A multiobjective network design problem with equity constraints

Multiobjective network design and routing problems include cost, accessibility, environmental concerns, revenue and equity among other objectives. Focusing on regional equity, the concept of coverage from facility location analysis has been introduced in network design and routing models. However, the problem of distributional equality, recently introduced in facility location literature, has not yet been strongly considered in network design/coverage models. The authors introduce one such model, emphasising on the criterion of regional equity to accessibility among remote, dispersed, rural communities. More specifically, they detect a subset S, of n given elements, which constitute the nodes of a salesman tour, such that: every node not on the tour is within some predetermined covering distance standard, T, of a node that is on the tour and distributional equality in travel distances of nodes not in S to the nerest node in S, is maximised. The authors end with a numerical example applied on the maritime transport network design of the Aegean Islands.