Charles ReVelle

THE LOCATION OF EMERGENCY SERVICE FACILITIES

This paper views the location of emergency facilities as a set covering problem with equal costs in the objective. The sets are composed of the potential facility points within a specified time or distance of each demand point. One constraint is written for each demand point requiring “cover,” and linear programming is applied to solve the covering problem, a single-cut constraint being added as necessary to resolve fractional solutions.

Location analysis: A synthesis and survey

Abstract The mathematical science of facility siting has attracted much research in discrete and continuous optimization over nearly four decades. Investigators have focused on both algorithms and formulations in diverse settings in the private sector (e.g., industrial plants, banks, retail facilities, etc.), and the public sector (e.g., ambulances, clinics, etc.). Each formulation has differences and similarities relative to the others, but the peculiarities of each problem provide the fuel for the hundreds of investigations. The presence of non-linearities and requirements for zero–one variables head the list of challenges that have occupied researchers in this active and expanding field. We review here the many facets of this exciting and centrally placed field through reference to both seminal works and current reviews.

The Maximum Availability Location Problem

A probabilistic version of the maximal covering location problem is introduced here. The maximum available location problem (MALP) positions p servers in such a way as to maximize the population which will find a server available within a time standard with (alpha) reliability. The maximum availability problem builds on the probabilistic location set covering problem in concept and on backup covering and expected covering models in technical detail. MALP bears the same relation to the probabilistic location set covering problem as the deterministic maximal covering problem bears to the deterministic location set covering problem. The maximum availability problem is structured here as a zero--one linear programming problem and solved on a medium-sized transportation network representing Baltimore City.

A bibliography for some fundamental problem categories in discrete location science

Following a brief taxonomy of the broad field of facility location modeling, this paper provides an annotated bibliography of recent papers in two branches of discrete location theory and modeling. In particular, we review papers related to (1) the median and plant location models and (2) to center and covering models. We show how the contributions of the papers we review are embedded in the field. A summary and outlook conclude the paper.

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.

SIMULTANEOUS SITING AND ROUTING IN THE DISPOSAL OF HAZARDOUS WASTES

The development of a system of storage facilities for spent fuel rods from commercial nuclear reactors requires solution of a model which simultaneously sites the storage facilities, assigns reactors to those facilities and chooses routes for the shipment of the spent fuel. The problem is multiobjective in its transportation component because shipment is made under two criteria: minimum transportation burden and minimum perceived risk. We blend methods of shortest paths, a zero-one mathematical program for siting, and the weighting method of multiobjective programming to show how to derive optimal solutions to this problem. Applications of the methodology demonstrate how transportation burden and risk influence location decisions and the dual role of siting/routing models in transportation policy analysis. The model is a prototype for the shipment and storage of any hazardous waste whose characteristics make the process of shipment itself an activity with risk.

The Plant Location Problem: New Models and Research Prospects

The plant location problem has been studied for many years. Yet, a number of important real world issues and variants have not been investigated or resolved and merit further attention and research. This paper describes new statements of the problem 1 with new and different objectives, 2 with multiple products and multiple machines in which new models of production are considered, and 3 with spatial interactions.

Heuristic concentration: Two stage solution construction

Abstract By utilizing information from multiple runs of an interchange heuristic we construct a new solution that is generally better than the best local optimum previously found. This new, two stage, approach to combinatorial optimization is demonstrated in the context of the p-median problem. Two layers of optimization are superimposed. The first layer is a conventional heuristic the second is a heuristic or exact procedure which draws on the concentrated solution set generated by the initial heuristic. The intention is to provide an alternative heuristic procedure which, when dealing with large problems, has a higher probability of producing optimal solutions than existing methods. The procedure is fairly general and appears to be applicable to combinatorial problems in a number of contexts.

Counterpart Models in Facility Location Science and Reserve Selection Science

Five classes of zero–one programming models for discrete facility location problems are compared to counterpart models for the selection of conservation reserves. The basic problem of siting facilities to cover demand for services is analogous to the problem of selecting reserves to support species diversity. The classes of models include the set covering and maximal covering models, as well as models for backup and redundant coverage. Issues of reliability and uncertainty are addressed by chance constrained covering models and maximal expected covering models. Exact and heuristic solution approaches are discussed. Multi-objective and economic issues are considered.

A Lagrangean heuristic for the maximal covering location problem

Abstract We develop a Lagrangean heuristic for the maximal covering location problem. Upper bounds are given by a vertex addition and substitution heuristic and lower bounds are produced through a subgradient optimization algorithm. The procedure was tested in networks of up to 150 vertices. A duality gap was generally present at the end of the heuristic for the larger problems. The test problems were run in an IBM 3090-600J ‘super-computer’; the maximum computing time was kept below three minutes of CPU.