Vladimir Marianov

The Queueing Maximal availability location problem: A model for the siting of emergency vehicles

Abstract The Maximal Availability Location Problem (MALP) has been recently formulated as a probabilistic version of the maximal covering location problem. The added feature in MALP is that randomness into the availability of servers is considered. In MALP, though, it is assumed that the probabilities of different servers being busy are independent. In this paper, we utilize results from queuing theory to relax this assumption, obtaining a more realistic model for emergency systems: the Queueing MALP or Q-MALP. We also consider in this model that travel times or distances along arcs of the network are random variables. We show here how to site limited numbers of emergency vehicles, such as ambulances, in such a way as to maximize the calls for service which have an ambulance available within a time or distance standard with reliability α — using a queueing theory model for server availability. We also propose some extensions to the basic model. Formulations are presented and computational experience is offered.

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

Models are presented for the optimal location of hubs in airline networks, which take into consideration the congestion effects. Hubs, which are typically the most congested airports, are modeled as M/D/c queuing systems. A formula is derived for the probability of a number of customers in the system, which is later used to propose a capacity constraint. This constraint limits the probability of more than b airplanes in queue, to be smaller than or equal to a given value. Due to the computational complexity of the formulation, the model is solved using a heuristic based on tabu search. Computational experience is presented together with an example using a data set available in the literature.

The queuing probabilistic location set covering problem and some extensions

Abstract The deterministic location set covering problem seeks the minimum number of servers and their positions such that each point of demand has at least one server initially stationed within a time or distance standard. In an environment in which servers are frequently busy, the problem can be cast as the probabilistic location set covering problem. In the probabilistic formulation, the coverage constraint becomes an availability constraint: a requirement that each point of demand has a server actually available within the time standard, with alpha reliability. The objective of minimizing the required number of servers remains the same. An earlier probabilistic statement of this problem assumed that the server availabilities were independent. In this paper, queuing theory is applied to the development of the availability constraints. This new generation of probabilistic location model thus corrects the prior assumption of independence of server availability. Formulations are presented and computational experience is offered, together with an extension: the Maximin Availability Siting Heuristics, MASH.

Foundations of location analysis

Pioneering Developments in Location Analysis.- Uncapacitated and Capacitated Facility Location Problems.- Median Problems in Networks.- Continuous Center Problems.- Discrete Center Problems.- Covering Problems.- Equilibria in Competitive Location Models.- Sequential Location Models.- Conditional Locational Problems on Networks and in the Plane.- The Location of Undesirable Facilities.- Stochastic Analysis in Location Research.- Hub Location Problems: The Location of Interacting Facilities.- Exact Solution of Two Location Problems via Branch-and-Branch.- Exploititng Structure: Location Problems on Trees and Treelike Graphs.- Heuristics for Location Problems.- The Weiszfeld Algorithm: Proof, Amendments, and Extensions.- Lagrangean Relaxation-Based Techniques in the Solution of Facility Location Problems.- Gravity Modeling and its Impact on Location Analysis.- Voronoi Diagrams and their Uses.- Central Places: The Theories of von Thunen, Christaller, and Losch.

Probabilistic, Maximal Covering Location—Allocation Models forCongested Systems

When dealing with the design of service networks, such as health andemergency medical services, banking or distributed ticket-selling services, the location of servicecenters has a strong influence on the congestion at each of them, and, consequently, on thequality of service. In this paper, several probabilistic maximal coveringlocation—allocation models with constrained waiting time for queue length are presentedto consider service congestion. The first model considers the location of a given number ofsingle-server centers such that the maximum population is served within a standard distance, andnobody stands in line for longer than a given time or with more than a predetermined number ofother users. Several maximal coverage models are then formulated with one or more servers perservice center. A new heuristic is developed to solve the models and tested in a 30-node network.

Location–Allocation of Multiple-Server Service Centers with Constrained Queues or Waiting Times

Recently, the authors have formulated new models for the location of congested facilities, so to maximize population covered by service with short queues or waiting time. In this paper, we present an extension of these models, which seeks to cover all population and includes server allocation to the facilities. This new model is intended for the design of service networks, including health and EMS services, banking or distributed ticket-selling services. As opposed to the previous Maximal Covering model, the model presented here is a Set Covering formulation, which locates the least number of facilities and allocates the minimum number of servers (clerks, tellers, machines) to them, so to minimize queuing effects. For a better understanding, a first model is presented, in which the number of servers allocated to each facility is fixed. We then formulate a Location Set Covering model with a variable (optimal) number of servers per service center (or facility). A new heuristic, with good performance on a 55-node network, is developed and tested.

Facility location for market capture when users rank facilities by shorter travel and waiting times

A firm wants to locate several multi-server facilities in a region where there is already a competitor operating. We propose a model for locating these facilities in such a way as to maximize market capture by the entering firm, when customers choose the facilities they patronize, by the travel time to the facility and the waiting time at the facility. Each customer can obtain the service or goods from several (rather than only one) facilities, according to a probabilistic distribution. We show that in these conditions, there is demand equilibrium, and we design an ad hoc heuristic to solve the problem, since finding the solution to the model involves finding the demand equilibrium given by a nonlinear equation. We show that by using our heuristic, the locations are better than those obtained by utilizing several other methods, including MAXCAP, p-median and location on the nodes with the largest demand.

A branch-and-price algorithm for the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows

In the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows, the set of customers is the union of delivery customers and pickup customers. A fleet of identical capacitated vehicles based at the depot must perform all deliveries and profitable pickups while respecting time windows. The objective is to minimize routing costs, minus the revenue associated with the pickups. Five variants of the problem are considered according to the order imposed on deliveries and pickups. An exact branch-and-price algorithm is developed for the problem. Computational results are reported for instances containing up to 100 customers.

A conditional p-hub location problem with attraction functions

We formulate the competitive hub location problem in which customers have gravity-like utility functions. In the resulting probabilistic model, customers choose an airline depending on a combination of functions of flying time and fare. The (conditional) followers hub location problem is solved by means of a heuristic concentration method. Computational experience is obtained using the Australian data frequently used in the literature. The results demonstrate that the proposed method is viable even for problems of realistic size, and the results appear quite robust with respect to the leaders hub locations.

Teachers' support with ad-hoc collaborative networks

Efforts to improve the educational process must focus on those most responsible for implementing it: the teachers. It is with them in mind that we propose a face-to-face computer-supported collaborative learning system that uses wirelessly networked hand-held computers to create an environment for helping students assimilate and transfer educational content. Two applications of this system are presented in this paper. The first involves the use of the system by students, transforming classroom dynamics and enabling collaboration and interaction between the students and the teacher. In the second application, the system is used to help teachers update their knowledge of subject content and exchange methodological strategies.