In case of multi-attribute decisions, when a decision maker has a limited budget for data collection, then the decision maker has to decide on the number of samples to observe from each alternative and its attributes. This allocation decision is of importance when the observation process is uncertain, such as with physical measurements. This thesis presents a sequential allocation approach in which measurements are conducted one at a time. Prior to making a measurement the decision-maker’s current knowledge of the attribute values is used to identify the attribute and alternative pair to sample next using all these allocation procedures. The thesis discusses a simulations study that was performed to compare the Sequential Allocation Approach, Proportional Allocation Approach and Uniform Allocation Approach. We evaluated the frequency of selecting the true best alternative when the attribute value observations contain discrete random measurement error. The results indicate that the sequential approach is significantly better than the other approaches when the budget is small; as the budget increases, its advantage decreases.