Ambulance location and relocation models

This article traces the evolution of ambulance location and relocation models proposed over the past 30 years. The models are classified in two main categories. Deterministic models are used at the planning stage and ignore stochastic considerations regarding the availability of ambulances. Probabilistic models reflect the fact that ambulances operate as servers in a queueing system and cannot always answer a call. In addition, dynamic models have been developed to repeatedly relocate ambulances throughout the day. 2002 Elsevier Science B.V. All rights reserved.

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Ambulance Location and Relocation Models

Lot sizing and scheduling — Survey and extensions

This contribution summarizes recent work in the field of lot sizing and scheduling. The objective is not to give a comprehensive literature survey, but to explain differences of formal models and to provide some first readings recommendations. Our focus is on capacitated, dynamic, and deterministic cases. To underscore the importance of the research efforts, current practice is described and its shortcomings are exposed. Mathematical programming models where the planning horizon is subdivided into several discrete periods are given for both, approaches that are well-established and approaches which may represent tomorrow's state of the art. Two research directions are discussed in more detail: Continuous time models and multi-level lot sizing and scheduling. The paper concludes with some advice for future research activities.

Lot sizing and scheduling: Survey and extensions

Research on facility location is abundant. However, this research does not typically address the particular conditions that arise when locating facilities to service large-scale emergencies, such as earthquakes, terrorist attacks, etc. In this work we first survey general facility location problems and identify models used to address common emergency situations, such as house fires and regular health care needs. We then analyze the characteristics of large-scale emergencies and propose a general facility location model that is suited for large-scale emergencies. This general facility location model can be cast as a covering model, a P-median model or a P-center model, each suited for different needs in a large-scale emergency. Illustrative examples are given to show how the proposed model can be used to optimize the locations of facilities for medical supplies to address large-scale emergencies in the Los Angeles area. Furthermore, comparison of the solutions obtained by respectively using the proposed mo...

A modeling framework for facility location of medical services for large-scale emergencies

Modeling co-located servers and dispatch ties in the hypercube model

Improvement on existing techniques for multilevel lot sizing in material requirements planning was sought by developing a theoretical and mathematical basis for the problem. Such a foundation was employed to design a heuristic which was superior in both cost performance and computational efficiency, and provided consistent results regardless of designated environmental factors. This represents a significant advantage over other algorithms tested here and within the literature, in that their performances are dependent upon various lot-sizing environmental factors.



The heuristic is based on the technique for order placement and sizing (TOPS), a single-item technique, and utilizes a mechanism for linking interdependent lot-sizing decisions. The inputs are applied in a sequential manner to constitute sequential TOPS with incremental look-down (STIL). A two-phase experimental design was employed to evaluate the performance of STIL against optimality and other heuristics. Results from the initial phase of simplified problems revealed practical indifference from optimality for the new algorithm. Phase 2 emphasized the relative strength and consistency of the proposed heuristic versus all other rules tested over more difficult examples. The final stage also indentified environments in which STIL performed particularly well. These were more descriptive of common industrial settings than were cases in which existing methods have been shown to be effective.

An Improved Heuristic for Multilevel Lot Sizing in Material Requirements Planning

Officers in police patrol cars operate in a complex stochastic environment. In addition to handling dispatcher-assigned calls for service from the public, they patrol to pose a threat of apprehension to would-be offenders and undertake certain on-site interventions to help improve general public safety. The on-site work, often highly discretionary, is called patrol-initiated activity. It includes issuing tickets for traffic violations, building checks, car checks, pedestrian checks and assisting motorists. In many cities patrol-initiated activities and calls for service consume comparable amounts of officers' time. In this paper we develop a spatially-oriented queueing-type model of a police patrol force that allows each of N patrol cars to be in one of three states: 1 busy, on a call for service; 2 busy, on a patrol-initiated activity; 3 free, on patrol. Designed for computer solution, the model yields N nonlinear equations whose unknowns are the workloads of the N patrol cars. Other performance measures of patrol can be computed easily in terms of the workloads. The incorporation of patrol-initiated activities represents an improvement over previous OR/MS models, and could result in more informed police management decisions regarding patrol beat design, workload smoothing among officers, and reduction of neighborhood-specific inequities in police accessibility. The methods of this paper are potentially applicable to other urban services, including taxi and maintenance operations.

Police Patrol-Initiated Activities Within a Systems Queueing Model

The maximum expected covering location problem (MEXCLP) is reformulated using a separable programming approach. The resulting formulation—nonlinear maximum expected covering location problem (NMEXCLP)—guarantees optimality and also solves more quickly than previous heuristic approaches. NMEXCLP allows two important extensions. First, minor formulation changes allow the specification of the minimum number of times each node is to be covered in order to satisfy expected coverage criteria. Second, coverage matrices can be constructed that consider two different types of coverage simultaneously. Both extensions are useful for ambulance location problems and are demonstrated in that setting.

Applications and Implementation A SEPARABLE PROGRAMMING APPROACH TO EXPECTED COVERAGE: AN APPLICATION TO AMBULANCE LOCATION

This paper presents a zero-one linear formulation of the multilevel lot-sizing problem for materials requirement planning systems without capacity constraints. The model is an efficient statement of the problem and has a structure that is particularly convenient for research work. In addition, it is demonstrated that the relaxed linear programming solution to this formulation will always be integer. The results of a rather large computational history are reported along with a variable reduction methodology that allows for the solution of reasonably sized research problems.

Mark A. McKnew

Papers

Modeling co-located servers and dispatch ties in the hypercube model

An Improved Heuristic for Multilevel Lot Sizing in Material Requirements Planning

Police Patrol-Initiated Activities Within a Systems Queueing Model

Applications and Implementation A SEPARABLE PROGRAMMING APPROACH TO EXPECTED COVERAGE: AN APPLICATION TO AMBULANCE LOCATION

An Efficient Zero-One Formulation of the Multilevel Lot-Sizing Problem