Planning models for burns care

Abstract

Specific near optimal solutions for the New York State burn care planning problem are given. Sensitivity of the near optimal solution and system performance to variation of regional arrival rates and/or the average length of stay is examined as well as the parametric analysis of the referral preference orderings.

The medical care of severe burn injury is a highly sophisticated process best carried out in specialized intensive care units referred to as burn units or burn centers. The creation and maintenance of a burn facility is very expensive for the supporting institution and the community. Because of this hlgh cost of treatment and the relatively small volume of severe burn patients, there has been much interest in the development of burn services on a regional or statewide basis. In New York State, the New York State Department of Health (NYSDH) is required by state law to approve the construction of new health care facilities as well as any proposed changes in the structual capacity or program of services in any existing facility. This research has developed both descriptive and prescriptive models to aid NYSDH in the process of planning burn care for New York State.

The number of possible sites for burn facilities are limited due to the restrictive requirements for support services and equipment. For this reason, system optimization is concerned with allocation of resources rather than facilities location. Two algorithms are presented which find near optimal solutions with respect to the objective functions: (1) maximization of the minimum regional level of service, and (2) minimization of the range of regional level of service values.

First, a closed planning region analysis is presented. Each of the eight New York HSAs is modeled for a single facility operating as the exclusive source of burn care for the region, with the M/G/c/c queue. Performance is evauated by two measures: (1) level of service and (2) average occupancy, both of which are functions offacility capacity. It is shown that it is not possible to achieve high values of both performance measures simultaneously for small planning regions under the regional concept. Substantial improvement in service and economy through consolidation of regions and centralization of facilities is also documented.

A MULTIFACILITY model has been developed to detail the dperations of a system of burn facilities linked together by a complete referral process. The referral policy assures that the overflow from each facility in the system will be placed according to a referral preference ordering which is specific to that facility and exhausts the set of other system facilities. The model is based on the theory of continuous time Markov chains. The equilibrium solution to the state probability distribution is derived through a modification of the Gauss-Seidel iterative method. The key measures of performance are the level of service and average occupancy for each component facility and the total system.