USING A QUADRATIC PROGRAMMING APPROACH TO SOLVE SIMULTANEOUS RATIO AND BALANCE EDIT PROBLEMS

Often, items collected by the Economic Census are first subjected to ratio edit tests and associated corrections to ensure consistency within the questionnaire and within the industry and are then subsequently “balanced” to ensure additivity with other data items. With this two-step procedure, the balanced data often fail to satisfy the original ratio edit tests. In most cases, this does not pose a data quality problem. However, there are situations in which it is undesirable to “undo” the original ratio edit corrections to satisfy additivity: examples include marginal totals in two-dimensional balance complexes and derived items that combine previously ratio-edited items with unedited items. We present an approach that first uses non-linear (quadratic) programming to find data “adjustment” solutions that satisfy such simultaneous balancing and ratio editing problems and then performs controlled rounding to obtain integer solutions.