Facility Location Concepts, Models, Algorithms and Case Studies
This book deals with location problems. Location problems establish a set of facilities (resources) to minimize the cost of satisfying a set of demands (customers) with respect to a set of constraints. There are four components that describe location prob
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Hub Location Problem Masoud Hekmatfar and Mirsaman Pishvaee
One of the novel topics in location problems is the hub location problem. There are plenty of applications for the hub location problem; therefore, this section is dedicated to introducing this problem to readers. The preface is composed of three parts: apprehensions, definitions, and classifications of the hub location problem. In this chapter we discuss services such as, movement of people, commodities and information which occurs between an origin-destination pair of nodes (see A–B in Fig. 11.1 as an origin-destination pair). Each origin-destination pair needs a service different from other pairs. Thus, the commodities carried from i to j are not interchangeable with the commodities carried from j to i . If we have N nodes and if each node can be either an origin or a destination, we’ll have N.N 1/ origin-destination pairs of nodes in a network which form a fully connected network (a network in which all nodes are connected together). Notice that i j pair is different from j i pair. A sample network with six nodes is presented in Fig. 11.1 (Daskin 1995). Assuming that we have different traffic services in this network and that each vehicle can service five origin-destination pairs every day, with 18 vehicles, we will be able to service ten nodes every day. If we set one of the nodes as a hub1 node and connect it to all of the other nodes, which are introduced as spoke, we will have 2.N 1/ connections to service all origin-destination node pairs. This network is presented in Fig. 11.2 (Daskin 1995). In this network, if there are different traffic services and if each vehicle can service five origin-destination pairs every day, with 18 vehicles, we will be able to service 46 nodes every day. Thus, with fixed traffic resources, we can service more cities with a hub network than with a completely connected network2. 1
Hub means the ball in the center of a wheel and Campbell (1994) defined it as “the facilities that are servicing many origin-destination pairs as transformation and tradeoff nodes, and are used in traffic systems and telecommunications.” 2 This argument ignores vehicles’ capacity. It should be clear that the volume of goods or the number of people transported on each link in the hub-and-spoke network will be considerably greater than the number transported on each link of the fully connected network. This also ignores differences in the distances between nodes as it assumes that the number of origin-destination pair trips a vehicle can service is independent from the distances between the nodes. R.Z. Farahani and M. Hekmatfar (eds.), Facility Location: Concepts, Models, Algorithms and Case Studies, Contributions to Management Science, c Physica-Verlag Heidelberg 2009 DOI 10.1007/978-3-7908-2151-2 11,
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Fig. 11.1 A fully connected network with 6 nodes and 30 origin-destination pairs (Daskin 1995)
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Fig. 11.2 A hub and spoke network with 6 nodes and 30 origin-destination pairs (Das
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