Discrete Optimization
The re-planning and scheduling of surgical cases in the operating room department after block release time with resource rescheduling

https://doi.org/10.1016/j.ejor.2019.04.037Get rights and content

Highlights

  • Surgical Case re-Planning and Scheduling with resource re-scheduling.

  • A Column Generation and Local Branching Heuristic is proposed.

  • Different speed-up techniques to accelerate the column generation.

  • Heuristics and local branching are applied to find (near-) optimal solutions.

  • Experiments are conducted upon artificial and real-life data.

Abstract

The decisions on the strategic and tactical level contained in the operation room scheduling process are based on the expected demand. This demand is used to construct the master surgery schedule in a block booking system, which serves as a base for the planning and scheduling of surgical cases. However, in the operational phase, the actual demand may differ from the expected demand. This leads to increased waiting times, the cancellation of surgical cases and an inefficient utilisation of the operation room department for surgeons with spare capacity. In this paper, we study the Surgical Case re-Planning and Scheduling problem with resource re-scheduling that arises at block release time where the operation room planner tries to balance the capacity and the demand on the operational level. To that purpose, changes with respect to the surgeon schedule and the nurse roster are considered to adequately re-plan and schedule surgical cases. The problem under study minimises the number of changes related to the patient planning, the patient waiting time and the resource re-scheduling cost. We propose a three-phase heuristic that uses column generation to construct a high-quality feasible solution, which is further improved via local branching. Computational experiments have been conducted on an artificial dataset generated in a controlled and structured manner and on real-life data. Results demonstrate that our approach is able to produce (near-)optimal solutions and show the contribution of the different algorithmic building blocks.

Introduction

The Operating Room (OR) department is acknowledged as a key department in hospitals. About 40% of hospital costs and more than 60% of hospital admissions belong to this department (Pham & Klinkert, 2008). Thus, managing the OR department efficiently is an important issue for improving hospitals’ utilization. For that purpose, the OR management focuses on the OR scheduling process. In most hospitals, this process follows a block booking system that includes three hierarchical decision phases (Batun, Denton, Huschka, & Schaefer, 2011). The first level concerns the Case Mix Planning (CMP) problem where the OR manager divides available OR time between surgical disciplines or surgeons. The second level addresses the Master Surgery Scheduling (MSS) problem and assigns a specific time slot denoted as a triple (day, room, block) to surgeons based upon the distributed time in the CMP problem to construct a cyclic surgeon schedule. Finally, at the third level, surgical cases are first planned over the time horizon (i.e. the Surgical Case Planning (SCP) problem) and then the planned surgeries are scheduled and sequenced over that day (i.e. the Surgical Case Scheduling (SCS) problem). This implies that surgeries are assigned to a specific day and time slot. It is important to point out that the master surgery schedule reserves the allotted time blocks in a specific room for surgeons to carry out their surgical cases until some predefined moment in time, which is referred to as the cut-off time or the block release time. At block release time, usually 24 hours in advance, the time slots that are still available are released and can be assigned to other surgeons and/or surgeries of any discipline, usually on a First-Come-First-Served basis (Gupta, Denton, 2008, Magerlein, Martin, 1978).

In this paper, we address the Surgical Case re-Planning and Scheduling (SCrPS) with resource re-scheduling problem that arises at block release time. We assume that each surgeon provides a planning of elective inpatients and possibly a set of add-on cases to the OR manager relevant for the operational time horizon under consideration, i.e. the next upcoming days. The inpatients that are already planned, are previously assigned to a particular day in the time horizon and a room by the surgeon based on the MSS. Surgical cases can be planned in the relevant time horizon by the surgeon until block release time. Add-on or secondary elective cases are surgical cases that are preferred to be performed during the re-planning horizon but the involved surgeon does not have enough OR capacity (Herring, Herrmann, 2011, Pham, Klinkert, 2008). At block release time, both elective cases and add-on cases are known and the demand can be accurately determined. Note that we do not consider non-elective cases and we assume the OR manager has reserved buffer capacity for these cases.

At block release time, any free OR time of a particular surgeon is released and made available to other surgeons to allow the addition of add-on cases to the schedule. In order to further improve the efficiency of the OR resources and to meet the actual patient demand, the set of already planned inpatients is re-planned and simultaneously scheduled over the relevant time horizon together with the add-on cases. In this operational problem, the re-planning and scheduling of surgical cases is guided by patient-to-day re-planning preferences and the patient waiting time. The patient-to-day re-planning preferences are defined based upon relevant patient-specific characteristics such as the patient medical urgency and patient re-planning considerations minimising the number of changes to the original surgical case planning.

In order to re-assign available OR time to a surgical case of another surgeon or discipline, different resource re-scheduling decisions are required to ensure feasibility while minimising the number of schedule changes. The required adaptations to the resource schedules are motivated by the fact that the master surgery schedule and nurse schedule are composed to deal with the expected demand. The actual demand for a surgeon or discipline, however, may differ from this expected demand such that changes are necessary to better match resource capacity and patient demand. In order to release the unused OR time and to change the surgeon schedule as defined by the MSS, we visit the Surgeon re-Scheduling (SrS) problem. Moreover, since changes to the surgical case planning and surgeon schedule impact the required nurse mix, the Nurse re-Scheduling (NrS) problem is considered as well. Sufficient skilful nurses should be available to carry out a particular surgical case. Including resource re-scheduling helps to manage changes in the patient planning and offers a better match with the patient demand.

The problem under study is formulated as a decomposed mixed integer programming (MIP) problem thriving on column variables, which represent feasible schedules of surgical cases for a specific room and a single day. We propose a three-stage heuristic solution methodology to find high-quality solutions within a short timespan. In the first stage, we apply column generation and various problem-related speed-up techniques to solve the relaxed problem. In the second step, we present three heuristic algorithms to transform the fractional solution obtained in the first phase to an integer solution. In the last step, we use a local branching to further improve the quality of the solution. The local branching uses an MIP formulation based upon the original time-indexed variables. The proposed methodology leads to optimal or near-optimal solutions in a short timespan and outperforms other solution methodologies. Experiments are conducted on a large dataset generated in a controlled and structured manner and on real-life instances to show the computational performance of the proposed algorithm and to give insight in the objective function structure on the solution quality.

The remainder of the paper is organised as follows. In Section 2, we discuss the related literature. In Section 3, we give a precise problem description and a mathematical formulation of the problem under study. Section 4 discusses the three-stage solution methodology. In Section 5, we validate the performance of each component of the proposed procedure and explore different settings of the parameters characterising the methodology and objective function structure. Section 6 provides concluding remarks and directions for future research.

Section snippets

Literature review

The problem under study is connected to many well-established OR scheduling problems. In the following, we briefly review the related literature on the surgical case planning and scheduling problem (Section 2.1) and re-scheduling problems in the OR department (Section 2.2), with special attention to the re-scheduling of surgical cases and the personnel resources, i.e. surgeons and nurses.

Problem description

In this paper, we tackle the Surgical Case re-Planning and Scheduling with Resource re-Scheduling (SCrPS-RrS) problem that arises at block release time. We assume that the strategic and tactical OR decisions have been taken, which implies the MSS and the associated nurse roster are known and are constructed based on the expected patient demand. The problem under study has an operational character. We assume that each surgeon provides a list of patients to the OR manager relevant for the time

Solution methodology

In the literature, different methodologies for the surgical case planning and/or scheduling problem thrive on mathematical programming and a problem formulation based on the Dantzig-Wolfe decomposition to provide a tighter convex hull for the MIP problem (Cardoen, Demeulemeester, Beliën, 2009, Doulabi, Rousseau, Pesant, 2016, Fei, Chu, Meskens, 2009, Lamiri, Xie, Zhang, 2008). As column generation may converge slowly to find the optimal LP solution, we have included different speed-up

Computational experiments

In this section, we provide computational insights into the proposed procedure. In Section 5.1, we describe the test design and parameter settings used in the experimental analysis and elaborate on the methodology based on which our dataset is constructed. Note that we generated problem instances in a controlled and structured manner. These settings are validated based upon preliminary experiments and are discussed with practitioners of the university hospital UZ Gent (Ghent, Belgium). In

Conclusions

An OR department of a hospital faces the problem at block release time to release unused OR time and reassign these available time slots to other surgeons in order to meet the actual surgical demand and to maximise the OR efficiency. In order to schedule surgical cases effectively and reassign the available OR time to other surgeons, the involved surgeons and nurses need to be re-scheduled to ensure resource feasibility. The contribution of this manuscript is threefold. First, we are the first

Acknowledgments

We acknowledge the support of the Ghent University Hospital (UZ Gent, Belgium) and particularly the support of Philippe Boucherie for giving insight in the problem and providing relevant real-life data. In addition, we would like to thank the anonymous referees, whose comments undoubtedly improved the manuscript.

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