Surgical case scheduling as a generalized job shop scheduling problem
Introduction
Surgery is an important activity in most hospitals and clinics since it is estimated to generate around two thirds of hospital revenues [22]. On the other hand, it accounts for approximately 40% of hospital resource costs, including the costs of personnel (surgeons, anaesthetists, nurses, etc.) and facilities (operating rooms, intensive care beds, etc.) [27]. Surgery takes place in a context of challenging trends such as heavy expenditure on health care [32], increasing rates in health care costs [8], and rising surgery demand due to aging populations and technological advances that have broadened the scope of surgical interventions [16].
In this context, hospital management is subject to ever mounting pressures to control surgical costs while ensuring quality of care for surgical patients in a timely manner. A successful cost containment strategy must integrate decision-making at all levels: strategic, tactical, and operational. At the operational level, one of the main problems is surgical case scheduling (SCS) [16].
Although the benefits of efficient scheduling systems are publicized in many industrial applications, few successes have been reported in healthcare. In fact, a recent survey on operating room (OR) management in Switzerland in 2001 shows that hospital management is not satisfied with the current SCS practice. Only 26% of the survey interviewees are somewhat happy with the scheduling systems, while 31% are not happy and 29% are strongly dissatisfied [38].
This paper investigates SCS problems and proposes an integrated solution approach using mathematical programming methods. It is structured into six sections. Section 2 describes various SCS problems. Section 3 presents a literature review. Section 4 proposes a mixed integer linear programming (MILP) model for SCS and discusses the model. This model is based on a novel extension of the well-known job shop scheduling problem. Section 5 gives an example to illustrate the model and presents preliminary computational results with practical-sized instances. Section 6 concludes the paper.
Section snippets
Problem descriptions
Surgical services are offered at both hospitals and ambulatory surgical centers (ASC). Patients in hospitals are called inpatients and patients in ASCs are called outpatients. Typically, outpatient cases are shorter, less complex and less variable than inpatient cases. Outpatients often have same-day surgery and do not stay overnight in ASCs, while inpatients are hospitalized one or more days before surgery and stay in the hospital after surgery for continuing care. Many hospitals are
Literature review
SCS can be viewed as a part of a broader process which can be called surgical process scheduling. A classical reference is the paper by Malgerin and Martin [28] where surgical process scheduling comprises two steps. First, advance scheduling gives patients some future date for surgery. Second, allocation scheduling determines the sequence and resource assignment of the cases in a given day. While allocation scheduling is within the scope of SCS, advance scheduling is not. It is indeed a case
A mixed integer linear programming model for SCS
This section models the elective surgical case scheduling problem as a multi-mode blocking job shop (MMBJS), a new extension of the well known Job Shop problem, and develops a mixed integer linear programming (MILP) formulation of the MMBJS.
An illustrative example
Consider a hypothetical example of a small integrated hospital with two ORs {OR1, OR2}, one staffed PACU bed {P}, and one staffed ICU bed {IC}. The ORs are open from 8:00 to 16:00. The PACU bed is open from 8:00 to 17:00 while the ICU bed are available all the time. The hospital has three surgeons {S1, S2, S3}, two anaesthetists {A1, A2}, two perioperative nurses {N1, N2}, and one preoperative nurse {N3}. Each ORi is staffed with one nurse and one anaesthetist . The OR block allocation
Conclusion
This paper identifies and analyzes the SCS problem including scheduling elective and add-on cases for both inpatients and outpatients. The SCS problem is modelled as a new extension of the known JS called MMBJS. A corresponding MILP formulation is developed and computational experiments are conducted.
The paper points out the importance of connecting surgical stages in scheduling any surgical case and coordinating multiple resources during any surgical step. SCS should take a holistic view of
Acknowledgements
The first author thanks the committees of the EURO Summer Institute 2005 and the Swiss Operations Research Society for making it possible to attend the Summer Institute “OR in health care” in Southampton, 2005. We are also grateful to Prof. Chung-Yee Lee and Prof. Renato de Matta for the ASC data sets used in this paper.
References (41)
Minimizing makespan in a blocking flowshop using genetic algorithms
International Journal of Production Economics
(2001)- et al.
Multiresource shop scheduling with resource flexibility
European Journal of Operational Research
(1998) Strategies to reduce delays in admission into a PACU from Operating Rooms
Journal of PeriAnesthesia Nursing
(2005)- et al.
Operating theatre planning
International Journal of Production Economics
(2003) - et al.
Deterministic job-shop scheduling: Past, present, and future
European Journal of Operational Research
(1999) - et al.
Job-shop scheduling with blocking and no-wait constraints
European Journal of Operational Research
(2002) - et al.
Scheduling multipurpose batch process industries with no-wait restrictions by simulated annealing
European Journal of Operational Research
(2000) - et al.
Efficiency of the operating room suite
The American Journal of Surgery
(2003) Introduction to Sequencing and Scheduling
(1974)- et al.
Surgical process scheduling: A conceptual literature review
Journal of Health Systems
(1997)
Mount Sinai hospital uses integer programming to allocate OR time
Interfaces
Shop scheduling problem with multiprocessor tasks on dedicated processors
Annals of Operations Research
Tabu-search for the multi-mode job-shop problem
OR Spektrum
Outpatient scheduling in health care: A review of literature
Production and Operations Management
An integrated approach for modeling and solving the general multiprocessor jobshop scheduling problem using Tabu search
Annals of Operations Research
Which algorithm for scheduling add-on elective cases maximizes OR utilization? Use of bin packing algorithms and fuzzy constraints in OR management
Anesthesiology
Optimal sequencing of urgent surgical cases
Journal of Clinical Monitoring and Computing
How to schedule elective surgical cases into specific Operating Room to maximize efficiency of use of OR time?
Anesthesiology
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