Competitive Facility Location with Selfish Users and Queues

Dan, Teodora; Marcotte, Patrice

doi:10.1287/opre.2018.1781

Cited by 23 publications

(20 citation statements)

References 30 publications

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“…It can be easily verified that ∇h(p) is strongly monotone with modulus 1 for 0 < p ≤ 1 (the Jacobian matrix is positive definite diagonal, and the smallest possible eigenvalue is 1, see also Dan and Marcotte 2019). From the definitions of p and p , we have Thus the approximation error of the upper-level objective function ( 18) is O( 1 K ).…”

Section: Discussionmentioning

confidence: 90%

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Urban Bike Lane Planning with Bike Trajectories: Models, Algorithms, and a Real-World Case Study

Liu¹,

Shen

2018

SSRN Journal

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We study an urban bike lane planning problem based on the fine-grained bike trajectory data, which is made available by smart city infrastructure such as bike-sharing systems. The key decision is where to build bike lanes in the existing road network. As bike-sharing systems become widespread in the metropolitan areas over the world, bike lanes are being planned and constructed by many municipal governments to promote cycling and protect cyclists. Traditional bike lane planning approaches often rely on surveys and heuristics. We develop a general and novel optimization framework to guide the bike lane planning from bike trajectories. We formalize the bike lane planning problem in view of the cyclists' utility functions and derive an integer optimization model to maximize the utility. To capture cyclists' route choices, we develop a bilevel program based on the Multinomial Logit model. We derive structural properties about the base model and prove that the Lagrangian dual of the bike lane planning model is polynomial-time solvable. Furthermore, we reformulate the route choice based planning model as a mixed integer linear program using a linear approximation scheme. We develop tractable formulations and efficient algorithms to solve the large-scale optimization problem. Via a real-world case study with a city government, we demonstrate the efficiency of the proposed algorithms and quantify the trade-off between the coverage of bike trips and continuity of bike lanes. We show how the network topology evolves according to the utility functions and highlight the importance of understanding cyclists' route choices. The proposed framework drives the data-driven urban planning scheme in smart city operations management.

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Section: Discussionmentioning

confidence: 90%

“…Motivated by Dan and Marcotte (2019), we devise a linear approximation approach that approximates the convex parts in the objective function of (LL) by piecewise linear functions. Specifically, we sample from [0, 1] K points {p 1 , p 2 , .…”

Section: Bike Lane Planning With Route Choicesmentioning

confidence: 99%

Urban Bike Lane Planning with Bike Trajectories: Models, Algorithms, and a Real-World Case Study

Liu¹,

Shen

2018

SSRN Journal

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“…Our model's objective is to decide where preventive healthcare service facilities have to be located, whether they provide high quality, and how long patients have to wait for an appointment to maximize participation. Wang et al (2002); Marianov et al (2008) and Dan and Marcotte (2019), inter alia, developed mixed integer nonlinear programs that account for probabilistic clients' choices based on linear continuous waiting times. In contrast, we avoid the continuous nature of queuing theory since it is difficult for clients to evaluate a difference between, e.g., 2 and 2.1 weeks.…”

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confidence: 99%

Preventive healthcare facility location planning with quality-conscious clients

2020

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Pursuing the overarching goal of saving both lives and healthcare costs, we introduce an approach to increase the expected participation in a preventive healthcare program, e.g., breast cancer screening. In contrast to sick people who need urgent medical attention, the clients in preventive healthcare decide whether to go to a specific facility (if this maximizes their utility) or not to take part in the program. We consider clients' utility functions to include decision variables denoting the waiting time for an appointment and the quality of care. Both variables are defined as functions of a facility's utilization. We employ a segmentation approach to formulate a mixed-integer linear program. Applying GAMS/CPLEX, we optimally solved instances with up to 400 demand nodes and 15 candidate locations based on both artificial data as well as in the context of a case study based on empirical data within one hour. We found that using a Benders decomposition of our problem decreases computational effort by more than 50%. We observe a nonlinear relationship between participation and the number of established facilities. The sensitivity analysis of the utility weights provides evidence on the optimal participation given a specific application (data set, empirical findings).

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“…Mai and Lodi (2020) propose multicut OA inequities for groups of demand points and implement them in a cutting-plane approach. Different from most existing static CFLP models, Dan and Marcotte (2019) considered random utility based on both travel time and queuing delay at facilities, leading to a MINLP formulation. They derived a piecewise linear approximation and a heuristic method for solving this model.…”

Section: Literature Reviewmentioning

confidence: 99%

Sequential Competitive Facility Location: Exact and Approximate Algorithms

Qi¹,

Jiang²,

Shen³

2021

Preprint

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We study a competitive facility location problem (CFLP), in which two firms sequentially select locations of new facilities, in order to maximize their market shares of customer demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. Through integer programming methods, we derive an equivalent, single-level MINLP reformulation. In addition, we exploit the problem structures and derive two classes of valid inequalities, one based on submodularity and the other based on concave overestimation. We apply these inequalities in a branch-and-cut algorithm to find a globally optimal solution to CFLP. Furthermore, we propose an approximation algorithm for solving CFLP that is computationally more effective. Notably, this algorithm admits a constant approximation guarantee. Extensive numerical studies demonstrate that the exact algorithm can significantly accelerate the solving of CFLP on problem instances that have not been solved to optimality by existing methods. The approximation algorithm can find near-optimal solutions even more quickly.

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Competitive Facility Location with Selfish Users and Queues

Cited by 23 publications

References 30 publications

Urban Bike Lane Planning with Bike Trajectories: Models, Algorithms, and a Real-World Case Study

Urban Bike Lane Planning with Bike Trajectories: Models, Algorithms, and a Real-World Case Study

Preventive healthcare facility location planning with quality-conscious clients

Sequential Competitive Facility Location: Exact and Approximate Algorithms

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