The facility location problem described in this paper comes from an industrial application in the slaughterhouse industry of Norway. Investigations show that the slaughterhouse industry experiences economies of scale in the production facilities. We examine a location-allocation problem focusing on the location of slaughterhouses, their size and the allocation of animals in the different farming districts to these slaughterhouses. The model is general and has applications within other industries that experience economies of scale. We present an approach based on linearization of the facility costs and Lagrangean relaxation. We also develop a greedy heuristic to find upper bounds. We use the method to solve a problem instance for the Norwegian Meat Co-operative and compare our results to previous results achieved using standard branch-and-bound in commercial software.
Broek, van den, J. J. J., Schütz, P., Stougie, L., & Tomasgard, A. (2006). Location of slaughterhouses under economies of scale. European Journal of Operational Research, 175(2), 740-750. https://doi.org/10.1016/j.ejor.2005.05.025