The Resource Levelling Problem (RLP) is a variation of resource-constrained scheduling problems with major applications in manufacturing. A critical path is determined for a set of jobs/items that needs to be manufactured or assembled to form a final product. In capacity planning, each of these jobs is associated with a predetermined load or 'hassle' factor (resource level). When these jobs are scheduled together in a planning horizon, different profiles with respect to the resource levels are developed. The objective of the RLP is to minimise the maximum resource peaks by moving jobs within their slack times. RLP is an NP-Hard combinatorial optimisation problem and therefore, no optimal algorithm is known. A few studies have been done on this problem during 1960's and early 1970's and various heuristics suggested (see [W64], [D66], [BFC62], [D73]). However, no recent studies have been done despite recent developments in algorithmic techniques. The objective of this project is to develop new algorithmic approaches to the RLP. In Chapter 1 we provide a definition of the problem using an example from the manufacturing industry. Chapter 2 presents a review of preprocessing techniques, which are useful in improving the performance of Integer Programming methods. In Chapter 3 we develop four Mixed Integer Programming (MIP) formulations. Our analysis shows that time-indexed formulations perform better for the RLP. In Chapters 4 and 5 we present three global heuristic methods; Simulated Annealing, Tabu Search and a Perturbation algorithm. We conclude that, these algorithms are feasible and good approaches to the RLP. The perturbation algorithm was found to perform better than the rest. Chapter 6 provides a discussion on how the theory of Human-Computer Interaction can be used to improve the solution of the RLP by providing a good Interface design. Lastly we summarise our project in Chapter 7 and suggest areas of further research.