A two-level Hierarchical Nested Cooperative Location model

Abstract

This paper introduces the two-level Hierarchical Nested Cooperative Location (HNCL) model, extending the literature on discrete cooperative covering problems. We analyse the problem of locating facilities arranged in a two-level nested hierarchy and cooperating to maximize the covered demand. Facilities are characterized by different coverage decay functions according to the hierarchical level they belong to (upper and lower). Cooperation occurs between facilities at the same level (intra-level cooperation) and at different levels (inter-level cooperation) of the hierarchy according to mechanisms modelled through joint coverage functions. Two budget constraints are introduced for the total cost the decision-maker is willing to incur for locating facilities at each level. The HNCL problem is first formulated as a mixed-integer non-linear programming (MINLP) model; then, an equivalent mixed-integer linear program (MILP) is developed. We tested the HNCL model on instances randomly generated and extracted from a real-world network. The results are provided and discussed, highlighting the contribution of cooperative coverage compared to the individual one.