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

Exploring multiple viewshed analysis using terrain features and optimisation techniques

The calculation of viewsheds is a routine operation in geographic information systems and is used in a wide range of applications. Many of these involve the siting of features, such as radio masts, which are part of a network and yet the selection of sites is normally done separately for each feature. The selection of a series of locations which collectively maximise the visual coverage of an area is a combinatorial problem and as such cannot be directly solved except for trivial cases. In this paper, two strategies for tackling this problem are explored. The first is to restrict the search to key topographic points in the landscape such as peaks, pits and passes. The second is to use heuristics which have been applied to other maximal coverage spatial problems such as location-allocation. The results show that the use of these two strategies results in a reduction of the computing time necessary by two orders of magnitude, but at the cost of a loss of 10% in the area viewed. Three different heuristics were used, of which Simulated Annealing produced the best results. However the improvement over a much simpler fast-descent swap heuristic was very slight, but at the cost of greatly increased running times. © 2004 Elsevier Ltd. All rights reserved

The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches

In this paper we introduce the Single Period Coverage Facility Location Problem. It is a multi-period discrete location problem in which each customer is serviced in exactly one period of the planning horizon. The locational decisions are made independently for each period, so that the facilities that are open need not be the same in different time periods. It is also assumed that at each period there is a minimum number of customers that can be assigned to the facilities that are open. The decisions to be made include not only the facilities to open at each time period and the time period in which each customer will be served, but also the allocation of customers to open facilities in their service period. We propose two alternative formulations that use different sets of decision variables. We prove that in the first formulation the coefficient matrix of the allocation subproblem that results when fixing the facilities to open at each time period is totally unimodular. On the other hand, we also show that the pricing problem of the second model can be solved by inspection. We prove that a Lagrangean relaxation of the first one yields the same lower bound as the LP relaxation of the second one. While the Lagrangean dual can be solved with a classical subgradient optimization algorithm, the LP relaxation requires the use of column generation, given the large number of variables of the second model. We compare the computational burden for obtaining this lower bound through both models

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

Ambulance Emergency Response Optimization in Developing Countries

The lack of emergency medical transportation is viewed as the main barrier to the access of emergency medical care in low and middle-income countries (LMICs). In this paper, we present a robust optimization approach to optimize both the location and routing of emergency response vehicles, accounting for uncertainty in travel times and spatial demand characteristic of LMICs. We traveled to Dhaka, Bangladesh, the sixth largest and third most densely populated city in the world, to conduct field research resulting in the collection of two unique datasets that inform our approach. This data is leveraged to develop machine learning methodologies to estimate demand for emergency medical services in a LMIC setting and to predict the travel time between any two locations in the road network for different times of day and days of the week. We combine our robust optimization and machine learning frameworks with real data to provide an in-depth investigation into three policy-related questions. First, we demonstrate that outpost locations optimized for weekday rush hour lead to good performance for all times of day and days of the week. Second, we find that significant improvements in emergency response times can be achieved by re-locating a small number of outposts and that the performance of the current system could be replicated using only 30% of the resources. Lastly, we show that a fleet of small motorcycle-based ambulances has the potential to significantly outperform traditional ambulance vans. In particular, they are able to capture three times more demand while reducing the median response time by 42% due to increased routing flexibility offered by nimble vehicles on a larger road network. Our results provide practical insights for emergency response optimization that can be leveraged by hospital-based and private ambulance providers in Dhaka and other urban centers in LMICs

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

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