The paper presents a mathematical model and a simulation model of the freight trains classification process. We model the process as a queueing system with a server which is represented by a hump at a marshalling yard. We distinguish two types of shunting over the hump; primary shunting represents the classification of inbound freight trains over the hump (it is the primary function of marshalling yards), and secondary shunting is, for example, represented by the classification of trains of wagons entering the yard via industrial sidings. Inbound freight trains are considered to be customers in the system, and all needs of secondary shunting are failures of the hump because performing secondary shunting occupies the hump, and therefore inbound freight trains cannot be sorted. All random variables of the model are considered to be exponentially distributed with the exception of customer service times which are Erlang distributed. The mathematical model was created using method of stages and can be solved numerically employing a suitable software tool. The simulation model was created using coloured Petri nets. Both models are tested in conditions of a marshalling yard.

This paper focuses on solving the problem of how to assign locomotives to assembled trains optimally. To solve the problem, linear programming is applied. The situation we model in the paper occurs in the conditions of a transport operator that provides rail transport in the Czech Republic. In the paper, an extended locomotive assignment problem is modeled; the transport operator can use different classes of the locomotives to serve individual connections, some connections must be served by a predefined locomotive class, and the locomotives can be allocated to several depots at the beginning. The proposed model also takes into consideration the fact that some connections can be served by the locomotives of external transport companies or operators. The presented model is applied to a real example in order to test its functionality.

The creation of a flight schedule and the associated crew planning are clearly among the most complicated tasks in terms of traffic preparation. Even with a relatively small number of pilots and aircraft, numerous specific constraints arising from real operations must be included in the calculation, thus increasing the complexity of the planning process. However, even in a precision-planned operation, non-standard situations often occur, which must be addressed flexibly. It is at this point that an operational solution must be applied, the aims of which are to stabilize the flight schedule as soon as possible and minimize the financial impacts resulting from the non-standard situation. These problems are resolved by the airline’s Operational Control Center, which also uses various software approaches to solve the problem. The problem is approached differently by large air carriers, which use software products to address it, and small and medium-sized air carriers, which resolve the issue of operational rescheduling intuitively, based on the experience of dispatchers. However, this intuitive approach can lead to inaccuracies that can lead to unnecessary financial losses. In this paper, we present an optimization model that can serve as a tool to support the decision-making of employees of the operations centers of smaller and medium-sized air carriers.

The paper describes a mathematical programming approach used for the lineplanning problem in urban public transport. The input data include...

In regular as well as nonscheduled air transport, extraordinary situations occasionally occur, which may fundamentally disrupt the flight schedule. Fundamental disruptions of flight schedules affect not only passengers but also the airline. One of the areas that are negatively affected by the disruption is the crew plan. Due to extraordinary events, it happens that a flight is delayed, and the crew will not be at the destination airport at the prescribed time and the airline will not be able to assign it on further flights according to the original plan. Such situations can be resolved either by deploying any other available crew or by delaying the flight appropriately until the previously planned crew is available. Assigning a new crew entails additional costs for the airline, as it has to assign more flight staff than had been originally planned. Furthermore, delayed flights lead to paying passengers financial compensation, incurring additional costs for airlines. Therefore, it is important that the airline is able to resolve any irregularity situations so that the additional costs incurred to deal with the irregularity situations are kept at a minimum. The paper presents one possible approach, a mathematical model that can be used to solve such a situation. The presented mathematical model may be the basis for the decision support system of the operations center worker who is responsible for the operational management of flight crews. The model will primarily aim at smaller airlines that cannot afford expensive software and often rely on manual solutions. However, a manual solution may not always be the best, as the operator, who plans the processes, may not consider all the constraints. Another important factor that makes the decision processes more difficult is that it is usually necessary to decide in a short period of time. The solution proposed in this paper will allow the operator to make a quick decision that will also be the most advantageous for the airline. This is because the proposed method is an exact approach, which guarantees finding the optimum solution. In this article, we are only dealing with pilot crews.