Location models for airline hubs behaving as M/D/c queues

Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and {\em c} servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of {\em b} airplanes in queue, to be lesser than a value $\alpha$. Due to the computational complexity of the formulation. The model is solved using a meta-heuristic based on tabu search. Computational experience is presented.Hub location, congestion, tabu-search

Hierarchical location-allocation models for congested systems

In this paper we address the issue of locating hierarchical facilities in the presence of congestion. Two hierarchical models are presented, where lower level servers attend requests first, and then, some of the served customers are referred to higher level servers. In the first model, the objective is to find the minimum number of servers and their locations that will cover a given region with a distance or time standard. The second model is cast as a Maximal Covering Location formulation. A heuristic procedure is then presented together with computational experience. Finally, some extensions of these models that address other types of spatial configurations are offered.Hierarchical location, congestion, queueing

Median problems in networks

The P-median problem is a classical location model “par excellence”. In this paper we, first examine the early origins of the problem, formulated independently by Louis Hakimi and Charles ReVelle, two of the fathers of the burgeoning multidisciplinary field of research known today as Facility Location Theory and Modelling. We then examine some of the traditional heuristic and exact methods developed to solve the problem. In the third section we analyze the impact of the model in the field. We end the paper by proposing new lines of research related to such a classical problem.P-median, location modelling

Probabilistic maximal covering location-allocation models with constrained waiting time or queue length for congested systems

When dealing with the design of service networks, such as health and EMS services, banking or distributed ticket selling services, the location of service centers has a strong influence on the congestion at each of them, and consequently, on the quality of service. In this paper, several models are presented to consider service congestion. The first model addresses the issue of the location of the least number of single--server centers such that all the population is served within a standard distance, and nobody stands in line for a time longer than a given time--limit, or with more than a predetermined number of other clients. We then formulate several maximal coverage models, with one or more servers per service center. A new heuristic is developed to solve the models and tested in a 30--nodes network.Discrete facility location, queuing, emergency services location

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

The P-median problem in a changing network: The case of Barcelona

In this paper a p--median--like model is formulated to address the issue of locating new facilities when there is uncertainty. Several possible future scenarios with respect to demand and/or the travel times/distance parameters are presented. The planner will want a strategy of positioning that will do as ``well as possible'' over the future scenarios. This paper presents a discrete location model formulation to address this P--Median problem under uncertainty. The model is applied to the location of fire stations in Barcelona.Discrete facility location, scenarios, emergency services location

A Mixed Integer Linear Program for the Rapid Transit Network Design Problem with Static Modal Competition (Short Paper)

We present a mixed integer linear program for the rapid transit network design problem with static modal competition. Previous discrete formulations cannot handle modal competition for realistic size instances because of the complexity of modeling alternatives for each flow in the network. We overcome this difficulty by exploiting a pre-assigned topological configuration. Results of a case study will be presented at the conference

Product line optimization with multiples sites

We consider the problem faced by a retailer that selects the set of products to allocate in finite capacity stores to maximize patronage. The purchase decision is made by customers that purchase exactly one product that maximizes her utility that depends on the product price, distance traveled to the store and reservation price, known to the retailer. The retailer's bilevel optimization problem is transformed into an integer optimization formulation. Small size instances are solved optimally, while for large instances, we explore Benders Decomposition, Branch and Cut and Cut and Branch to solve the problem. Our computational results show that the proposed Cut and Branch method obtains the best results, and improves on the current state of the art

Hierarchical location-allocation models for congested systems

In this paper we address the issue of locating hierarchical facilities in the presence of congestion. Two hierarchical models are presented, where lower level servers attend requests first, and then, some of the served customers are referred to higher level servers. In the first model, the objective is to find the minimum number of servers and their locations that will cover a given region with a distance or time standard. The second model is cast as a Maximal Covering Location formulation. A heuristic procedure is then presented together with computational experience Finally, some extensions of these models that address other types of spatial configurations are offered