Dissertation projects

Heuristic solution methods for the resource-constrained project duration minimization problem with partial-renewable resources and general time relations

The number and complexity of executed projects has increased significantly in the economy during the last years. Accordingly, project management and especially project scheduling become more and more important. A well-known problem from the literature that has already been studied many times is the so-called resource-constrained project duration minimization problem with general time relations (RCPSP\max). The goal in solving this problem is to schedule a project or its sub-processes in such a way that the project duration is minimized and at the same time all resource and time constraints are met. In the case of the latter, RCPSP/max can be both minimum and maximum time constraints, i.e. general time relationships between the activities of the project.

Usually, renewable resources are considered in the context of the resource-constrained project duration minimization problem. However, this type of resource reaches its limits when modeling more flexible resource constraints. In this case, so-called partial-renewable resources are used, which have received little attention in the literature so far. They represent a generalization of renewable and non-renewable resources. Analogous to non-renewable resources, they have a total capacity, which, however, does not refer to the entire planning horizon, but only to an arbitrary subset of the periods. If activities of the project under consideration are executed in these capacitated periods, they consume the resource according to their given resource requirements during this time. With the help of such partially renewable resources, for example, flexible working time models or temporally flexible maintenance work on machines can be taken into account.

The goal of the dissertation project is the development of heuristic solution methods for the described problem of the resource-constrained project duration minimization problem with partial-renewable resources and general time relations (RCPSP\max-π). In the context of this, a construction heuristic for generating the best possible initial solutions will first be designed. For this purpose, on the one hand a construction-based approach, in which the operations of the project are scheduled successively, but not necessarily as early as possible in terms of time and resources, and on the other hand a relaxation-based approach will be considered and compared. Subsequently, local search methods or population-based methods are to be developed in order to further improve the constructed initial solutions. Furthermore, renewable resources to the RCPSP\max-π -ρ will be added to the problem and the developed methods will be adapted accordingly.

Extensions and solution procedures for the resource renting problem.

The number and complexity of projects carried out in companies has increased considerably in recent years. Accordingly, project management, and in particular project planning, is becoming increasingly important. In the context of project management, a project is understood as a set of activities, as well as the time relationships between them. The execution of an activity within a project requires resources during the entire execution time, whereby the cost-minimal provision of the necessary resources is a target value of project planning. A frequently considered resource type are renewable resources which are not "consumed" during use, but are available again in the following planning period; typical examples of this resource type are machines or employees.

The resource renting problem (RRP) assumes that the resources required for a project are not purchased or already available, but have to be rented temporarily. Rented resources play a particularly important role in the planning of construction projects. Heavy equipment such as excavators, cranes or bulldozers are often rented explicitly for temporary use on a construction site.

There are two types of costs involved in renting resources, quantity-based provision costs and time-based rental costs per unit of quantity and time. The latter correspond to the rental cost of a machine per day, the first type of cost is incurred by renting a unit of resource. These can be e.g. transport costs, since an excavator cannot drive itself to its place of operation but an expensive transport on a suitable truck is necessary.

The RRP consists of two subproblems, a scheduling problem, where the task is to generate a time-allowable schedule for a project, and the rental policy problem, which is used to rent the resources needed for a schedule as cheaply as possible. The problem is to decide when resources should be provided and when they should be given away. One difficulty is that in certain situations it may be convenient to keep resources even though there is temporarily no need for them, since providing them again would be more expensive than paying the rental costs for the unused period.

In this dissertation project, different MILP formulations for the resource renting problem will be developed and investigated. The basis for this is provided by formulations for the resource-constrained project duration minimization problem and the resource leveling problem, which are well-known from the project management literature. Furthermore, the focus is to develp a heuristic solution procedure in which the RRP is decomposed step by step into smaller subproblems and solved (Fix&Optimize). Subsequently, the problem shall be extended by substitutable resources to the RRP\sub and the developed methods shall be adapted accordingly.

Transport optimization in empties container networks of Volkswagen AG

Volkswagen Konzernlogistik GmbH & Co. OHG is responsible for planning, controlling and monitoring the transport networks in the Volkswagen AG group network. This includes the transport of externally manufactured components from suppliers to the Group-wide production plants, which is carried out almost exclusively in returnable load carriers due to the fact that transporting individual, loose components makes no sense from either an economic or a logistical point of view. After arriving at the plant, the loaded load carriers are lined up as needed on the production line or transported just-in-time to the production line before the parts are removed for assembling the vehicle. In order to close the load carrier cycle and to ensure that future component deliveries can also be made in the returnable load carriers, it is imperative that the empties are transported back from the plants to the suppliers. These transports, which do not directly add value, are cost-intensive and cause high CO2 emissions. Last but not least, as part of the Group strategy "TOGETHER 2025⁺"and the derived goTOzero strategy, Volkswagen has committed itself to reducing CO2 emissions by 30% by 2025 compared with 2018 and to achieving CO2 neutrality in its balance sheet by 2050.

The aim of this dissertation project is to plan the transport of empties from plants to suppliers as efficiently as possible with regard to current and future requirements. In close cooperation with Volkswagen Group Logistics, new concepts for load carrier allocation in the transport network are to be developed and compared using an experimental performance analysis based on realistic test instances. The main challenge is the sheer size of the optimization problem on the one hand and the complexity of the process structures on the other hand. For example, the transport problem to be solved involves not only around 50 plants, more than 1,000 suppliers and around 50 universal load carrier types, but also shipment lead times, degressive transport costs and different modes of transport. Due to the fact that the underlying Dynamic Multicommodity Fixed Charge Transport Problem belongs to the class of NP-hard problems in combination with the size of the instances to be solved, standard solvers reach their limits. Therefore, the main focus of the research project shall be the development of heuristic solution approaches. In a first step, a realistic instance set for the problem of transporting empties will be generated. In the next step, existing network approaches are to be taken up for the problem structure at hand and new approaches are to be conceptualized before solution procedures are developed for the generation of best possible feasible solutions. The focus here is on the development of construction heuristics specific to the problem. Subsequently, the solutions generated this way are to be further improved by the use of suitable improvement procedures.