A posteriori error bounds in linear programming aggregation

A major topic in aggregation of linear programming problems is the estimation of the aggregation error, i.e., the computation of bounds for the loss of optimality which results from the coarsening of information caused by aggregation. A widely used method to compute bounds for variable-aggregated linear programs was developed by Zipkin [2, p. 41, 3]. Several extensions and modifications have been proposed. We present an overview of these bound computation methods and extend the methods in case that: (1) several dual solutions are available and (2) optimal disaggregation is performed. By means of a small numerical study, indications for the quality of the bounds are derived. The discussion is restricted to column (i.e. variable) aggregation.