Equilibrium Facility Location on Networks

Miller, Tan; Friesz, Terry L.; Tobin, Roger L.

doi:10.1007/978-3-662-03280-0

Cited by 59 publications

(29 citation statements)

References 46 publications

(106 reference statements)

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“…In the area of competitive location there has been a high research activity on game-theoretic models for facility location during the last decades [18,33]. In these models facility owners are players that decide where to open a facility.…”

Section: Related Workmentioning

confidence: 99%

Competitive Cost Sharing with Economies of Scale

Hoefer

2009

Algorithmica

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We consider a general class of non-cooperative buy-at-bulk cost sharing games, in which k players make investments to purchase a set of resources. Each resource has a certain cost and must bought to be available to the players. Each player has a certain constraint on the number and types of resources that she needs to have available, and she can specify payments to make a resource available to her. She strives to fulfill her constraint with the smallest investment possible. Our model includes a natural economy of scale: for a subset of players capacity must be installed at the resources, and the cost increase for a resource r is composed of a fixed price c(r) and a global concave capacity function g. This cost can be shared arbitrarily between players.We consider the existence and total cost of pure-strategy exact and approximate Nash equilibria. In general, prices of anarchy and stability depend heavily on the economy of scale and are (k/g(k)). For non-linear functions g pure Nash equilibria might not exist, and deciding their existence is NP-hard. For subclasses of games corresponding to covering problems, primal-dual methods can be applied to derive cheap and stable approximate Nash equilibria in polynomial time. In addition, for singleton games optimal Nash equilibria exist. In this case expensive exact as well as cheap approximate Nash equilibria can be computed in polynomial time. Most of these results can be extended to games based on facility location problems.

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Section: Related Workmentioning

confidence: 99%

Competitive Cost Sharing with Economies of Scale

Hoefer

2009

Algorithmica

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“…Second, we can formulate the dynamic Cournot-Nash equilibrium model as a variational inequality, or essentially as T variational inequalities, given the independence of each period from all other periods. For purposes of brevity, we simply state this and refer the reader to Miller, Tobin and Friesz (1991), and Tobin, Miller and Friesz (1995) for detailed discussions of equivalent variational inequality formulations of Cournot-Nash equilibrium models. Additionally, these citations will provide the interested reader with detailed background on both the development of, and key characteristics of Cournot-Nash static and dynamic models -discussions that we again omit in this paper for purposes of brevity.…”

Section: De…nition and Formulationmentioning

confidence: 99%

“…First, as noted, in contrast to a static version of this model (Miller, Tobin, and Friesz, 1992), the dynamic model addresses the timing of location decisions in addition to simply the actual location choice. Further, one can easily modify the dynamic model to evaluate such alternatives as staged capacity location (as we will illustrate later) and expansion (see Miller, Friesz, and Tobin, 1995). Such an extension for example, allows a …rm to determine if it is more pro…table in certain cases to locate and then expand its capacity at a site over time in response to increasing market demands, rather than to initially construct a large facility.…”

Section: De…nition and Formulationmentioning

confidence: 99%

Reaction Function Based Dynamic Location Modeling in Stackelberg–Nash–Cournot Competition

et al. 2006

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We formulate a dynamic facility location model for a …rm locating on a discrete network. It is assumed that this locating …rm will act as the leader …rm in an industry characterized by Stackelberg leader-follower competition. The …rm's I competitors are assumed to act as Cournot …rms and are each assumed to operate under the assumption of zero conjectural variation with respect to their I 1 Cournot competitors. Using sensitivity analysis of variational inequalities within a hierachical mathematical programming approach, we develop reaction function based dynamic models to optimize the Stackelberg …rm's location decision. In the second half of this paper, we use these models to illustrate through a numerical example the enhanced insights yielded by a reaction based, dynamic approach

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“…Lu and Bostel [9] gave a facility location model for logistics systems including reverse flows. Although Miller et al [10] studied the location problem with equilibrium-constrained models and algorithms in detail, they were only single level models, which could not consider benefits both planners and customers.…”

Section: Introductionmentioning

confidence: 99%

A bi-level programming model and solution algorithm for the location of logistics distribution centers

Sun

Gao

2008

Applied Mathematical Modelling

197

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In this paper, by considering benefits of customers and logistics planning departments, a bi-level programming model is presented to seek the optimal location for logistics distribution centers. The upper-level model is to determine the optimal location by minimizing the planners' cost, and the lower gives an equilibrium demand distribution by minimizing the customers' cost. Based on the special form of constraints, a simple heuristic algorithm is proposed. Finally, a numerical example is used to illustrate the application of the method, which shows that the algorithm is feasible and advantageous.

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Equilibrium Facility Location on Networks

Cited by 59 publications

References 46 publications

Competitive Cost Sharing with Economies of Scale

Competitive Cost Sharing with Economies of Scale

Reaction Function Based Dynamic Location Modeling in Stackelberg–Nash–Cournot Competition

A bi-level programming model and solution algorithm for the location of logistics distribution centers

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