A Hierarchical Flow Capturing Location Problem with Demand Attraction Based on Facility Size, and Its Lagrangian Relaxation Solution Method

Abstract

This article presents a hierarchical flow capturing location problem (HFCLP) and proposes an effective Lagrangian heuristic solution method. The original flow capturing location problem (FCLP) aims to locate a given number of facilities on a network to maximize the total flow that can be serviced at facilities along their preplanned routes, such as daily commute to work. We extend the original model to allow a decision maker to select the size of facilities among m different size alternatives. Larger facilities are assumed to be more attractive and, therefore, can attract more customers, but they cost more to construct than smaller ones. Customers deviate from their preplanned routes to access a facility's service when the size of the facility is sufficiently large. The degree of deviation from the original path is measured by the additional distance customers have to go to access facilities, and the acceptable deviation distance becomes larger as the size of a facility increases. This article presents a new problem in which the number of facilities of each size and their locations are simultaneously determined so as to capture as much flow as possible within the total budget available for locating all facilities. We present an integer programming formulation of the problem and devise a Lagrangian relaxation solution method. The proposed algorithm is tested using road networks with 300 and 500 nodes. The results show that the method produces high-quality solutions in a fairly short time.

Heuristic approaches for the flow-based set covering problem with deviation paths

“…First, the FILM or FCLM (Berman et al, 1992;Hodgson, 1990) is a maximal coverage model that entails facility locations to serve passing flows which are considered as captured if a facility is located on the flow paths. The model has been evolving to capture more realistic concerns, such as the different sized facilities (Tanaka and Furuta, 2012) and flow uncertainty (Teodorović and Šelmić , 2013). A critical issue -limited vehicle range, that was neglected in the FILM or FCLM was incorporated in the FRLMs (Kim and Kuby, 2005Upchurch et al, 2009), a new set of maximal flow coverage models that consider the effects of limited vehicle ranges for undertaking long-distance trips via multi-stop refueling.…”

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

“…The problem determines simultaneously both the locations of the facilities and their service start times so as to maximally cover flows that can consume the service at one of the facilities after work and be home by a given time. Tanaka and Furuta () extended the basic FIP to allow a decision‐maker to select the size of facilities among several size alternatives, where larger but more‐costly facilities can induce larger deviation from the shortest path and thereby attract more demand. Chung and Kwon () introduced a multi‐period planning model in which decisions about facility locations are made over several years.…”

Evasive flow capture: Optimal location of weigh‐in‐motion systems, tollbooths, and security checkpoints

“…Below, we summarize the characteristics of various FCPs found in the literature. Different aspects of these problems include: Deviations from preplanned trips where a flow is considered captured not only if a facility (e.g., gas station and restaurant) is located along the predetermined path of a flow, but also in its relative proximity . Limited capacity of the facilities , as well as decisions about the size of facilities . Temporal aspects such as time spent in a facility , determining service start times , and multiperiod planning where decisions about the facility locations are made over several years . Multiple counting of consumers in which the level of consumption depends on the number of facilities (e.g., billboards) that customers encounter , and consumers' preference for obtaining a service at the beginning, middle, or end of their trips . Probabilistic information about the travel origins, turning movements to visit facilities, and customer arrival and service rates . Competition between facilities that have the same or different owners . Synthesis with demand coverage, where flow capture (e.g., intercepting customers along their trips) is addressed jointly with covering fixed customers residing at nodes . …”

“…2. Limited capacity of the facilities [5,50], as well as decisions about the size of facilities [49]. 3.…”