Facility location, Flow interception, Flow-based demand, Transportation network,
This article addresses the pickup problem, wherein patrons briefly interrupt their predetermined journeys to obtain a simple good, such as fast food or a video, and then resume their journeys. This is a problem from the class known as the flow-interception location problems. Traditional flow-interception location models (FILMs) are used to select service locations such that the intercepted flows are maximized. In these traditional models, only flow quantities are considered; these models do not consider where a pickup is made in a journey. However, in the real world, consumers often wish to obtain a product or service at or near a specific location along their trips. The pickup model (PUP) proposed here considers consumers' locational preferences, providing a much broader, more realistic approach than FILM (a special case of PUP) to problems in the private and public sectors. By considering which patrons are served where, PUP transforms the FILM into a flow-interception location-allocation model, providing a fruitful garden for further research. Geographic information systems and optimization engines are integrated to investigate the PUP model in realworld transportation systems. Reported findings demonstrate that the optimal locations identified by traditional models arise solely from network flow structure, whereas the optimal locations identified by PUP result from trade-offs between network flow structure and the importance of proximity to preferred locations. One important discovery is that PUP solutions are superior to those of traditional FILMs if consumers have locational preferences. Up-to-date, real-world transportation networks provide a realistic test-bed for this and other models of the flow-interception type. IntroductionOne of the most important ways an industrial firm, retail outlet, or government agency can enhance its chances of success is to identify a good location. One approach is to use location-allocation models that optimally locate service facilities and allocate demand to them. Traditional location models such as the p-median model (ReVelle and Swain 1970) and the maximal covering location model (Church and ReVelle 1974) deal with demands expressed at fixed locations in the network (point-based demand). Demands for many services are, however, expressed by flows in a network. Since the early 1990s (Hodgson 1990;Berman, Larson, and Fouska 1992), there has been considerable research interest, represented by about 40 published academic articles, in the flow-interception location model (FILM), in which demand is represented as flows traveling on origin-destination (OD) paths of the network (flow-based demand). FILM can be applied to the strategic location of automatic teller machines, convenience stores, fast food outlets
Flow-intercepting problems have received considerable interest, represented by about 40 academic publications, since the early 1990s. Point-based demand aggregation also has received much research interest in both industry and academia. Systematic studies of flow data aggregation for flow-intercepting problems have not, however, been reported to date. Our research highlights the importance of flow-based demand aggregation and develops a framework for aggregating such demand. This framework represents the first systematic study of aggregation for flow-intercepting location models (FILM). The standard FILM is the perfect model for our goals-its aggregation errors are easy to understand and its outputs are easy to measure and compare. Our research uses geographic information systems, optimization, and heuristic technologies to examine the special network flow structure of a real-world transportation system and to develop a comprehensive method of aggregating data for the standard FILM. We apply our method to the 2001 afternoon peak traffic data for Edmonton, Alberta (the sixth largest Canadian city) and find this application to be extremely efficient. We discover that in the Edmonton traffic flow network, a large number of paths have very small flows; major flows are concentrated in a limited number of paths; and a large number of small-flow paths and a large number of low-flow nodes on local streets have negligible effects on facility locations for FILM. We speculate that most real-world transportation systems may have similar characteristics.
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