multi-layer (multi-commodity) network flow model where each layer represents a locomotive/carriage group, and the requirement of servicing each trip exactly once is modeled by cover/partitioning constraints. In this paper, we concentrate on railway specific requirements and present special techniques to model and optimize locomotive and carriage groups with shared capacities. These techniques erable us to solve large-scale practical problem instances of German Railways into optimality.

Requirement for, and Design of, an Operations Control System for Railways

In this paper, we discuss computer-based systems that support operations control for railways. Specifically, we focus on the design of decision support tools for dispatchers. We have studied requirements of systems supporting operations control processes from the expert/user point of view for the German railway, “Deutsche Bahn AG.” The main goal is to help dispatchers ensure passenger traffic with the best possible quality in a dense network with more than 30,000 trips daily. We suggest that such a computer-based system must support the dispatcher in recognizing forthcoming conflicts as early as possible, rescheduling of passenger connections taking into account customers’ acceptance and cost, and reallocating vehicles/crews in a convenient way.

Improving Vehicle Scheduling Support by Efficient Algorithms

In this paper, the minimum fleet size problem is investigated: Find the minimum number of vehicles to serve a set of trips of a given timetable for a transportation system. First, we present an algorithm for the basic problem requiring only linear-time after suitably sorting input data. This improves a quadratic-time greedy algorithm developed in [Su95]. Our algorithm was implemented and tested with real-life data indicating a good performance. Generated diagrams on vehicle standing times are shown to be useful for various tasks. Second, Min-Max-results for the minimum fleet size problem are discussed. We argue that Dilworth’s chain decomposition theorem works only if unrestricted deadheading, i.e., adding non-profit ‘empty’ trips, is permitted and thus its application to the case of railway or airline passenger traffic is misleading. To remedy this lack, we consider a particular network flow model for the no deadheading case, formulate a Min-Max-result, and discuss its implications- along with efficient algorithms-for vehicle as well as trip and deadhead trip scheduling.

A network flow approach to crew scheduling based on an analogy to an aircraft/train maintenance routing problem

Airlines’ and railways’ expensive resources, especially crews and aircraft or trains are to be optimally scheduled to cover flights or trips of timetables. Aircraft and trains require regular servicing. They are to be routed as to regularly pass through one of the few maintenance bases, e.g., every three to four operation days for inspection. Apart from complicating workrules, crews are to be scheduled so as to “pass through” their home bases weekly for a two-day rest. This analogy is utilized in order to recognize opportunities for integrating classical planning processes for crew scheduling, and to transfer solution methodologies. A mixed-integer flow model based on a state-expanded aggregated time-space network is developed. This mathematical model, used to solve large-scale maintenance routing problems for German Rail’s intercity trains, is extended to the airline crew scheduling problem where maintenance states are replaced by crew states. The resulting network flow approach to an integrated crew scheduling process involving multiple crew domiciles and various crew requests is tested with problems from a European airline. A decision support system and computational results are presented.

Supporting Planning and Operation Time Control in Transportation Systems

Providers of public transportation systems, like airlines and railway companies, are usually faced with a complex planning and control process consisting of several phases, like demand estimation, timetable construction, resource allocation, e.g., for vehicles and crews, and operation time control. The control phase includes rescheduling of connections according to corporate rules and resource reallocation. We discuss computer-based decision support systems capable of supporting such processes. Especially, the case of integrated planning and control phases for railway passenger traffic will be presented: The integrated system being developed involves techniques, like optimisation, simulation, and knowledge-based components as well as common user interface and object-oriented architecture. Results of the planning phase are forwarded to operation time control. Components developed to support the control phase can be used to improve planning quality by what-if analyses.

Handling rest requirements and preassigned activities in airline crew pairing optimization

For the complex task of scheduling airline crews, this paper discusses the integration of rostering requirements into the crew pairing optimization process. Our approach is based on a network flow model which uses a state expanded network to represent pairing chains for crew members at different domiciles. We enhance this model by proposing a refined representation of rest requirements along with preassignments such as pairings from the previous planning period, office and simulator activities as well as vacation and part-time leaves. In particular, we introduce the concept of availability blocks to mitigate the loss of information following from the aggregated anonymous flow of crew members in the network model. Experimental results with real world data sets show that the refined model remains tractable in practical settings.

Future Demand Uncertainty In Personnel Scheduling: Investigating Deterministic Lookahead Policies Using Optimization And Simulation.

One of the main characteristics of personnel scheduling problems is the multitude of rules governing schedule feasibility and quality. This paper deals with an issue in personnel scheduling which is both relevant in practice and often neglected in academic research: When evaluating a schedule for a given planning period, the scheduling history preceding this period has to be taken into account. On the one hand, the history restricts the space of possible schedules, in particular at the beginning of the planning period and with respect to rules a scope transcending the planning period. On the other hand, the schedule for the planning period under consideration affects the solution space of future planning periods. In particular if the demand in future planning periods is subject to uncertainty, an interesting question is how to account for these effects when optimizing the schedule for a given planning period. The resulting planning problem can be considered as a multistage stochastic optimization problem which can be tackled by different modeling and solution approaches. In this paper, we compare different deterministic lookahead policies in which a one-week scheduling period is extended by an artificial lookahead period. In particular, we vary both the length and the way of creating demand forecasts for this lookahead period. The evaluation is carried out using a stochastic simulation in which weekly demands are sampled and the scheduling problems are solved exactly using mixed integer linear programming techniques. Our computational experiments based on data sets from the Second International Nurse Rostering Competition show that the length of the lookahead period is crucial to find good-quality solutions in the considered setting.