A comparison of linear reformulations for multinomial logit choice probabilities in facility location models

Haase, Knut; Müller, Sven

doi:10.1016/j.ejor.2013.08.009

Cited by 88 publications

(40 citation statements)

References 11 publications

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“…More realistic models where the price of service depends on location should also be considered. On the algorithmic side, three avenues can be pursued: (i) the design of improved approximations for the nonlinear terms involved in the semi-exact method, and (ii) the design of fast heuristics for determining good sets of facility locations, from which efficient methods for determining optimal service rates can be initiated and, finally (iii) the investigation of approximations based on the exact mixed integer formulation of the logit-based location models proposed by [Haase, 2009], [Benati and Hansen, 2002], [Zhang et al, 2012], and numerically analyzed by [Haase and Müller, 2014]. [Marianov et al, 2008] Marianov, V., Ríos, M., andIcaza, M. J.…”

Section: Conclusion and Extensionsmentioning

confidence: 99%

Competitive Facility Location with Selfish Users and Queues

Dan

Marcotte

2019

Operations Research

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In a competitive environment, we consider the problem faced by a service firm that makes decisions with respect to both the location and service levels of its facilities, taking into account that users patronize the facility that maximizes their individual utility, expressed as the sum of travel time, queueing delay, and a random term. This situation can be modeled as a bilevel program that involves discrete and continuous variables, as well as linear and nonlinear functions. We design for its solution an approximation algorithm that provides "quasi-optimal" solutions, as well as heuristics that exploit the very structure of the problem.

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Section: Conclusion and Extensionsmentioning

confidence: 99%

Competitive Facility Location with Selfish Users and Queues

Dan

Marcotte

2019

Operations Research

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“…De-Los-Santos et al (2017) developed a linear approximation by using that one alternative with fixed utility is available. An overview of common linearizations of the logit model is given by Haase and Müller (2014).…”

Section: Passenger Route Choicementioning

confidence: 99%

Railway Timetabling With Integrated Passenger Distribution

Hartleb

Schmidt²

2019

SSRN Journal

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Timetabling for railway services often aims at optimizing travel times for passengers. At the same time, restricting assumptions on passenger behavior and passenger modeling are made. While research has shown that passenger distribution on routes can be modeled with a discrete choice model, this has not been considered in timetabling yet. We investigate how a passenger distribution can be integrated into an optimization framework for timetabling and present two mixed-integer linear programs for this problem. Both approaches design timetables and simultaneously find a corresponding passenger distribution on available routes. One model uses a linear distribution model to estimate passenger route choices, the other model uses an integrated simulation framework to approximate a passenger distribution according to the logit model, a commonly used route choice model. We compare both new approaches with three state-of-the-art timetabling methods and a heuristic approach on a set of artificial instances and a partial network of Netherlands Railways (NS). Highlights• We propose a novel timetabling approach with integrated passenger distribution model • Two mixed integer linear programs for this problem are developed • One uses a linear distribution model, the other a simulation of passenger distribution • One integrates a linear distribution, the other a simulation of passenger distribution • We compare our models/programs in experiments to state-of-the-art timetabling methods • Integrating a passenger distribution model can help to find better timetables Declarations of interest none Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. 2

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“…When dealing with optimization and especially facility location, Haase and Müller (2014) have tested different linearizations of the multinomial logit model (MNL) for the problem of selecting a subset of r sites maximizing coverage, i.e. the part of the demand that does not go to competitors.…”

Section: Introductionmentioning

confidence: 99%

Robust Location of New Housing Developments Using a Choice Model

Garcia

Alfandari

2015

SSRN Journal

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We consider the issue of choosing a subset of locations to construct new housing developments maximizing the satisfaction of potential buyers. The allocation of demands to the selected locations is modeled by a choice model, based on the distance to the location, realestate prices and incomes. We study two robust counterparts of the optimal location problem, where uncertainty lies on demand volumes for the first one, and on customer preferences for the second one. In both cases, the parameters subject to uncertainty appear both in the objective function and constraints. The second robust model combines a scenario-based approach with nominal, price-centric and distance-centric scenarios on customers preferences, and an uncertainty budget approach that limits the number of cities that can deviate from the nominal scenario. Computational experiments are conducted on instances of the Paris region to analyze the tractability of the problem and its robust counterparts, and derive insights for the new housing development issue.

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A comparison of linear reformulations for multinomial logit choice probabilities in facility location models

Cited by 88 publications

References 11 publications

Competitive Facility Location with Selfish Users and Queues

Competitive Facility Location with Selfish Users and Queues

Railway Timetabling With Integrated Passenger Distribution

Robust Location of New Housing Developments Using a Choice Model

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