Purchasing management is a relatively new scientific research field, partly due to the fact that purchasing has only recently been recognized as a factor of strategic importance to an organization. In this thesis, the author focuses on a selection of strategic and tactical purchasing decision problems. New quantitative models are developed for these decision problems using a range of mathematical techniques, thereby contributing to the further development of purchasing theory and its appliation in practice.The selected purchasing decision problems are:-ROI improvement drivers from a purchasing perspective-allocation of cost savings in a purchasing consortium-strategies for tendering procedures-fixed-price contracts versus spot market buying-supplier switching strategies for single sourcing-electronic procurement roll-out strategie