A Two-Stage Optimization Model for In-Patient Transfers

A major problem in large urban hospitals is patient misplacement—the daily necessity of placing newly admitted patients in inappropriate beds because of varying demands, discharge patterns, and medical requirements. It is highly desirable to relocate as many misplaced patients as possible. Usually, transfers are arranged by comparing bed-vacancy lists with misplaced patient lists, a procedure that misses many transfer possibilities.

Initially, we formulated this problem as a linear program. However, because of problem size, solution on a daily basis is economically infeasible. We resolved this by reformulating the problem as a two-stage model. Aggregation is used for the first stage, taking advantage of the special structure of this linear program to form one of substantially reduced size. The second stage is a computerized search algorithm that disaggregates the first-stage optimal solution into the form required for its implementation by the hospital. A test run using actual hospital data demonstrates the model's effectiveness. Finally, we discuss plans for implementation.