Geographical Analysis

The Probabilistic Minisum Flow Interception Problem: Minimizing the Expected Travel Distance until Intercept under Probabilistic Interception

Early View

We develop a variant of the flow interception problem (FIP) in which it is more desirable for travelers to be intercepted as early as possible in their trips. In addition, we consider flows being intercepted probabilistically instead of the deterministic view of coverage assumed in the FIP literature. We call the proposed model the probabilistic minisum FIP (PMFIP); it involves minimizing the sum of the expected distance that each flow travels until intercepted at a facility among placed facilities. This extension allows us to evaluate the effect of facility location under any given value of the interception probability and to apply the model to a variety of situations. We apply the proposed model to an example network by assuming a hypothetical situation in which people gather at a stadium from various nodes on the network, and receive some goods or services on the way to the stadium. We analyze optimal solutions obtained by varying the number of facilities and interception probability. It is shown that the expected travel distance until intercept is greatly reduced by means of a few optimally located facilities under a moderate interception probability.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.