Location-location routing problem and its application on refugee camps

Abstract

In the classical Location Routing Problem (LRP), the customers are at xed and known locations. Given the known customer locations, in LRP models, decisions are taken for distribution center locations and corresponding vehicle routes. However; for some public applications the locations of customers can also be decision variables coming from a discrete set. In this study we consider such an application where the locations of demand nodes will be determined while considering the distribution center location(s) and corresponding vehicle routes. To the best of our knowledge this variant of LRP has not been de ned in the location literature before. We refer this problem as Location-Location Routing Problem(L-LRP). We observe that, refugee camp location and management problem is a direct application of the L-LRP. In refugee camps certain public services are required to protect health, safety, dignity, etc. of the refugees. Thus, authorities should plan regular public service visits to the refugee camps to provide these services. In the refugee camp location problem authorities decide the locations of hosting institutions and routes of service providers originated from these institutions. Actually, in addition; authorities also decide the locations of these refugee camps. For the L-LRP, a linear mixed integer mathematical formulation is developed. To obtain results in shorter times with preserving solution qualities, a two-stage math-heuristic algorithm is presented. The computational analysis of mathematical formulation and heuristic algorithm are conducted on a real data set obtained from Southern part of Turkey.