Dealing with Perceived Fairness when Planning Doctor Shifts

in Hospitals

Renaud De Landtsheer

, Ga

etan Delannay

and Christophe Ponsard

CETIC Research Centre, Gosselies, Belgium

GeezTeem, Malonne, Belgium

Keywords:

User Acceptance, Scheduling, Rostering, Fairness, Metaheuristics.

Abstract:

Producing planning of doctors’ roles, including night shifts, on-call shifts (doctor can be called back in case

of need), and regular working day in a hospital is complex and it is often difﬁcult to effectively address all real

world constraints. Furthermore, the produced solution requires a very good user acceptance to be effectively

deployed in production. This paper reports on the application of metaheuristics to solve a planning problem

in an hospital and focuses on user acceptance aspects of an algorithm. One of the key aspects to ensure user

acceptance is to ensure the comprehensibility of the delivered solution. This includes the understanding of

both the algorithm itself and its executions. The algorithm is a composition of local search, greedy algorithms,

tabu search, and a few additional metaheuristic principles, and proved both good and fast enough.

1 INTRODUCTION

In the hospital environment, efﬁcient coordination is

of prime importance, notably to ensure that neces-

sary workforce is available at the required time, with

the required competences. This is because an hospi-

tal has to cope with possibly large ﬂows of patients

that cannot be interrupted, and medical care requires

a set of speciﬁc competencies. Medical workforce is

needed at different roles throughout the week. These

include regular working role, on-site night shifts, and

on-call duty. Roles planning must obey a given set of

rules about resting time and cope with peoples’ non-

availabilities. Some equity between people is also re-

quired to maintain a good working atmosphere.

Setting up such planning is time consuming and

can be the source of personal frustrations since plan-

ning composition, when is performed by a human col-

league, can always be perceived as not objective and

thus unfair. Fairness in duty rostering is emphasised

in guidelines of many countries (NSW, 2015; NHS,

2016).

This paper presents a dedicated metaheuristic-

based algorithm that has been developed to automati-

cally compose such planning. The algorithm has been

designed to maximize user acceptance and perceived

fairness of the delivered planning. This means the al-

gorithm produces a “transparent solution”. Together

with the planning it also gives a clear trace explana-

tion of the taken decisions regarding a number of con-

straints or several priorities including constraints im-

pacting the fairness both at short and long term. To

make this trace comprehensible by doctors, the algo-

rithm relies on a relatively simple metaheuristic.

Of course the doctor scheduling problem (DSP)

and also the related nurse scheduling problem (NSP)

have received a large attention and solutions to those

problems have been proposed based on a large spec-

trum of techniques generally based on heuristic ap-

proaches such as tabu search, simulated annealing,

stochastic optimization, genetic algorithms or ant

colony optimization (Burke et al., 2004; Gendreau

et al., 2007; De Causmaecker and Vanden Berghe,

2011). Yet, planning algorithms can always be bi-

ased in one way or another by the person in charge of

the planning, and well-established generic algorithms

such as CP, LNS, or MIP can be perceived by the user

as efﬁcient, but obscure black boxes. This might raise

suspicions regarding the fairness of the tool. A funda-

mental design choice of our approach is to not rely on

an existing optimization framework but to implement

a dedicated search procedure. The risk to reach a sub-

optimal solution was balanced with other constraints

such as the need to fully justify the resulting planning

and also some integration constraints.

This choice of developing an ad-hoc, simple meta-

heuristic is further discussed in the light of the user

feedback collected from real world deployment. The

320

Landtsheer, R., Delannay, G. and Ponsard, C.

Dealing with Perceived Fairness when Planning Doctor Shifts in Hospitals.

DOI: 10.5220/0006657403200326

In Proceedings of the 7th International Conference on Operations Research and Enterprise Systems (ICORES 2018), pages 320-326

ISBN: 978-989-758-285-1

deployment was conducted by the MedErgo company

which triggered this research and has integrated the

result in the scope of their product, with name Nice-

Watch (MedErgo, 2016).

The paper is structured as follows: Section 2

presents the considered planning problem and its con-

straints with a focus on equity. Section 3 presents the

technical approach to solve the problem and the con-

sidered metaheuristics. Then, Section 4 discusses on

the different mechanisms that have been deployed in

order to maximize user acceptance. Section 5 presents

related work sharing the same concerns of facilitating

the user acceptance. Finally, Section 6 draws some

conclusions and research perspectives.

2 PROBLEM STATEMENT

This section presents the considered rostering prob-

lem, with a focus on aspects that can cause doctor

frustration.

A planning ranges over a given period of time, and

deﬁnes, for each day of this period of time and each

role, who among the set of available doctors will ﬁll

in this role. Roles can be regular workday at a given

place (anaesthetist in operating theatre no 2, emergen-

cies), on-site night duty, or home based on-call duty.

With respect to rostering, doctors are character-

ized by a set of legal and organizational attributes

such as contractual availability, qualiﬁcation, maxi-

mal number of duty per month, degree of seniority

and assignable duty roles.

Besides, there is also a set of personal constraints

to be considered, including personal days off that

are considered as strong constraints as soon as they

are granted, and personal preferences regarding duty

roles. These can be positive or negative preferences.

Planning must also obey as set of legal rules re-

garding resting times:

• a duty role at the hospital lasts for 24 or 25 hours.

If happening during the week, it starts during the

normal working hour starting at 8 am and lasts

till 9 am the next day. If it occurs on a Saturday,

Sunday or legal holiday, it starts at 9 am and ends

at 9 am the next day. A duty role happening be-

tween and including Sunday to Thursday is auto-

matically followed by a day off. For a duty role

occurring on a Friday, the doctor gets half a day

off that can (s)he can place anywhere. For a duty

role happening on a Saturday, the next Monday is

a day off. Legal holidays are treated as Sundays,

and days before legal holidays as Fridays.

• A doctor can only fulﬁl a single role at a time.

• At any time, among all roles requiring a given

qualiﬁcation, one of them at least must be occu-

pied by a senior doctor. For instance, emergencies

and anaesthetist roles.

• A doctor cannot be working or on any form of

duty when on holiday or when off its contractual

working days in case of part time contract.

• There must be at least ﬁve days between two con-

secutive duties of the same doctor.

• In any period of four weeks, a doctor can have at

most one duty occurring during the weekend.

• In case of a part time worker, a resting time fol-

lowing a duty cannot happen when the doctor is

not working according to the contract.

• A resting time cannot occur during holiday.

A consequence of the compensation system for

duty roles is that some of them are more attractive

than others. Duty roles happening on a Thursday are

the most attractive, since the doctor gets an extended

weekend of three consecutive days. The least attrac-

tive roles are the ones happening during the week-

end, since the compensation is smaller and they are

not covering regular working hours, so that the doc-

tor loses half a day off at the end. Friday and other

week days duties are in between. This attractiveness

is the main cause of frustration with duty roles as-

signment. Planning composition should therefore

be fair among doctors about this attractiveness of

duties. Inside a large doctor’s team, it’s indeed im-

possible to set up a monthly planning that takes into

account all the loads or attractiveness of this peculiar

month. One must thus ﬁgure out a way to spread out

the workload among individuals and over longer time

frames.

To summarize and prioritize, a planning must

comply with the following elements:

1. ﬁrst, it must comply with the strong constraints

here above;

2. then, the personal preferences must be considered;

3. ﬁnally, the attractiveness of the planning must be

evenly spread across all doctors.

Some inequities can be tolerated temporarily, but

they must be compensated the next month. As dis-

cussed in the introduction, the planning must ensure

some fairness between doctors, and must propose

some mechanism to ensure that doctor have a good

perception that the algorithm was fair, even though

the planning might trigger some personal frustration.

There is also a requirement that the algorithm

must be deterministic. This ensures that the person

in charge of triggering the runs of the algorithm does

Dealing with Perceived Fairness when Planning Doctor Shifts in Hospitals

321

not have the possibility to trigger the algorithm on de-

mand to select a solution that better ﬁts some non-

expressed desires. As a consequence, all random

functions used in our algorithm, notably to break ties,

rely on a deterministic pseudo-random generator.

A last non-functional requirement is the efﬁciency

of the planning engine: it must be able to generate a

complete schedule for a single month within a few

seconds.

3 SOLUTION DESIGN

3.1 Key Design Choices

It is difﬁcult to ensure a good comprehensibility of the

algorithm and its execution using existing scheduling

engines relying on state-of-the-art algorithms. While

they are efﬁcient and can deal with fairness, they are

also quite complex and hard to understand for non

computer scientists, and they are not designed to pro-

vide a traceability of the resulting solution. In order to

deal with this issue, a key decision is to implement a

dedicated search engine not relying on any framework

such as OscaR, Gecode, OR-tools, LocalSolver or any

others (OscaR Team, 2012; Gecode Team, 2017; OR-

tools Team, 2017; Benoist et al., 2011).

Attractiveness of the planning is a key element of

doctor satisfaction, so that it must be quantiﬁed in or-

der to reason upon it. The approach is to deﬁne a score

of discomfort for each doctor on a given planning. All

duties get a score of discomfort; the less attractive, the

higher is this score. The discomfort of a doctor for a

given planning is the sum of the discomfort of all du-

ties (s)he is assigned to in this planning.

With this mechanism of discomfort score, we can

model attractiveness, and compensate inequities from

one month to another one, by accumulating the score

of discomfort across months.

To ﬁnd a solution, a greedy approach is used. Be-

cause it might fail to ﬁll in a role, we therefore intro-

duced the notion for a role of being unassigned. The

key points are summarised here and detailed in the

rest of this section.

• The main loop is a simple loop that allocates doc-

tors to roles. It iterates onto unassigned roles, and

assigns them to a doctor.

• The role is selected to be among the unassigned

ones, as the one that has the fewest possible doc-

tors, in view of the strong constraints and with an

ordering based on the expressed preferences (pos-

itive or negative). In case of equality, a random

role is selected.

• Relaxation is used in case the system reaches a

step with no possible assignment. In this case a

role that was assigned to a doctor is unassigned to

generate the necessary degree of freedom.

• Diversiﬁcation and cycle detection are also used

to avoid the system iterating over the same set of

partial allocations, leading to a dead end.

3.2 Metaheuristic: Greedy Approach

The algorithm itself is a greedy approach, with possi-

bility to undo some of the greedy decisions. At each

iteration a role is picked up, and a doctor is selected

for this role. The algorithm has the possibility to re-

lax an assignment in case of no doctor can be selected

for the considered role. Finally, a tabu component

is added to prevent relaxing assignments too quickly,

and help escape local impossibilities.

Basically, the greedy search iterates on roles is

a well-chosen order, and assign the current role to a

doctor. It is summarised in Listing 1.

Listing 1: Greedy Algorithm for Role Assignment.

w h i l e ( r o l e T o A s i g n i s n o t em pty ){

v a l c u r r e n t R o l e =

s e l e c t r o l e i n r o l e T o A s s i g n

m i n i mizing d egr e eO f Fr e edo m ( r o l e )

v a l d o c t o r T o A s s i g n =

s e l e c t d o c t o r i n a d m i s s i b l e D o c t o r ( c u r r e n t R o l e )

max i miz i ng a f f i n i t y ( d o c t o r , c u r r e n t R o l e )

a s s i g n ( c u r r e n t R o l e , d o c t o r T o A s s i g n )

u p d a t e degr e e o f f ree d om a nd a d m i s s i b l e D o c t o r

}

The iteration on roles is based on the degree of

freedom of the role. Roles with the smallest degree of

freedom are assigned ﬁrst. The degree of freedom of

a role is the number of doctors that can be assigned to

this role, given the strong constraints and the existing

assignments. It is updated every time an assignment is

performed, or relaxed. A role assignment may impact

the degree of freedom of another role because some

constraints impose a minimal delay between shifts,

notably through a resting period.

Ties for roles as well as doctor selection are bro-

ken based on a deterministic pseudo-random selec-

tion. We deliberately use a deterministic generator

because we want several runs of the algorithm to pro-

duce the same output.

The afﬁnity between a doctor and a role is a

weighted sum involving:

• the preference (positive or negative) between the

role and the doctor.

• the attractiveness of the considered role, based on

weighting along the features of the role.

ICORES 2018 - 7th International Conference on Operations Research and Enterprise Systems

322

• a cumulated satisfaction score of the considered

doctor that sums up the attractiveness of the past

and already assigned role to this doctor.

3.3 Relaxing in Case of Impossibility

In case the algorithm reaches a point where the cur-

rent role cannot be fulﬁlled by any doctor, one or more

assignments are relaxed to provide the necessary free-

dom to the considered role. These are all related to the

same doctor, who is then assigned to that role.

The doctor is selected such that he can be assigned

to the role after some other assignments are relaxed.

This excludes all doctors that are not available this

day, based on their contract, for instance. The se-

lected doctor also minimizes the number of assign-

ments that are to be relaxed. Ties are broken based

on a deterministic pseudo-random selection, again to

ensure that the algorithm is deterministic.

3.4 Dealing with Allocation and

Deallocation Cycles

The relaxation performed in case of a role cannot

be assigned can lead to the algorithm oscillating in

a closed loop: a role “a” cannot be assigned, so an

assignment involving role“b” is relaxed. In turn to as-

sign role “b” the algorithm can relax role “a”, etc. To

prevent this, each assignment is added to a “tabu list”.

The tabu list is determined by setting a number

of iterations during which the assigned role cannot be

relaxed by the relaxation procedure.

4 PROTOTYPING AND

VALIDATION

The proposed algorithm was implemented for Med-

Ergo, a Belgian company provides a web-based soft-

ware application for doctor planning, called Nice-

Watch (MedErgo, 2016). The system is composed of

a global database containing the actual planning, and

a web-based user interface in which doctors can post

their own constraints, query their planning, interact

with other doctors to barter duty roles, etc. A speciﬁc

interface is also available to the coordinator to visual-

ize all individual constraints, and set up the planning.

This interface is depicted in Figure 1.

A corollary of the need to implement the full

search procedure is that the algorithm could actually

be developed by a skilled developer not specialist in

optimisation with only some support from an expert.

The implementation was carried out in Python, an

Figure 1: Partial with of the planning interface with possible

constraints and allocations types.

Open Source multi-paradigm programming language

focusing more on expressiveness and ease of integra-

tion than on performance as it is usually interpreted

(van Rossum, 1991). The implementation was per-

formed following an Agile approach. This allowed

us to quickly validate that the algorithm performance

would not be a bottleneck and then to progressively

improve that performance to deal with more complex

constraints and to produce the justiﬁcation reports.

Shifts are typically scheduled each month based

on the available doctor staff. The validation example

presented here is composed of about 50 doctors which

needs to ensure 5 simultaneous watch roles, some at

every day, some only on week days. Table 1 shows

the staff request for a typical month of 31 days.

Table 1: Typical Role Request for Different Watches.

Watch role # days

1 Intensive care 31

2 Anesthetist 1st watch 31

3 Anesthetist 2nd watch 31

4 Anesthetist 1st watch (recall) 31

5 Anesthetist 2nd watch (recall) 22

6 Day hospital 22

Figure 1 shows the planning interface displaying

both the constraints (coloured square without num-

ber) and the proposed allocation (coloured square

with number). The legend details the full set of pos-

sible constraints and allocations. During the planning

process a full allocation trace is generated and avail-

able for checking the allocation process. A typical

trace is displayed in Listing 2 for the ﬁrst two slots of

some allocated day.

Dealing with Perceived Fairness when Planning Doctor Shifts in Hospitals

323

Listing 2: Justiﬁcation Trace.

4 / 0 / 4 P r e f =1 P = 6.53 Av=30 DDC| U n a v a i l a b l e ( o f f )

1 / 0 / 1 P r e f =1 P = 5.90 Av=27 MAF

4 / 0 / 4 P r e f =1 P = 5.74 Av=31 MH

4 / 0 / 5 P r e f =1 P = 8.03 Av=31 DL

4 / 0 / 4 P r e f =1 P = 8.15 Av=31 KS

. . .

Day X − S l o t 1 − A l l o c a t e d t o : MAF

4 / 0 / 4 P r e f =1 P = 8.72 Av=30 CC | U n a v a i l a b l e ( o f f )

4 / 0 / 4 P r e f =1 P = 9.11 Av=31 KB | minDistanceKO

1 / 0 / 2 P r e f =1 P = 3.94 Av=21 RCA| minU nf av DistanceK O

1 / 0 / 2 P r e f =1 P = 4.15 Av=27 SC | mi nD is ta nc eK O

1 / 0 / 2 P r e f =1 P = 4.44 Av=18 WM

1 / 0 / 2 P r e f =1 P = 4.52 Av=22 VN

2 / 0 / 3 P r e f =1 P = 4.86 Av=31 VRP

. . .

Day X − S l o t 2 − A l l o c a t e d t o : WM

For each slot, a list reviewing possible doctor al-

locations is compiled. The list starts with doctors that

cannot be allocated with a justiﬁcation code whose

explanation is detailed in Table 2. It is followed by a

prioritised list of doctors using the ranking procedure

described in the previous section. The ﬁrst available

doctor is the allocated one.

Table 2: List of Justiﬁcation in Allocation Traces.

Justiﬁcation Description

Unavailable Date is within the strong constraints

of the doctor (according to work

contract and vacations)

Unwanted Date is within the doctor’s wishes

not to be on duty

MaxFrequency

Reached

Maximum quota is reached for doc-

tor’s wanted watches

MaxFrequency

ReachedOutside

Maximum quota is reached for doc-

tor’s unwanted watches

RecoveryRule

Broken

This day is already assigned or is a

recovery day

MinDistanceKO The minimal delay between two

wanted watches cannot be re-

spected

MinDistance

UnwantedKO

The minimal delay between two

unwanted watches cannot be re-

spected

minUnfavourable

DistanceKO

The minimal delay between two un-

favourable dormant watches cannot

be respected

minUnfavourable

DistanceOutside

The minimal delay between two un-

favourable dormant watches cannot

be respected

noSenior No senior doctor would have been

assigned to a set of paired roles

BlackListed This doctor cannot be assigned here

because it will lead to an impossi-

bility to complete the schedule later

Our tool was deployed in production in August

2016 in different Belgian hospitals, as part of the

NiceWatch web-based platform (MedErgo, 2016). Al-

though our solver is not has been developed using

standard data structures, the overall performance is

quite good as scheduled can be produced within a few

seconds and allow the user to wait for the result.

5 RELATED WORK

In DSP, fairness constraints are identiﬁed along other

constraints and typically formulated as the fair dis-

tribution of different types of shifts among doctors

with the same experience in (Gendreau et al., 2007).

Fairness received speciﬁc attention in the emergency

room context (Ferrand et al., 2011; Santos and Eriks-

son, 2014; Devesse et al., 2016).

MIP based heuristics have been used to create bal-

anced scheduling from the set of doctors (Devesse

et al., 2016). Integer programming has also been used

to take into account constraints of the schedule, dif-

ferent preference ranks w.r.t. shifts, and the histori-

cal data of previous schedule periods to maximize the

global satisfaction about the proposed shift schedule

(Lin et al., 2014). The resulting shifts and days-off

were fair and met the staff satisfaction.

In local search, an objective function is expressed

as a weighted sum of soft constraint violations. Such

an objective function has the advantage of being both

easy to understand and to implement. However, they

can produce unfair solutions because some high qual-

ity allocations can compensated low quality ones. A

solution proposed by (Smet et al., 2012) is to use a

function where the quality of the worst individual al-

location will directly impact the overall solution qual-

ity. In doing so, a planing will not be improved at the

expense of the worst individual case. Experimental

results have conﬁrmed the resulting solution is more

fair, nevertheless a drawback is that the search seems

less efﬁcient given the new structure of the function.

In addition to the lack of explanation traceability, this

reinforces us about our dedicated approach.

A complete overview of techniques for NSP with

some hint about how to come with personal con-

straints is presented in (Burke et al., 2001). Evolu-

tionary algorithms are quite commonly used and an

approach for the formulation of the ﬁtness function

has proven to be very powerful both to enable ex-

tendibility and to provide a quick and explanatory

mechanism. We achieved the same results using our

own approach and our belief is that the technique used

is not the key point but rather the ability to take into

account the right set of constraints, including histori-

cal data as well as the ability to produce justiﬁcations.

The requirement for traceability also favour better ar-

ICORES 2018 - 7th International Conference on Operations Research and Enterprise Systems

324

chitecture which in turn ease the ability to deal with

more complex real-world constraints.

6 CONCLUSION

This paper reports on our research to develop a meta-

heuristic that intertwines mechanisms borrowed from

various technical origins (local search, greedy, tabu

search, etc.) with a speciﬁc attention to enable a good

fairness of the produced planning. A key point is that

the transparency on fairness constraints is more im-

portant than the level of optimality of the solution for

user acceptance. While a off-the self solution would

certainly achieve better results (i.e. less discomfort)

than our approach and also cope with fairness, it is

hard to achieve a good level of transparency with them

and hence there is a risk of early rejection. Our ap-

proach on the contrary is able to achieve transparency

about “even discomfort”. It also has the capacity to

evolve to reduce the level of discomfort. In the end,

the overhead of having to implement the algorithms

without relying on a framework is also not so high

when balanced with those advantages.

The proposed solution already proved quite use-

ful and could establish a good level of trust and peace

among users. Of course it can be improved. For ex-

ample, it should be noted that not every discomfort

can be assigned to a single shift but can also result

from a sequence/set of shifts/tasks can also lead to

discomfort. Our present work does not consider this

and could be extended in this direction. In this pro-

cess, the current data structures will probably show

their limits by slowing down the computation. To

cope with this, we could rely on data structures en-

abling incremental evaluation for faster exploration of

the search space as done by local search solvers (Os-

caR Team, 2012). At this point it is interesting to con-

sider switching to such a framework as users are less

challenging the system fairness. In the process we

will also be able to carry out computational compar-

ison between both approaches. We also plan to work

on a traceability feature for this framework.

The proposed approach could also be applied to

other areas of scheduling where fairness and user ac-

ceptance are important issues (e.g. care pathways)

with however the drawback that the underlying frame-

work is not generic and must thus be revisited for each

new problem.

ACKNOWLEDGEMENTS

This research was partly funded by the Walloon regi-

on as part of the PRIMa-Q CORNET project (nr.

1610019). We warmly thanks MedErgo for allowing

us to share this case.

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