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In this article, we present heuristic methods for the vehicle scheduling problem that solve it by reducing the problem size using different variable fixing approaches. These methods are constructed in a way that takes some basic driver requirements into consideration as well. We show the efficiency of the methods on real-life and random data instances too. We also give an improved way of generating random input for the vehicle scheduling problem.

This article introduces the schedule assignment problem for public transit, which aims to assign vehicle blocks of a planning period to buses in the fleet of a transportation company. This assignment has to satisfy several constraints, the most important of which is compatibility, meaning that certain blocks can only be serviced by buses belonging to given types. Other constraints come from the fact that the problem considers a long-term plan for several days or weeks, which means that daily parking and periodic maintenance activities also have to be taken into account. We give a state-expanded multi-commodity flow network for the above problem. This model takes parking constraints into account, and also assigns preventive maintenance tasks to buses after serving blocks for a fixed amount of time. The solutions of this model are presented for real-life and randomly generated instances.

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As environmental awareness is becoming increasingly important, alternatives are needed for the traditional forward product flows of supply chains. The field of reverse logistics covers activities that aim to recover resources from their final destination, and acts as the foundation of the efficient backward flow of these materials. Designing the appropriate reverse logistics network for a given field is a crucial problem, as this provides the basis for all operations connected to the resource flow. This paper focuses on design questions in the supply network of waste wood, dealing with its collection and transportation to designated processing facilities. The facility location problem is studied for this use-case, and mathematical models are developed that consider economies of scale and the robustness of the problem. A novel approach based on bilevel optimization is used for computing the exact solutions of the robust problem on smaller instances. A local search and a tabu search method is also introduced for solving problems of realistic sizes. The developed models and methods are tested both on real-life and artificial instance sets in order to assess their performance.