Surgery Scheduling in Flexible Operating Rooms by using a Convex Surrogate Model of Second-Stage Costs

TL;DR

This work model the elective surgery planning problem in a hospital with operation rooms shared by elective and emergency patients by a two-stage stochastic program, and shows that the second-stage costs can be replaced by a convex piecewise linear surrogate model that can be computed in a preprocessing step.

Abstract

We study the elective surgery planning problem in a hospital with operation rooms shared by elective and emergency patients. This problem can be split in two distinct phases. First, a subset of patients to be operated in the next planning period has to be selected, and the selected patients have to be assigned to a block and a tentative starting time. Then, in the online phase of the problem, a policy decides how to insert the emergency patients in the schedule and may cancel planned surgeries. The overall goal is to minimize the expectation of a cost function representing the assignment of patient to blocks, case cancellations, overtime, waiting time and idle time. We model the offline problem by a two-stage stochastic program, and show that the second-stage costs can be replaced by a convex piecewise linear surrogate model that can be computed in a preprocessing step. This results in a mixed integer program which can be solved in a short amount of time, even for very large instances of the problem. We also describe a greedy policy for the online phase of the problem, and analyze the performance of our approach by comparing it to either heuristic methods or approaches relying on sampling average approximation (SAA) on a large set of benchmarking instances. Our simulations indicate that our approach can reduce the expected costs by as much as 30% compared to heuristic methods and is able to solve problems with $1000$ patients in about one minute, while SAA-approaches fail to obtain near-optimal solutions within 30 minutes, already for $100$ patients.

Figures (11)

• Figure 1: Standard breakdown of OR management tasks into successive decision stages. This paper focuses on operative decisions (advanced planning, appointment scheduling and online scheduling)
• Figure 2: Classification of patients after solving the APASP (leftmost frame) and after executing the online policy in scenario $\omega$ (rightmost frame).
• Figure 3: Schedule in a block for a realization $\omega$ of the uncertainty. In this realization, the tentative starting time $T_2^\omega$ is too large, which causes idle time in the block, while $T_3^\omega$ is too small, which results in waiting time. The last operation in the block completes after time $T$, which generates some overtime. Note that the tentative starting time $T_i^\omega$ usually does not depend on the scenario $\omega$ and is set to the value of $t(i)$ computed in the APASP, unless a migration of patient $i$ occurs in the scenario $\omega$ during the OSP.
• Figure 4: Summary of interactions between the different components of the EESPP
• Figure 5: Cost of $N=1000$ instances of the second-stage problem for a block $b$ of specialty $s=\texttt{ORTH}$, as a function of the total expected duration. The solid line shows the piecewise-linear approximation $f_{\texttt{ORTH}}$ with $R=3$ pieces, for $6$ different cost structures.