Operating Room Managers’ Use of Integer Programming for Assigning Block Time to Surgical Groups: A Case Study

TLDR

Hospitals must equitably allocate fixed operating‑room block time to surgical groups, but target shares rarely align with whole‑block multiples, complicating scheduling. This study reports a hospital’s use of integer programming to minimize the gap between each group’s target share and its actual OR time assignment. An integer‑programming model assigns specific ORs on specific days to surgical groups, fitting calculated time shares into the master schedule while minimizing shortfall. The algorithm achieved 99.7% schedule accuracy (sd 0.1%) across 11 hospitals and simulations show accuracy above 97% with four or more ORs, demonstrating a systematic, successful assignment method.

Abstract

A common problem at hospitals with fixed amounts of available operating room (OR) time (i.e., “block time”) is determining an equitable method of distributing time to surgical groups. Typically, facilities determine a surgical group’s share of available block time using formulas based on OR utilization, contribution margin, or some other performance metric. Once each group’s share of time has been calculated, a method must be found for fitting each group’s allocated OR time into the surgical master schedule. This involves assigning specific ORs on specific days of the week to specific surgical groups, usually with the objective of ensuring that the time assigned to each group is close to its target share. Unfortunately, the target allocated to a group is rarely expressible as a multiple of whole blocks. In this paper, we describe a hospital’s experience using the mathematical technique of integer programming to solve the problem of developing a consistent schedule that minimizes the shortfall between each group’s target and actual assignment of OR time. Schedule accuracy, the sum over all surgical groups of shortfalls divided by the total time available on the schedule, was 99.7% (sd 0.1%, n = 11). Simulations show the algorithm’s accuracy can exceed 97% with ≥4 ORs. The method is a systematic and successful way to assign OR blocks to surgeons.