Error bound comparisons for aggregation/disaggregation techniques applied to the transportation problem

A priori and a posteriori error bounds for a transportation problem model at different levels of aggregation were statistically compared. An experimental design was used to (1) examine the size and significance of correlation between all pairs of the a priori error bound, a posteriori error bound and actual error and (2) quantify the size and significance of the difference of a posteriori error bound from the actual error. Two different methods for calculating a posteriori error bounds were utilized. Results are for aggregating customers in a transportation model using one aggregation strategy and varying the level of aggregation on a set of randomly generated problems. Results show significant correlation between a posteriori error and actual error. A priori error is not significantly correlated with actual error. These preliminary results indicate that calculating the a posteriori error bound to select the appropriate aggregation level is a helpful strategy since the a posteriori bound varies in the same way that the actual error varies. In addition, one method of calculating the a posteriori bound is determined to be significantly tighter than the other method of calculating the a posteriori error bound.