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.

Material Substitution in a manufacturing process

Consider a mechanical design engineer working for an automotive gear manufacturing company who wants to substitute an aluminum alloy for gray cast iron.  When looking at material selection problem for design, substitution of a material requires knowledge of various attributes of the material to be substituted and the potential substitutes. As mentioned in the Dieter and Schmidt [14], while considering aluminum alloy as an alternative to gray cast iron, there are many variations of aluminum alloy available as shown in Table 1. There are various attributes of these different cast iron, like strength and corrosion resistance, that are paramount to the performance of these aluminum alloys.  According to Dieter and Schmidt, cast iron has Valid strength (18 ksi), ultimate tensile strength (22ksi), shear strength (20 ksi) and elongation (0.5 inch). The corresponding strength properties of aluminum alloys are better than that of cast iron. 

There is uncertainty in the performance of the alloys which comes from the uncertainty in the attributes of these alloys. The firm can take samples to reduce the uncertainty of the attributes considering a budget constraint.