Reducing Inpatient Congestion Through Surgical Scheduling in a Multi-site Network of Hospitals: A case Study that Applies Pooling Principles Through Mixed Integer Programming and Simulation Modelling

Abstract

Canadian hospitals experience downstream capacity resources, which reduces the total quality of care. The Master Surgical Schedule (MSS) is a primary driver of these downstream resources, including inpatients beds. This literature addresses this concern by utilizing a mathematical model to develop a MSS to minimize excess capacity in a series of nearby hospitals that share resources and governing bodies. The objective of this research is to develop a Mixed Integer Programming (MIP) model to generate MSSs in conjunction with a simulation model to quantify and illustrate the resulting changes. A two-step iterative approach was applied to the MIP and simulation where the historical inpatient LOS for each surgeon for the MIP is adjusted by adding the historical standard deviation multiplied by the ratio of excess capacity used in the simulation versus the MIP. A stopping criterion was established and the approach was followed until convergence, or a suboptimal loop was found.

The simulation model demonstrated statistically significant reductions using a student t- test for α=0.05, up to 47% in total excess capacity using the MSSs developed by the MIP. The iterative approach did not initially converge using the initial adjustment formula, getting caught in a suboptimal loop. To overcome this, a range of predetermined adjustment factors was considered for the MIPs inpatient LOS data set to fully evaluate the solution set. By making these adjustments, the data sets were able to converge for (0.225, 0.25) standard deviations. The case study demonstrates the benefits of pooling principles for nearby hospitals, and provides a unique iterative approach to dealing with variability within a MIP model.