ELSEVIER European Journal of Operational Research 83 (1995) 200-219 EUROPEAN JOURNAL OF OPERATIONAL RESEARCH Theory and Methodology The hub location and routing problem Turgut Aykin RUTGERS, The State University of New Jersey, Newark, NJ 07102, USA Received November 1991; revised May 1993 Abstract In this paper, we consider the hub location and routing problem in which the hub locations and the service types for the routes between demand points are determined together. Rather than aggregating the demand for the services, flows from an origin to different destination points are considered separately. For each origin-destination pair, one-hub-stop, two-hub-stop and, when permitted, direct services are considered. In the system considered, the hubs interact with each other and the level of interaction between them is determined by the two-hub-stop service routes. A mathematical formulation of the problem and an algorithm solving the hub location and the routing subproblems separately in an iterative manner are presented. Computational experience with four versions of the proposed algorithm differing in the method used for finding starting solutions is reported. Keywords: Location; Distribution; Heuristics 1. Introduction Although several studied involving location of new facilities with fixed amounts of interfacility flows have appeared in the literature (e.g. multifacility location problem, p-median and p-center problems with mutual communication, Kolen, 1986, and Chhajed and Lowe, 1992), previous research on the location-allocation problem was focused primarily on the situations involving location of non-interacting new facilities. It is usually assumed that new facilities would not interact with other new facilities nor would they interact with the demand points assigned to other new facilities. This assumption of the location-allocation problem has been relaxed recently in the studies on the hub location problems on the plane E 2 (O'Kelly, 1986; Aykin, 1988). In a system employing hubs, item flow occurs between demand points through a set of new facilities (hubs) acting as switching/concentration points. Flows between two demand points, say i and j, are either sent through one hub, if both i and j are served by the same hub (that is, from i to hub and from hub to j), or through two hubs, if they are served by different hubs (that is, from i to hub serving i, from hub serving i to hub serving j and finally from hub serving j to j). Thus, besides the interactions between the hub facilities and demand points considered in the location-allo- cation problem, interactions between the hubs themselves exist due to the flows channelled between them. These inter-hub flows affect both the location and the allocation decisions. The hub location problem on the plane E 2 with one and two hubs was first studied by O'Kelly (1986) and with three hubs 0377-2217/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD! 0377-2217(93)E0173-U