some assignments undone and run the algorithm to check whether or not a feasible solution is still possible. This would be the case if, for instance, a trainee is required to restart a certain activity because a particular coverage constraint can no longer be satisfied given the partial schedule. This last feature contributes significantly to the willingness of schedulers to accept the software, since it recognizes the fact that they still have the last word. The software only assists in building the schedules, i.e., it helps in solving difficult ‘combinatorial puzzles’, but the final decisions are still made by (human) scheduler(s) and not by the PC.
2.9
Conclusions and future research
In this chapter, the problem of building long term trainee schedules has been stud- ied. The first part of the chapter deals with a specific class of trainee scheduling problems for which a decomposition scheme on the activities could be applied. Col- umn generation could be applied to find the LP relaxation of the new model and several branching schemes have been proposed to drive the solution into integrality. Extensive computational results have indicated how the different problem dimen- sions influence the problem difficulty and how the different speed-up techniques contribute to the efficiency of the solution procedure.
Next, the decomposition on the activities approach has been compared with a more traditional decomposition on the trainees approach. The computational tests re- vealed that decomposition on the trainees is clearly outperformed by decomposition on the activities. The modeling power of both decomposition techniques has also been discussed. Since most staff scheduling problems have a lot of constraints that apply at the level of individual staff members, decomposition on staff members could be used in a wider range of problems. In the rare case that most constraints apply at the level of the activity schedules, decomposition on the activities is more suitable. Activity-based decomposition is also appropriate if each combination of activity schedules automatically satisfies all individual staff member constraints. This was the case for the considered trainee scheduling problem in the first part of this chapter.
The following part has shown how the developed approach can easily be turned into an effective heuristic algorithm. Therefore, five heuristic extensions have been
proposed. The developed application was tested on two real-life problems and computational results are given. These results illustrate how the different heuristic extensions could improve the solution quality if the problem is too complex to find a (proven) optimal solution.
Finally, a graphical user interface (GUI) has been developed. The GUI allows for easy data input, constraint specification and modification of the algorithmic set- tings. Moreover, certain parts of the schedule could be frozen before the algorithm is run and proposed solutions could be easily modified.
Concerning future research topics, it would be interesting to identify other staff scheduling problems for which decomposition on the activities could be applied. Given the interesting computational properties, this approach could also be suitable to calculate lower bounds for a number of staff scheduling problems for which the above mentioned conditions do not hold. The idea is to remove a part of the individual staff member constraints in order to optimize the relaxed problem using activity-based column generation. Another interesting research direction includes the study of metaheuristic approaches (like, e.g., simulated annealing, tabu search, genetic algorithms or ant colony heuristics) for this problem and see how these compare to the heuristic branch-and-price procedure.
Visualizing the demand for
various resources as a
function of the master
surgery schedule: A case
study
This chapter presents a software system that visualizes the impact of the master surgery schedule on the demand for various resources throughout the rest of the hospital. The master surgery schedule can be seen as the engine that drives the hospital. Therefore, it is very important for decision makers to have a clear image on how the demand for resources is linked to the surgery schedule. The software presented in this chapter enables schedulers to instantaneously view the impact of, e.g., an exchange of two block assignments in the master surgery schedule on the expected resource consumption pattern. A case study entailing a large Belgian surgery unit illustrates how the software can be used to assist in building better surgery schedules.
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3.1. Introduction
3.1
Introduction
The operating room can be seen as the engine that drives the hospital as the ac- tivities inside the operating room have a dramatic impact on many other activities within the hospital. For instance, patients undergoing surgery are expected to recover over a number of days. Consequently, bed capacity and nursing staff re- quirements are dependent on the operating room schedule. The software system described in this chapter visualizes the impact of the master surgery schedule on the demand for all kinds of resources like beds, staff (nurses, anaesthetists, etc.), specialized equipment, radiology and so on.
It has been widely accepted that visualization is a simple yet powerful tool for man- aging complex systems like health care service units. Strum et al. (1997) propose a resource coordination system for surgical services (RCSS) using distributed com- munications. They present user interfaces that are designed to mimic paper lists and worksheets used by health care providers. These providers enter and main- tain patient-specific and site-specific data, which are broadcasted and displayed for all providers. The basic difference between RCSS and our system is that RCSS is designed to work online, preventing and solving resource capacity problems by effective communication, while our system works offline and is designed to facili- tate the development of better long term cyclic surgery schedules. Carter (2000) describes the successful application of a commercial package, called ORSOS, which is an enterprise-wide surgery scheduling and resource management system. The system autonomically manages all of the hospitals’ surgical staff, equipment and inventory using an engine that considers all of the clinical, financial and opera- tional criteria that must be addressed for each surgical event. The difference with our system is that the emphasis lies on the third stage, the detailed elective surgery scheduling, while our system is designed for the second stage.
Simulation packages are often used to analyze and visualize surgical units. Good surveys of simulation approaches in health care clinics can be found in Klein et al. (1993), Jun et al. (1999) and Standridge (1999). Simulation models that focus on the bed occupancy can be found in Dumas (1984) and (1985) and Wright (1987). A specific simulation model for predicting nursing staff requirements has been de- scribed by Duraiswamy et al. (1981). Swisher et al. (2001) highlight the graphical visualization features of their object-oriented simulation package for health care
clinics. The advantage of simulation, compared to our system, is the capability to analyze stochastic processes and to model more complex discrete-event like re- lationships. The disadvantage is that building a good simulation model is often very time and cost intensive, which makes it less suitable for quickly analyzing sim- ple what-if scenarios, e.g., for assisting in the development of a new cyclic surgery schedule.
In Chapter 1 we have argued that developing operating room schedules can be seen as a three stage process. The model described in this chapter (and also the models presented in the succeeding chapters) is situated in the second stage and as such distinguishes itself from studies situated in the first or the third stage.
The purpose of the system presented in this chapter is threefold. First, schedulers can use it for detecting resource conflicts and constructing workable schedules. Sec- ond, the system can greatly assist during the master surgery schedule bargaining process. Visualizing a resource conflict is often far more convincing than hours of discussion with unsatisfied surgeons for not being scheduled by their preferences. Third, the system can be of great value for persuading hospital managers to invest in extra resource capacity. Insufficient resource capacities may not always be visi- ble at first sight. It may, for instance, be the case that, although enough resource capacity is available for the individually summed needs for all resources over all surgeons, still no schedule can be found that provides enough capacity of each re- source for each surgeon at each time instance.
The remainder of this chapter is structured as follows. Section 3.2 explains the underlying model. Section 3.3 introduces the surgical unit that is the subject of the case study. Section 3.4 presents the graphical user interface of the software, providing the reader with a visualization of the surgery schedule and its impact on the resource consumption. Finally, Section 3.5 draws conclusions and lists some topics for future research.