A novel maximum dispersion territory design model arising in the implementation of the WEEE-directive

The problem discussed in this paper is motivated by the new recycling directive Waste Electrical and Electronic Equipment of the European Commission. The core of this law is, that each company which sells electrical or electronic equipment in a European country has the obligation to recollect and recycle an amount of returned items which is proportional to its market share. To assign collection stations to companies, in Germany for one product type a territory design approach is planned. However, in contrast to classical territory design, the territories should be geographically as dispersed as possible to avoid that a company, respectively its logistics provider responsible for the recollection, gains a monopoly in some region. First, we identify an appropriate measure for the dispersion of a territory. Afterwards, we present a first mathematical programming model for this new problem as well as a solution method based on the Greedy Randomized Adaptive Search Procedure methodology. Extensive computational results illustrate the suitability of the model and assess the effectiveness of the heuristic.