Brian Boffey

A comparison of Lagrangean and surrogate relaxations for the maximal covering location problem

Abstract We compare heuristics based on Lagrangean and surrogate relaxations of the Maximal Covering Location Problem (MCLP). The Lagrangean relaxation of MCLP used in this paper has the integrality property and the surrogate relaxed problem we solve is the LP relaxation of the original 0−1 knapsack problem. The heuristics were compared using 331 test problems available in the literature, corresponding to networks ranging from 55 to 900 vertices. The gaps obtained with both heuristics were very low and did not differ substantially among themselves for the several problem sets used, in accordance with theoretical results reviewed in the paper. When the initial set of multipliers was determined using a valid bound for MCLP the computing times did not differ significantly between the Lagrangean and surrogate heuristics.

A review of congestion models in the location of facilities with immobile servers

Capacity effects are investigated, particularly as regards congestion of facilities with immobile (or fixed) servers. A review is given of research to date in this area, together with some related work. First, general implications of facility capacities being capacitated are discussed with regard to assignment of users to facilities, time (or distance) transformations, integrality, feasibility, equity and load balancing. Then models using both system choice and user choice assignment are presented, and hierarchical problems covered briefly. Finally, there is a summary and a discussion together with some possible future research directions.

A hierarchical model for the location of perinatal facilities in the municipality of Rio de Janeiro

Abstract We present a 3-level hierarchical model for the location of maternal and perinatal health care facilities in Rio de Janeiro. Relaxations and heuristics are developed for this model and computational results are given for problems available in the literature, for networks ranging from 10 to 400 vertices. The quality of the solutions produced by the procedures we developed do not differ significantly among themselves. The model is also applied to a case study corresponding to real 1995 data of the municipality of Rio de Janeiro.

Load balancing and capacity constraints in a hierarchical location model

Recent work on the location of perinatal facilities in the municipality of Rio de Janeiro resulted in the development of an uncapacitated, three-level hierarchical model. An important issue that arose during the course of the research was the need to include some form of capacity constraints into the model, especially in the higher, resource intensive level of the hierarchy. This need was felt from technical discussions related to the research work and from contacts with municipality health officials. A capacitated model is presented and solved using a Lagrangean heuristic. For smaller problems optimal solutions are found using CPLEX; it is found that the heuristic usually gives high quality solutions. Next a bi-criterion model is formulated in which the additional objective measure is the imbalance in facility loading. This is solved exactly for a small problem and approximately for the 152-vertex Rio de Janeiro data. � 2004 Elsevier B.V. All rights reserved.

Dual-based heuristics for a hierarchical covering location problem

A 2-level hierarchical extension of the maximal covering location problem is considered and an effective method for its solution developed. A combined Lagrangean-surrogate (L-S) relaxation is defined which reduces to a 0-1 knapsack problem. Tests were carried out using a subgradient-based heuristic incorporating the L-S relaxation, with the resulting knapsack problems being solved both with and without the integrality constraints relaxed. Results were obtained for test problems available in the literature ranging from 55-node to 700-node networks. These were compared, where possible, with exact results obtained using CPLEX. It was found that computing times were reasonable.

An algorithm to locate perinatal facilities in the municipality of Rio de Janeiro

In order to reduce infant mortality in the municipality of Rio de Janeiro it is desired to encourage all mothers-to-be to attend the appropriate health care facilities. A 3-level hierarchical prenatal–neonatal health care system is described together with a basic model for optimising accessibility to facilities. A genetic algorithm to solve the basic model is developed and some numerical experience reported. Extensions to the basic model and planned future research are briefly indicated.

Models for multi-path covering-routing problems

Research on covering has concentrated on problems where the facilities are small inrelation to their cover sets and can justifiably be regarded as points. However, representationby a point is not reasonable for all facilities. In this paper, our objective is to consider pathcovering problems and study them with particular emphasis on multi-path models. We introducea new problem, 2-MPSP, then formulate it and some of its variants. We also outlinetwo solution approaches for solving the 2-MPSP problem.

Practical aspects associated with location planning for maternal and perinatal assistance in Brazil

A study has been carried out aimed at reducing perinatal mortality in the municipality of Rio de Janeiro through a better distribution of health care facilities. The algorithmic aspects are detailed elsewhere and here the emphasis is on practical issues and difficulties encountered.A 3-level hierarchical model was developed. Both uncapacitated and capacitated versions are briefly described together with some results based on actual data. The project brought to light many contradictions between OR theory and practice in developing countries and, unfortunately, the models developed were not implemented by the municipality health authorities. Possible reasons for this outcome are analysed.

Spatial organization of an industrial area: Distribution of the environmental cost and equity policies

In this paper we introduce a methodology for a spatial organization of an Industrial Area with environmental criteria. In particular, we analyze in depth the impact of the realism (number of simulated wind directions) of airborne pollution spread models on the accuracy of their results. Based on the above experience, we propose a methodology for the distribution of the economic and environmental burden from the operation of polluting units in Industrial Areas to the firms and public respectively. Finally we introduce and compare appropriate environmental equity policies.

Location of single-server immobile facilities subject to a loss constraint

AbstractWaiting may be unacceptable, even a short time, at a facility providing a service involving medical or other emergencies. Hence, it is appropriate to locate such facilities so that the rate at which users are lost is limited. Each facility will here be modelled as an M/Er/m/N queueing system subject to a loss restriction constraint and the single-server case (m=1) will be treated in detail. Introduction of the Erlang distribution for service times allows a better fit of the model to actual values of both mean and variance than do currently available models that use an exponential distribution. Location of facilities will be such that the average travel time to a facility is minimized. It is shown how a deterministic constraint, equivalent to the loss constraint, can be generated resulting in an integer linear program, and values of a parameter ρc which facilitates this linearization are tabulated for various values of r, N and service level demanded. Numerical experiments are performed including an application loosely related to the location of neonatal clinics in the Municipality of Rio de Janeiro. Finally, there is a discussion of how further improved modelling of the service time distribution might be effected.