### Abstract

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.

Original language | English |
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Journal | Geographical Analysis |

DOIs | |

Publication status | Published - 2019 Jan 1 |

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### ASJC Scopus subject areas

- Geography, Planning and Development
- Earth-Surface Processes

### Cite this

**The Probabilistic Minisum Flow Interception Problem : Minimizing the Expected Travel Distance until Intercept under Probabilistic Interception.** / Tanaka, Kenichi; Kurita, Osamu.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The Probabilistic Minisum Flow Interception Problem

T2 - Minimizing the Expected Travel Distance until Intercept under Probabilistic Interception

AU - Tanaka, Kenichi

AU - Kurita, Osamu

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85065652653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065652653&partnerID=8YFLogxK

U2 - 10.1111/gean.12197

DO - 10.1111/gean.12197

M3 - Article

AN - SCOPUS:85065652653

JO - Geographical Analysis

JF - Geographical Analysis

SN - 0016-7363

ER -