DESCRIPCIÓN DE LAS CAUSAS Y LAS PROPUESTAS DE

Tables 3.1 to 3.20 help to place the problem tackled in this thesis within the context of the group of problems studied in the literature. They present a systematic overview of some dimensional parameters and objectives collected from a range of publications.

In this thesis we are particularly concerned with the real-world nature of the problems tackled: the flexibility of defining shift types, work regulations, skill categories, the applicability in practice, etc.

When only considering the short-term rostering problem, two main goals are distinguished: coverage and time related constraints for personnel (Table 3.1). It is mandatory to provide enough assigned personnel at any time of the planning period in ANROM at the expense of violations on time related constraints. The approaches in which personnel requirements are not hard allow decisions of management level in the short-term planning. In ANROM, however, we have not let the algorithm make coverage decisions. The model is interactive enough to change the personnel requirements when necessary. All the constraints in ANROM are modifiable and extendable but violations are allowed and explained. Those who have hard time related constraints all have fewer and less strict constraint types. In ANROM, schedules satisfying them all are not realistic.

[36, 39], De Causmaecker and Vanden Berghe [74]

144]

Kawanaka et al. [126] Chen and Yeung [56] Warner and Prawda

[216]: minimum coverage is obligatory

Warner [215]: minimum coverage can be violated on predefined days

Meisels et al. [138] Miller et al. [147]

Schaerf and Meisels [182] Okada [158], Okada and Okada [159]

Aickelin and Dowsland [5]

Time Related Berrada et al. [21] Warner [215]

Constraints for Personnel

Miller et al. [147]: feasi- bility set (3 constraints)

Miller et al. [147]: non- binding constraints ANROM: Burke et al. [34, 36, 37, 39]

Meisels et al. [138] Meyer auf’m Hofe [142, 144]

Table 3.1: Hard and Soft Constraints

The objectives differ from approach to approach, which is clear from the straightforward categories in Table 3.1. In Table 3.2, a list of pos- sible goals is presented in two different categories: the optimising and the heuristic approaches. Some of these examples include decisions of a higher level. Examples in which all the constraints and parameters are set are quite rare and are very often pure theoretical implementations of one single problem. Most systems allow the user to adapt some predefined constraints and penalty values to their own needs (Table 3.3). Flexible software systems, which are extendible with new constraints, are much more complex to generate solutions. Generally, the design of cyclical schedules requires more than short-term rostering decisions only (see also Section 3.2.5). However, once the requirements are set, cyclical schedules are much easier to generate than others because the search space is considerably smaller.

Most researchers allow small violations of the coverage constraints (see Table 3.5), and penalise them in a cost function. In the context of ANROM, personnel demands per shift or per time interval are expected to be satisfied. If they are not carefully defined by the users, a consistency check will indicate infeasibilities (Section 5.2). ANROM also provides several planning options to

time related constraints constructed with predefined patterns, the objective is to minimise

P

people (‘aversion’ for

the pattern)

[36], minimise _people (violations on soft con- straints)

Arthur and Ravindran [8]: minimise staff dis- satisfaction by minimis- ing the number of staff with ungranted requests Combined coverage and

time related constraints

Miller et al. [147]: nearly optimal solution gener- ated with a mathemati- cal algorithm

Okada [158], Okada and Okada [159]

Minimise number of em- ployees

Alfares [6] Easton and Mansour [85] Arthur and Ravindran [8]

Minimise personnel cost Tanomaru [201] Meyer auf’m Hofe [142] takes personnel costs into account in addi- tion to the cost for expenditure of work Minimise non-negative

coverage

Warner and Prawda [216]: the cost for ‘nurs- ing care shortage’ is minimised

Uniform distribution of shortages and surpluses over weekdays

Berrada et al. [21]

Minimise deviation be- tween scheduled nurses and demand

Ozkarahan [162]: min- imise nurse shortages and surpluses

Arthur and Ravindran [8]

Minimise deviation be- tween scheduled people and the total work capac- ity from the work regula- tions

Ozkarahan and Bailey [166]

Dowsland [5], Dowsland [84]

are fixed Warner [215]

Adaptable Musa and Saxena [153] Musa and Saxena [153]

Warner and Prawda [216]: a few organisa- tional constraints

Warner [215]: personal and unit wide ‘aversion’ for pat- terns

Miller et al. [147] Miller et al. [147]: personal ‘aversion’ for non-binding constraints

Okada [158]

User Definable ANROM, cost parame-

ters: Burke et al. [36]

ANROM: Burke et al. [36] Weil et al. [218]: generic

model can cope with dif- ferent legal regulations

ANROM, weights in Burke et al. [35]

Meyer auf’m Hofe [144] Meyer auf’m Hofe [144] Meisels et al. [138] Meisels et al. [138]

Table 3.3: Flexibility

find the best coverage in every situation (Section 5.6).

Most authors restrict the applicability of their models to some simplified examples of nurse rostering, with, for example, three different shifts, short planning horizons, a limited number of possible patterns for personnel members with an identical work regulation, etc.

Skill classes are hierarchically substitutable when higher skill classes can do jobs replacing lower skilled people (see Table 3.6). In other problems, people from different skill classes can substitute each other in a user defined way. The latter approach reflects the real-world situation as it occurs in Belgian hospitals best. Among the group of people with the same skill class, some are more experi- enced or have better management skills to replace the head of their department. In simplified research examples, the problems are often defined with equal constraints for all the personnel members. The assignment of schedules to people is then very arbitrary. More realistic examples take part time contracts into account and provide flexibility to define personal work agreements. It is also shown in Table 3.7 that in case of personnel shortage, many hospitals make use of a group of ‘float’ nurses, to assist temporarily. In the current version of ANROM, people from other wards can assist in very busy wards. There is a procedure to evaluate time related constraints over the different wards.

flexible with respect to annual leave and unex- pected events

possibility to define cyclical patterns (Con- straint 22) which can be superimposed on non-cyclical schedules

[34, 36, 39]

Muslija et al. [154] Warner [215]: manual preprocessing of the number of people who rotate day and night weeks

Aickelin [4], Aickelin and Dowsland [5]

Alfares [6] Smith [195]: not all the personnel members have a rotating schedule

Meyer auf’m Hofe [142, 144]

Chan and Weil [55] Miller et al. [147] Dowsland [84] Kawanaka et al. [126] Okada [158], Okada and Okada [159]

Schaerf and Meisels [182] Table 3.4: Cyclical and Non-cyclical Approaches

Some approaches generate schedules which consist of days off and on. The next step in the process, the assignment of actual shifts to people is left for a head nurse to do manually. Algorithms which are developed for use in practical healthcare environments do not work with three strictly distinct shift types (see Table 3.8). The activities in hospitals are so varied that a large number of user-definable shifts is allowed. In ANROM, start and end times can even be personal as a result of a negotiation with the hospital manager for practical reasons (see Section 2.2.4). The higher the number of shift types, and the more flexible they are, the larger the search space is.

Most researchers are aware of regular changes in personnel demands (Table 3.9). This is one of the reasons why pure cyclical schedules are generally not workable. It is a part of Warner and Prawda’s scheduling work [216] to predict the personnel requirements for the next few days. The personnel requirements are nearly always expressed as a number of people required per shift type or even per day. ANROM tackles the problem in a much more flexible way as a result of feedback from the users of this system in several Belgian hospitals. Not only is the number of possible shift types higher than in most problems encountered, but also the approach to compose a schedule with different combinations of shift types is exceptional.

Miller et al. [147] ANROM: unless certain cir- cumstances occur (see Section 5.2) Miller et al. [147] ANROM: unless certain cir- cumstances occur (see Section 5.2) ANROM: mini- mum, preferred, compromise, add hours, etc Warner [215] Warner and Prawda [216] Warner and Prawda [216] Ozkarahan [162] Kawanaka et al. [126] Ozkarahan [162] Isken and Hancock [121] Meyer auf’m Hofe [144] Isken and Hancock [121]

Meyer auf’m Hofe [144] defines mini- mum and standard staffing levels which are treated as fuzzy constraints, there is a considerably larger penalty for understaffing than for overstaffing Ahmad et al. [3] Ahmad et al. [3] only for day shifts Schaerf and Meisels [182] Okada [158], Okada and Okada [159] Schaerf and Meisels [182] Table 3.5: Coverage

able Number Skill Classes Weil et al. [218] Ozkarahan [162]

Musa and Sax- ena [153]

Schaerf and Meisels [182]

Scheduled Separately

Chen and Ye- ung [56] Okada and Okada [159] Arthur and Ravindran [8] Isken and Hancock [121] Kawanaka et al. [126] Warner [215] Okada [158]

Hierarchical Substitutability Aickelin [4],

Aickelin and Dowsland [5]

Meisels et al. [138]

Dowsland [84]

User Definable Sustitutability Miller et al.

[147]: a sub- group of the regular nurses might be the group of those who can per- form as head nurses Warner and Prawda [216]: small overlap (substitution) between skill classes al- lowed, not related to people individ- ually ANROM: Burke et al. [39, 34], see also Section 2.2.2

Table 3.6: Skill Categories

Short planning periods are much easier to generate schedules for. It can be an option to split the period into smaller intervals and to combine the schedules afterwards. In nearly all the cases this will lead to sub-optimal solutions. Table 3.10 gives examples of some of the realistic and theoretical approaches studied in this literature overview.

The number of personnel members in a hospital ward can vary from less than 10 to far over 100. In cases where the problem cannot be split into sub-problems, the algorithms must be powerful enough to solve problems with widely varying dimensions (Table 3.11).

Weil et al. [218]: full time nurses only

Warner and Prawda [216]: no distinction between people Chen and Yeung [56]

Mixed Workforce: Ozkarahan and Bailey [166]: different work regulations

FT & HT Musa and Saxena [153]: various part time options are possible

User Definable ANROM; see ‘work regulations’ in Section 2.4.3 Meyer auf’m Hofe [142, 144]

Chiarandini et al. [58] Schaerf and Meisels [182]

Warner [215]: people can have different ‘contracted work- loads’

Float Nurses in ANROM it is possible to let people work in more than one ward, see Section 5.3

Warner and Prawda [216]: generally, nurses are assigned to a unit and do not move around at zero cost; a few ‘float’ nurses do move around

Meyer auf’m Hofe [142, 144] constrains the expenditure of work

Trivedi and Warner [208] Table 3.7: Work Regulation

Table 3.12 presents purely theoretical models in addition to algorithms which are implemented in software packages for practical use. The generic systems belong to the most flexible and complex problems for nearly all the dimensional parameters presented in this section. In fact, the software systems in the right column of Table 3.12, are among the very few that offer automatic procedures for solving widely varying nurse rostering problems.

Tables 3.13 to 3.20 present a list of time related constraints, which belong to the category of soft constraints in ANROM (Section 2.4). Some researchers set strict values for the constraints, while others let them be user definable. If we compare the table with Table 3.12, it is clear that the most flexible defi- nitions exist in the approaches which are applicable in real scheduling situations.