has to be chosen. We illustrate the application of the delimiter for field α: in, out|β1; β2; β3|γ1|δ1; δ2. This example would imply that the planning or
scheduling problem deals with both inpatients and outpatients, i.e. elective patient scheduling.
In Section 3.2, we stated that multiple elements may be optionally further specified so that they also have to be integrated in the classification notation. Each further specification of an element will appear in brackets, as shown in Table 3.1. Similarly to the previous paragraph, though, multiple specifi- cations may be introduced in the notation for a single element. Therefore, we introduce a “−” as delimiting symbol. We illustrate this structuring approach for field γ: α1|β1; β2; β3|stoch(arr − dur)|δ1; δ2. This notation
indicates that the problem at hand explicitly deals with uncertainty, in par- ticular both arrival uncertainty and duration uncertainty.
It may occur that multiple subjects are addressed in the same operating room planning or scheduling problem. Think, for example, of the case in which patients have to be assigned to surgeons and a surgery date has to be assigned to the patients. When these decisions are dealt with in a sequential way, the classification scheme, as it is explained up to now, can be applied and would result in two problem statements, namely α| surg; other; β3 |γ|δ and α| pat; date; β3 |γ|δ. However, when both decisions
are studied simultaneously, the single problem statement would equal α| surg, pat; other, date; β3 |γ|δ. As such, we cannot identify the precise rela-
tion between the elements of parameter β1 and β2. Therefore, we introduce
a final delimiter “{}” to group statements that belong together. We only ap- ply the delimiter when ambiguity may occur. With respect to the example, we hence adapt the statement as follows: α| {surg; other; β3}{pat; date; β3}
|γ|δ.
3.4
Examples
In this section, we illustrate the applicability of the operating room plan- ning and scheduling classification scheme to various problems that are al- ready studied in the literature. We refer to the literature review of Chapter
2 for an analysis of the papers that we classify in this section. For some papers, we are unable to fill out the appropriate set of elements for some parameters. This is not because the sets of elements for the parameters are inadequate, but because the papers do not include any specific information on the particular parameters. This is often the case with respect to parame- ter α1that describes the patient characteristics (see Section 5.1). Therefore,
we introduce the abbreviation N S (not specified). It should be clear that if researchers systematically apply the proposed classification scheme in the future, such unclear statements will be eliminated.
Figure 3.1 may assist in the correct determination of a problem’s classifica- tion notation, as it recapitulates the fields, parameters, elements and further specifications that were introduced throughout this chapter. Note that the abbreviations of the elements are quite descriptive instead of mathematical, which should be beneficial for an easy comprehension of the classification notation. This comprehension should be furthermore improved by the ab- sence of blank entries in the scheme (i.e. for each parameter, at least one element has to be specified). Although we believe that this policy increases the clarity of the scheme, it may lengthen the problem’s notation.
The problem that is studied by Adan and Vissers [2] is classified as in, out | pat; date, cap; int(ICU − ward) | det | multi; util(over − under). From this notation, a lot of information can be deduced. The problem takes both inpatients and outpatients into account. It is formulated in terms of pa- tients or patient types for whom capacity has to be determined and a day or date has to be assigned. These decisions seem to have consequences for other facilities, in particular the wards and the ICU, as the operating room is studied in an integrated way. The problem does not explicitly incorporate uncertainty and is hence deterministic in nature. Multiple objectives are taken into account that are related to the utilization of resources. In the evaluation of the utilization levels, the authors even seem to make a differ- entiation between overutilization and underutilization.
3.4. Examples
Figure 3.1: Overview of the fields, parameters, elements and further specifications that constitute a classification scheme for operating room planning and scheduling problems
ward) | det | single; f in. In particular, they studied the financial implica- tions of changing the assignment of operating room capacity, which is re- served for outpatient surgery, to surgeons. They apply a deterministic view but link the operating room to the ICU and the hospital wards.
The operating room scheduling problem that is presented by Beli¨en and De- meulemeester [14] is summarized by the classification scheme as follows: in | disc; date, time; int(ward) | stoch(arr − dur) | single; level. The authors study the impact of changing the date and the time of operating room in- patient sessions, assigned to medical disciplines, on the demand of a single resource which they try to level. The changes in the operating room schedule seem to have repercussions on the hospital wards and this relation is incor- porated in the model. Both arrival uncertainty and duration uncertainty is embedded in the model.
The classification notation of the problem that is addressed by Van Houden- hoven et al. [276] can be written as follows: in | pat; date, room, cap; iso | stoch(dur) | multi; util, other. Based on this classification, we may assume that this research deals with the assignment of a date, a room and capacity to inpatients. The authors incorporate duration stochasticity. Since their focus is restricted to an isolated set of operating rooms, these durations denote the surgery durations. The various assignments are compared with respect to the operating room utilization and some other criterion, namely the number of freed operating rooms.
In Chapter 5, we come back to the classification scheme and apply it to the operating room scheduling problem that originated at the day-care center of the UZ Leuven Campus Gasthuisberg (see Section 5.2) and to the literature that is related to this topic (see Section 5.1).