Re-aggregation Approach to Large Location Problems

The majority of location problems are known to be NP-hard. An aggregation is a valuable tool that allows to adjust the size of the problem and thus to transform it to the problem that is computable in a reasonable time. An inevitible consequence is the loss of the optimality due to aggregation error. The size of the aggregation error might be significant, when solving spatially large problems with huge number of customers. Typically, an aggregation method is used only once, in the initial phase of the solving process. Here, we propose new re-aggregation approach. First, our method aggregates the original problem to the size that can be solved by the used optimization algorithm, and in an each iteration the aggregated problem is adapted to achieve more precise location of facilities for the original problem. We use simple heuristics to minimize the sources of aggregation errors, know in the literature as, sources A, B, C and D. To investigate the optimality error, we use the problems that can be computed exactly. To test the efficiency of the proposed method, we compute large location problems reaching 80000 customers.