An O(m² + mn²) algorithm for the bi-objective location problem on a network with mixed metrics

In this paper, we formulate the Euclidean maximin with the network minisum bi‐objective location model for a semi‐obnoxious facility on a transportation network that is embedded into the Euclidean plane. The Euclidean distance metric is used in modelling the undesirable characteristics of the facility, using the maximin objective, while the network shortest path distance metric is used for modelling the transportation cost to these facilities using the minisum objective. After identifying the problem properties, we develop an O(m² + mn²) algorithm for generating the efficient set and implement this algorithm in a realistic example involving the location of a semi‐obnoxious facility in the province of Bursa in Turkey.