A Mixed Integer Programming Model for Regional Planning of a Hospital Inpatient Service

This paper describes a quantitative model to aid in planning an efficient and effective hospital inpatient service among hospitals in a region. The planning is to be done by a regional health systems planning agency, which sets or enforces standards of accessibility and acceptability to be achieved through a modification of the current system, particularly the allocation of beds to the population-at-risk. The allocation is defined in terms of matching beds to demand, where demand is classified by geographical areas and by level of care required. The allocation is to be done such that the planning goals, expressed in constraints on accessibility and acceptability of the inpatient service, are satisfied. In particular, the population within the region should have access to an adequate supply of beds, and the inpatient service should be of appropriate level and quality to meet the demand of the population. The planning problem is formulated as a mixed integer mathematical programming model in which changes to the system are described in terms of the location, number, conformance, and level of beds. There are two types of input to the model—estimates of demand by geographic area and level, and a description of the current state of the hospital service in the region. The current state of the hospital service is described by the location, size, level, and conformance of the service at existing hospitals and the location of possible new sites. The solution to the model is the lowest cost modification to the system that satisfies the constraints, where “cost” is a measure of the resources needed to change the system. Results from applying the model to the medical-surgical service in a region with 15 hospitals are discussed.