Social Optimal Location of Facilities with Fixed Servers, Stochastic Demand, and Congestion

Castillo, Ignacio; Ingolfsson, Armann; Sim, Thaddeus

doi:10.1111/j.1937-5956.2009.01034.x

Cited by 50 publications

(37 citation statements)

References 32 publications

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“…Aboolian et al (2008b) generalized the results of Berman and Drezner (2007) by including in the objective function in addition to the expected travel and waiting cost, also the fixed cost of opening facilities and the variable cost of the servers. Castillo et al (2009) studied a problem similar to that of Aboolian et al (2008b). In their model, there is a centralized authority that determines the assignment of customers to the facilities (whereas Aboolian et al (2008b) assign customers to the closest facility).…”

Section: Congested Facilities With Immobile Serversmentioning

confidence: 99%

“…In their model, there is a centralized authority that determines the assignment of customers to the facilities (whereas Aboolian et al (2008b) assign customers to the closest facility). Also, Castillo et al (2009) use approximations for the expected waiting time. Finally, Baron et al (2008) analyzed the problem of determining the number, location and capacity of congested facilities under general assumptions such as spatially continuous demand, general server arrival and service distributions, and nonlinear costs.…”

Section: Congested Facilities With Immobile Serversmentioning

confidence: 99%

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Hub Location Problems: The Location of Interacting Facilities

Kara

Taner

2011

International Series in Operations Research &Amp; Management Science

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), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. PrefaceThis book is the final result of a number of incidents that occurred to us while discussing location issues with colleagues at conferences. Frequently we attended presentations, in which the authors quoted the well-known references that helped to make the discipline what it is today. Upon further inquiry, though, it turned out that some of these colleagues had never actually read the original papers. We then discussed among ourselves which contributions could be credited with shaping the field. And, lo and behold, we found that we, too, had neglected to read some of the papers that form the foundation of our science. Whether it was laziness or other things that got in the way, it had become clear that something had to be done. Our first thought was to collect the original contributions (once we could agree on what they were) and reprint them. When discussing this possibility with a publisher, we immediately ran into a roadblock in the form of copyright. While this appeared to have stopped our enthusiastic effort dead in its tracks, we kept on collecting and reading what we considered original contributions.This went on until we met Camille Price, who suggested that, rather than reprinting the original contributions, we should invite some of the leaders in our field and ask them to describe the original contribution, explain and interpret it, and comment on the impact that it had to the field. This was, of course, an excellent idea, and the response by our colleagues to our pertinent requests was equally enthusiastic. What you hold in your hands is the result of this effort.In other words, the purpose of this book is to provide easy access to the main contributions to location theory. The book is organized as follows. The introductory chapter provides an overview of some of the many facets of location analysis. This is followed by contributions in the main three fields of inquiry: minisum, minimax, and covering problems. The next chapters are part of an ever-growing list of nonstandard location models: models including competitive components, those that locate undesirable facilities, those with probabilistic features, and those that allow interactions between facilities. The following chapters discuss solution techniques: after a discussion of exact and heuristic techniques, we devote an entire chapter to Weiszfeld's method, and another to Lagrangean techniques. The last chapters of this book deal with the spheres of influence that the facilities generate and that attract viii customers to them, an...

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Section: Congested Facilities With Immobile Serversmentioning

confidence: 99%

Section: Congested Facilities With Immobile Serversmentioning

confidence: 99%

Hub Location Problems: The Location of Interacting Facilities

Kara

Taner

2011

International Series in Operations Research &Amp; Management Science

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“…A recent paper by Castillo et al (2002) considers a similar problem to the one discussed in this paper. The difference is that in Castillo et al (2002) there is a centralized assignment of customers to facilities and approximations are used for the probability of queuing delay, whereas in this paper customers are assigned to the closest facility and an exact queuing delay formula for the M/M/k is used.…”

mentioning

confidence: 95%

mentioning

confidence: 99%

“…The difference is that in Castillo et al (2002) there is a centralized assignment of customers to facilities and approximations are used for the probability of queuing delay, whereas in this paper customers are assigned to the closest facility and an exact queuing delay formula for the M/M/k is used. As a result the analysis is completely different from that in Castillo et al (2002). This paper is different from Berman and Drezner (2007) in that: (i) as mentioned earlier, in this paper the number of facilities is not limited and in the objective function the fixed cost of facilities and the variable cost of servers are also considered; (ii) whereas in Berman and Drezner (2007) the focus in solving the problem is on heuristics, in this paper, following a detailed analysis of the model, we propose an exact solution approach that is shown to be quite efficient in our computational analysis; and (iii) the solution procedures introduced in this paper can be modified to solve an extended model with service level constraints.…”

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confidence: 99%

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Location and allocation of service units on a congested network

2008

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We consider the problem of locating facilities and allocating servers on a congested network (LASCN). Demands for service that originate from the nodes are assumed to be Poisson distributed and the servers provide a service time that is exponentially distributed. The objective is to minimize the total cost of the system which includes a fixed installation cost, a variable server cost, a cost associated with travel time and a cost associated with the waiting time in the facility for all the customers. The problem is formulated using non-linear programming and subsequently analyzed. Results for exact and approximate solution approaches are reported. We also show that we can modify the approaches to solve the LASCN with constraints limiting both the travel time to the servers and the waiting time of customers.

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