Exact methods for the resource levelling problem

Project management in the present time is characterized by rapid advancements in many technologies, hardly calculable risks and very tight deadlines for nearly all kinds of projects. Planning and steering of projects under these conditions turns out to be a really tough job even for the most experienced project managers. To deal responsibly with project sponsors or customers, they must consider carefully the resources that are required to complete a project on time and within the estimated budget. As a consequence, the levelling of resources has faded into the focus of attention. Especially within the mid-term planning a deliberate resource allocation plan is important to avoid bottlenecks in the subsequent short-term resource planning or even during the execution of some project. Resources in this context could for example be employees, machinery or even scarce work spaces (like test stands in automotive development projects). An interesting application for resource levelling has been proposed in [3]. In maketo-order production all products are manufactured on the basis of a given set of customer orders with individual delivery dates. The production quantities of the final products are therefore externally given due to these orders. A so called Master Production Schedule (MPS) specifies the exact amounts of all main products and the corresponding times of production. The MPS is thereby usually determined in the mid-term planning and serves as input for the subsequent short-term planning. It has already been discussed in the literature that levelling resource requirements in the mid-term planning of projects is crucial to achieve good feasible solutions at subsequent planning steps because remarkable fluctuations in the utilization of resources like manpower or machinery often cause extra labor or financial expenditure (cf. [5]). In make-to-order production products are only produced on demand and hence the workload distribution over time cannot be balanced via inventory holding. Instead,