=Paper=
{{Paper
|id=Vol-2646/31-paper
|storemode=property
|title=How to Cope with Personnel Unavailability? Process Mining May Help!
|pdfUrl=https://ceur-ws.org/Vol-2646/31-paper.pdf
|volume=Vol-2646
|authors=Andrea Chiorrini,Claudia Diamantini,Domenico Potena,Emanuele Storti
|dblpUrl=https://dblp.org/rec/conf/sebd/ChiorriniDPS20
}}
==How to Cope with Personnel Unavailability? Process Mining May Help!==
https://ceur-ws.org/Vol-2646/31-paper.pdf
How to Cope with Personnel Unavailability?
Process Mining May Help!
(DISCUSSION PAPER)
Andrea Chiorrini, Claudia Diamantini, Domenico Potena and Emanuele Storti
DII, Polytechnic University of Marche, Ancona
{a.chiorrini,c.diamantini,d.potena,e.storti}@univpm.it
Abstract. Replacement planning is critical to guarantee continuity of
operations in business processes in case of personnel unavailability. In
this work, we propose a data-driven approach for supporting resource
replacement that makes use of logs of past process executions to model
a social network of resources. On this top, a similarity measure among
resources is exploited to assign tasks of unavailable resource to the avail-
able ones through an Integer Linear Model.
1 Introduction
In organization management, replacement planning consists in addressing short-
term lack of workforce that may be due to temporary or permanent unavailability
of personnel for several reasons, including for instance vacation, resignation or
illness. This issue has a larger impact on organizations when the unavailability
cannot be predicted in advance, such as during strikes or emergencies. A recent
example of the latter case is the COVID-19 outbreak, which is severely affecting
continuity of operations in many public administrations and private companies
worldwide.
Traditional approaches in the literature for resource scheduling and replace-
ment planning address the problem typically through business rules modeled by
domain experts. On the other hand, nowadays information systems (e.g., ERPs,
Workflow Management Systems, CRMs) are capable to track and monitor ev-
ery event occurring during a business process, such as what activities have been
executed, when and by whom. This valuable information can be exploited to
support more reliable kinds of data-driven analysis, e.g. through Process Mining
techniques.
This paper discusses a data-driven framework for planning of resource re-
placement. Through the analysis of past executions of business processes the
approach is aimed to model a sociogram, i.e. a social network describing how
Copyright c 2020 for this paper by its authors. Use permitted under Creative Com-
mons License Attribution 4.0 International (CC BY 4.0). This volume is published
and copyrighted by its editors. SEBD 2020, June 21-24, 2020, Villasimius, Italy.
resources collaborate with each other. Several metrics have been devised in the
literature to analyse different social relations among resources, including those
focusing on how work moves among performers and those considering that people
doing similar tasks have stronger relations than people doing completely different
things [5]. Here we focus on the both aspects, using a handover of work metric
(measuring how frequently work is transferred between two resources) and taking
into account capabilities of resources, to evaluate the costs for assigning those
activities that should have been performed by the unavailable resource(s), to
others. Finally, on the basis of this information, an Integer Linear Programming
(ILP) model is defined with the aim of selecting the set of candidate resources
to minimize the total cost of replacement.
The work fits into the field of organizational mining[4], focusing on the re-
sources (or actors) that performed events and their mutual cooperation in the
fulfillment of a process. In [3] an organizational mining framework has been
proposed for the discovery, rather than the enforcement, of patterns related to
resource assignment using declarative process modelling languages based on rule
templates. Our approach shares also the exploitation of an ILP model for task as-
signment with [2], although the work has a different purpose, namely proposing a
recommendation system to support process participants to take a risk-informed
decision in choosing the next task to execute out of a set of assigned tasks.
The novel contributions of this work are as follows: (1) we propose a so-
ciogram modeling the handover of work relation that extends traditional models
in the literature, by representing the specific type of the transferred activity; (2)
on its top, a measure of similarity among resources is defined by considering the
degree of collaboration between two resources, the performance and the experi-
ence of a resource to perform a given activity; (3) in order to find the best set of
resources to replace the unavailable one, an Integer Linear Programming model
is proposed to minimize a cost function taking into account similarity among
resources.
We propose here an example related to a phone repair process for a company,
that will be used throughout the paper. As shown in Figure 1, the process starts
with the registration of the repair request (A) and is followed by analysis of
defects (B). Then, the user is informed about the outcome (C) and in parallel
the repair subprocess is performed. This is achieved by executing either a simple
repair (D) or a complex one (E), and is ended by a test to verify whether the
repair solved the issues (F). In the negative case, the repair subprocess is re-
executed. Finally, if the test succeeds, the request is archived (G) and the process
ends. Let us assume the process involves 6 users, named James, Carrie (in charge
of administration activities A, C and G), Mark, Alec, Harrison and Peter (in
charge of analysis, repair and test, i.e. activities B, D, E and F). Every record in
the log refers to a specific case and is a sequence of events, each of which described
in terms of activity, resource and duration in a certain time unit (minutes in the
example), as shown in Table 1.
The example is inspired to the ProM 6 tutorial by H.M.W. (Eric) Verbeek at
http://www.promtools.org/prom6/downloads/prom-6.0-tutorial.pdf
Fig. 1. The example process model.
ID Trace
1 (A, James, 15), (B, Mark, 60), (C,James, 8), (D, Harrison, 25), (F,Alec, 18), (G, Carrie, 9)
2 (A,Carrie, 12), (B,Harrison, 74), (E,Harrison, 79), (F,Peter, 17), (C,James, 4), (G,James, 13)
3 (A,Carrie, 10), (B,Peter, 43), (D,Peter, 43), (F,Alec, 72), (C,Carrie, 7), (E,Harrison, 115),
(F,Alec, 20), (G,James, 14)
4 (A,James, 20), (B,Mark, 96), (C,James, 3), (D,Mark, 31), (F,Alec, 209), (D,Alec, 53),
(F,Peter, 23), (G,Carrie, 11)
Table 1. Running example: event log for the repair process. Time unit is minute.
The rest of this work is structured as follows: the next section presents a
novel handover of work metric and the sociogram model. Section 3 discusses
the proposed methodology for resource replacement. Finally, Section 4 reports
preliminary results and draws future research extension.
2 Social network for handover of work
In this section we introduce the terminology and a model of social network for
handover of work that is used in the rest of the paper.
Hereby we refer to the term activity as a task (or portion thereof) performed
to achieve a goal, and to resource as any member of personnel that is capable
to perform some activity.
Definition 1. (Event, Trace & Event Log)
Let A be a set of activities and R a set of resources. V = A × R is the set of
possible events, i.e., combinations of an activity and a resource. Given a resource
r, V (r) ⊆ V is the set of events in which r can take part. A trace is a possible
sequence of events, where C = V ∗ is the set of all possible traces. An event log
L is a subset of all bags (multi-sets) over C.
In our scenario, we assume the event log includes as attributes at least the
case id, the executed activity, the resource name and the timestamp when each
event has been performed. For convenience, we introduce the function πa (σ)
which returns the set of activities related to events of a trace σ.
From the event log, it is possible to characterize a resource r ∈ R in terms
of his/her capabilities, i.e. the set A(r) of activities that is able to perform. To
make an example, from the log in Table 1 we derive A(M ark)={B, D} and
A(Harrison)={B,D,E}.
Among the various relations that can be recognized in an event log between
two resources, we focus here on relations of possible causality, and specifically
to handover of work. Within a case there is a handover of work from a resource
r1 to a resource r2 if there are two subsequent activities a1 and a2 where a1
is completed by r1 and a2 by r2 . The metric can be defined and computed in
multiple ways [5], according to the degree of causality (direct or indirect), the
existence of multiple succession from a resource to itself (multiple self-transfer),
and the kind of succession, i.e. arbitrary succession between two subsequent
events in a trace or casual dependency. In this last case, a process model is
needed to recognize which is the correct flow of activities in a trace. To make an
example, with reference to the case 3, between events (A,Carrie) and (B,Peter)
there is a direct and casual succession, while between (F,Alec) and (C,Carrie)
there is a direct but arbitrary succession. Indeed, if we compare the log to the
process model in Figure 1, there is a causal relation between activities A and B,
but this does not hold between activities F and C.
In this work, we refer to the handover of work relation (1) by ignoring self-
transfers, (2) by considering indirect succession and (3) casual relation, i.e. we
take into consideration succession between activities, with any length, only if
aligned to the process model. The reason behind (1) is that the research question
of the work is related to resource replacement, for which considering handover
from the same resource is not helpful. The reason of (2) and (3) is related to the
need to correctly identify handover of work in real processes and avoid spurious
relations. Please note that a process model, if not available, can be discovered
through Process Discovery algorithms (e.g., Alpha Miner, Heuristic Miner, In-
ductive Miner). In the following we define the function and the formula for the
calculation of the metric.
Definition 2. (Handover of work)
Given r1 , r2 ∈ R, ax ∈ A(r1 ), ay ∈ A(r2 ), an event log L, a process model P
and a trace σ ∈ L, the function r1 ⊗σax ,ay r2 returns how many times r1 and
r2 executed respectively activity ax ∈ πa (σ) and ay ∈ πa (σ) such that a causal
relation between them in P exists. For the whole event log L, the function is
computed as:
X
qxy = r1 ⊗Lax ,ay r2 = r1 ⊗σax ,ay r2
σ∈L
Finally, the metric handover of work between r1 , r2 for activities ax , ay in L
is computed as:
X X
hxy = r1 L L
ax ,ay r2 = r1 ⊗ax ,ay r2 / ri ⊗Lax ,ay rj
ri ∈R rj ∈R
The metric is computed for a couple of resources r1 , r2 and with respect
to a couple of activities ax , ay by dividing the total number of proper casual
James Marc Carrie Harrison Alec Peter
James (A,B,0.5,2) (C,G,0.5,2)
Mark (B,C,0.5,2) (B,D,0.3,1) (D,F,0.25,1)
Carrie (C,G,0.25,1) (A,B,0.25,1) (A,B, 0.25,1)
Harrison (B,C,0.25,1) (D,F,0.25,1) (E,F,0.5,1) (E,F,0.5,1)
Alec (F,G,0.25,1) (F,G,0.25,1) (F,E,1.0,1) (D,F,0.25,1)
Peter (F,G,0.25,1) (B,C,0.25,1) (F,G,0.25,1) (D,F,0.25,1)
Table 2. Running example: handover matrix.
succession (with no self-transfer) by the total number of casual succession of
ax , ay between any two resources ri , rj , with i 6= j.
As for the running example, given resources James and Carrie, and activities
C and G, James L 2
C,G Carrie= 4 = 0.5, because the casual succession between
them happens 2 times (case 1 and case 4), but the casual succession of C and G
between any two resources occurs 4 times.
This information can be represented as a handover matrix, that is a matrix
N × N , where N < |R| is the number of active resources (i.e. resources that
executed at least 1 activity in the event log). Given two resources ri , rj ∈ R active
in L, the cell (i, j) of the handover matrix includes a tuple (ax , ay , hxy , qxy ), with
ax ∈ A(ri ) and ay ∈ A(rj ), if and only if hxy > 0. In Table 2 we report the
handover matrix for the running example.
From the matrix, a sociogram can be defined, i.e. a graph of social relations
where nodes are resources and an edge linking two resources is defined if a certain
social relation is recognized between them. We refer to the following definition
of a sociogram as a labeled multidigraph, i.e. a directed multigraph where two
nodes may be linked by multiple labeled edges.
Definition 3. (Sociogram)
Given a N × N handover matrix M , a sociogram G is defined as an 8-tuple
G = (ΣR0 , ΣE , R0 , E, s, t, `R0 , `E ) where:
– R0 ⊆ R is the finite set of N resources in M and E is a set of arcs representing
a handover of work relation;
– ΣR0 and ΣE are finite alphabets of the available vertex and arc labels,
s : E → R0 and t : E → R0 are two maps indicating the source and target
vertex of an arc;
– `R0 : R0 → ΣR0 and `E : E → ΣE are two maps describing the labeling of the
vertices and arcs.
In the following, for the sake of simplicity, we refer to a sociogram G as
a tuple G = (R0 , E), with E as a multi-set of arcs. Each arc e ∈ E will be
shortly represented as a tuple e = (ri , rj , (ax , ay , hxy , qxy )) linking two nodes
ri , rj ∈ R0 , being ri the source and rj the target of e, and (ax , ay , hxy , qxy )
the arc label. For convenience, we introduce the operations πh (ri , rj , ax ) =
{hxy : ∃e = (ri , rj , (ax , ay , hxy , qxy )) ∈ E} and πq (ri , rj , ax ) = {qxy : ∃e =
(ri , rj , (ax , ay , hxy , qxy )) ∈ E} which respectively return the values of handover
of work between ri (after ax has been completed) and rj , and the numbers of
times ax has been executed by ri before rj . Furthermore, the set Gri (ax ) =
{r0 ∈ R0 : ∃(ri , r0 , (ax , ay , hxy , qxy )) ∈ E} is introduced to return the subset of
resources for which an handover of work relation from ri after completing ax
exists.
Please note that, differently from the organizational mining literature, we
refer to a labeled multidigraph with multiple edges between two nodes. This
enables a greater expressiveness as we can encode not only the handover of
generic work between two resources, but also take into account which specific
activities one resource has handed over the other.
3 Resource replacement methodology
We assume an organization relying on a Business Process Management system
with monitoring capabilities of process execution. Execution traces are made
available as event logs, which are then analysed and elaborated through orga-
nizational mining techniques to derive the sociogram as described in Section
2. This information is used to drive the resource replacement, that returns the
set of specific resources that are selected to replace the missing ones, and their
allocation to activities.
Given a sociogram G = (R0 , E), an unavailable resource r ∈ R to replace and
a multi-set T = {a1 , . . . , ah } of activities assigned to r that must be performed by
some other resources, the goal is to determine a set of resources {r1 , . . . , rn } ⊆ R
that is collectively capable to replace r to perform activities in T . We take into
account a similarity factor such that resources being more compatible to the
one to replace are preferred. This takes into account handover of work relations,
capabilities of resources, performance and experience.
Similarity measure. Given a resource r ∈ R to replace, a candidate resource
ri ∈ R and an activity aj , the similarity between the r and rj for the specific
activity aj is defined as follows:
sim(r, ri , aj ) = ω1 · coll(r, ri , aj ) + ω2 · perf (r, ri , aj ) + ω3 · exp(r, ri , aj )
The function sim(r, ri , aj ) returns the degree of affinity between the two re-
sources on the basis of (1) the collaborations that have been established to per-
form the activity aj (i.e., coll(r, ri , aj )), (2) the speed with which aj has been per-
formed (i.e., perf (r, ri , aj )) and (3) the experience gained by the two resources in
carrying out the activity (i.e., exp(r, ri , aj )). User parameters ω1 , ω2 , ω3 ∈ [0, 1],
such that ω1 + ω2 + ω3 = 1, are introduced to weigh the three similarity factors.
In details, Gr (aj ) and Gri (aj ) (see Section 2) are the sets of resources to
whom respectively r and ri handed over work after performing activity aj . Let
ĥ(rx , ry , aj ) = |πh (rx1,ry ,aj )| · hi ∈πh (rx ,ry ,aj ) hi be the average handover of work
P
T is a multi-set because an activity may need to be performed multiple times in a
process.
between rx , executing aj , and ry . Finally, we introduce the function δ(x) which
returns x if x ≤ 1, and 1 otherwise. The coll function is defined ! as:
1 X ĥ(ri , r0 , aj )
coll(r, ri , aj ) = · δ . It ranges in [0, 1],
|Gr (aj )| 0 ĥ(r, r0 , aj )
r ∈Gr (aj )∩Gri (aj )
returning 0 when the two resources do not share any collaborations, 1 if ri
interacts with all collaborators of r with the same handover of work. The coll
function is introduced under the assumption that replacing a resource with some-
one acquainted to work in the same team and with similar handover relations is
preferable.
The perf (r, ri , aj ) function compares the time taken by the two resources to
carry out the activity aj . Let tr and tri be the average time respectively taken
by
tr
r and ri to perform aj , the perf function is defined as perf (r, ri , aj ) = δ tri .
The perf function ranges in [0, 1], values close to 0 mean that r is much faster
than ri . When ri is on average faster then r, assigning aj to ri is also better
than having it performed by r, hence the value of perf is set to the maximum.
The average times to perform an activity, if not available in the event log, can
be estimated from the model by considering the difference in time between two
causally related events.
Finally, the exp(r, ri , aj ) function compares the experience of the two re-
sources to perform aj , computed as the number of times the resource has carried
out the activity (qr (aj) and qri (aj ) respectively). The exp function is defined as
q
exp(r, ri , aj ) = δ qrri , where qr0 (aj ) = πq (r0 , rx , aj ). This function
P
rx ∈Gr0 (aj )
ranges in [0, 1]. Values close to 0 mean that the experience of ri is much smaller
than that of r, while the function takes the maximum value when the experience
of ri is greater than or equal to that of r.
Model specification. An Integer Linear Programming (ILP) model is aimed
to select the set of assignments of activities to resources in order to minimize
the total cost of resource replacement.
Given a sociogram G = (R0 , E) and a resource r ∈ R0 to replace, let C =
{ri ∈ R0 : ∃aj ∈ A(ri ) such that aj ∈ T } be the set of candidate resources
having at least one capability equal to one activity in T . Finally, Let |C| and |T |
be equal to k and h respectively.
We introduce the decision variable xij , ∀ri ∈ C and ∀aj ∈ T , equal to 1 if the
resource ri is selected for replacement of r to perform activity aj , 0 otherwise.
P k Ph
The objective function min cij xij represents the total cost of replacing
i=1 j=1
the resource r, taking into account the cost factor cij = 1 − sim(r, ri , aj ). An
additional constraint is set to impose that each activity in T is assigned to only
one resource of C to avoid multiple assignments. Finally, a further constraint
defines the binary nature of the decision variables, according to a 0-1 Integer
Linear Programming model.
4 Discussion and conclusion
In this work we propose a data-driven approach to support resource replacement
in organizations, based on a notion for handover of work that is capable to model
collaboration among resources on the basis of causal relations between activities.
Although we referred mostly to human-centric processes, the approach is general
enough to be applied in cases where a mix of users and machines cooperate
together, provided additional constraints on which resources cannot be selected
for replacement.
We report some preliminary results of an early experimentation done on
the real-world dataset published for the BPI Challenge 2012, referring to an
application process for personal loan. From the log we extracted the conform
subset, including 7974 traces and 47634 events, with an average number of 6
events per trace (from 3 to 41) and belonging to 8 event types (corresponding to
activity names), with 62 resources. We randomly selected a resource and a day
in the last 10 days of the log. The procedure is then repeated for all resources.
The average number of daily activities that needs to be reassigned per resource
is 6.9. On average, in our setting the replace phase took around 6 milliseconds
on average per resource to achieve a solution (with an ILP model including up to
1000 variables). The most demanding phase, on the other hand, is the creation of
the sociogram, which takes 285 seconds for the whole dataset. Further analysis
are not reported here for lack of space and will be deepened in future work. We
also plan to extend the model to take into account further social relations among
resources and the case of organisations that evolve over time [1]. Furthermore,
the average execution time for each activity and the current resource workload
will be considered as they can be exploited to add load-balancing constraints in
the replacement planning.
References
1. Annalisa Appice. Towards mining the organizational structure of a dynamic event
scenario. Journal of Intelligent Information Systems, 50(1):165–193, 2018.
2. Raffaele Conforti, Massimiliano de Leoni, Marcello La Rosa, Wil MP van der Aalst,
and Arthur HM ter Hofstede. A recommendation system for predicting risks across
multiple business process instances. Decision Support Systems, 69:1–19, 2015.
3. Stefan Schönig, Cristina Cabanillas, Stefan Jablonski, and Jan Mendling. A frame-
work for efficiently mining the organisational perspective of business processes. De-
cision Support Systems, 89:87 – 97, 2016.
4. Minseok Song and Wil M.P. van der Aalst. Towards comprehensive support for
organizational mining. Decision Support Systems, 46(1):300 – 317, 2008.
5. Wil MP Van Der Aalst, Hajo A Reijers, and Minseok Song. Discovering social net-
works from event logs. Computer Supported Cooperative Work (CSCW), 14(6):549–
593, 2005.
The experiments run on a 4-core 2.2GHz processor, 16 GB RAM. IBM ILOG CPLEX
API (version 12.9) was used for ILP model solving.