Military Manpower Planning
Towards Simultaneous Optimization of Statutory and Competence Logics using
Population based Approaches
Oussama Mazari Abdessameud
1
, Filip Van Utterbeeck
1
,
Johan Van Kerckhoven
1
and Marie-Anne Guerry
2
1
Royal Military Academy, Department of Mathematics, Avenue de la Renaissance, Brussels, Belgium
2
Vrije Universiteit Brussel, Department of Business Technology and Operations, Brussels, Belgium
Keywords: Military Manpower Planning, Statutory and Competence Logic, Flow Network.
Abstract: Military manpower planning aims to match the required and available staff. Statutory and competence
logics are two linked aspects of the military manpower management. Military manpower management
involves the long term planning with strategic goals, and also the short term human resources management
with operational goals. These two aspects are interdependent; therefore this article proposes a technique to
combine both logics in the same integrated model. A combined model allows the simultaneous optimization
for both logics. In this article we illustrate a model based on flow network. We present integer programming
and goal programming to find optimal solutions.
1 INTRODUCTION
The military organization is assigned a variety of
missions regarding the security of the country. To
ensure these missions, the organization defines a
hierarchic structure of job positions which have to
be fulfilled by soldiers with the right competences.
The military organization has a strict hierarchical
structure and can recruit only at the lowest ranks,
which restricts the recruitment policy; therefore
military manpower planning is of major importance.
In order to meet the organization’s demand over
the following years, human resources managers use
two manpower planning approaches, namely
statutory logic and competence logic. The
competence logic deals with the assignment of
soldiers with the required characteristics to each job
position in order to fulfill the operational goals and
reach the optimal competence manpower
distribution which is defined by specific required
personnel amounts on different job positions
groupings. This usually goes with a short term time
horizon. On the other hand, the statutory logic is
used to estimate the strategic evolution of the
statutory manpower distribution which is personnel
amounts on different ranks, usually over the long
term time horizon. It considers recruitment,
promotion and retirement policies. The strategic
logic goals are attainability and/or maintainability.
Attainability means reaching a targeted statutory
manpower distribution. Maintainability means
keeping this attained distribution and maintaining it
to get a steady state.
However, the two logics are interdependent and
affect each other. The assignment policy related to
competence logic should be adapted to the available
workforce which corresponds to the long term
planning prediction. Furthermore, strategic policies
must be modified if the assignment does not meet
the requirements. We define in this article a
technique to coalesce both logics in an integrated
model, which allows a simultaneous optimization of
the combination of the statutory and the competence
logics. The proposed model gives detailed
information about the impact of new human resource
management policies on the workforce distribution
in the coming years.
2 PROBLEM DESCRIPTION
The military organization has to be always fully
operational and ready. Therefore, it employs military
manpower planning to provide the optimal required
178
Abdessameud, O., Utterbeeck, F., Kerckhoven, J. and Guerry, M-A.
Military Manpower Planning - Towards Simultaneous Optimization of Statutory and Competence Logics using Population based Approaches.
DOI: 10.5220/0006565201780185
In Proceedings of the 7th International Conference on Operations Research and Enterprise Systems (ICORES 2018), pages 178-185
ISBN: 978-989-758-285-1
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
workforce able to fill the actual job positions needed
to accomplish the organization’s missions. The
military organization can recruit only at the lowest
military ranks (Jaquette et al., 1977) (Wang, 2005)
(Hall, 2009) and it has a well-defined and fixed
hierarchical structure which limits the possible
transitions.
In general, soldiers are characterized by a
military rank, an affiliation and individual skills and
competences. Military ranks define the hierarchy
between soldiers. The main role in the organization
is defined by the affiliation, for instance: infantry,
aviation and marine. Each affiliation has some
unique competences. We distinguish two types of
competences: the competence related to the
affiliation (ex: pilot for aviation), we call it basic
skill; and the one not related to any affiliation, which
we call an extra competence (ex: administration).
New recruits follow training to gain the first
basic skill of the affiliation, i.e. each recruited
trainee is assigned to an affiliation and follows basic
courses for a determined skill (Hall, 2015). The
trainee gets a promotion to the first active rank if he
succeeds in the training, which makes him eligible to
occupy a real job in the military organizational
structure.
Promotions are granted after serving for some
years in a certain rank. In order to get a promotion,
many factors are regarded. They can be related to
individual prerequisites as well as the whole
workforce situation. Promotions can be of two types
(Downes, 2015): push promotions depend only on
the individual prerequisites. Second, pull promotions
depend on the individual prerequisites and on the
vacancies available in the following rank, i.e.
fulfilling the required prerequisites of the next rank
does not mean getting the promotion automatically
due to the limitations in number for each rank.
Every job position has responsibilities that
define assigned missions and required knowledge;
thus there is the need to set access conditions to any
job position (Hall, 2009). The defined conditions are
related to the soldier’s rank and prerequisites.
Advanced ranks and job positions require more
trained personnel. Therefore, training is a continuous
task and not limited to new recruits. Moreover, each
job position has a level of priority. These priorities
define which position must be occupied before
others.
For many reasons, military organizations carry
out job transfers by changing soldiers’ job positions.
Each job transfer considers the match between
requirements of the job position and characteristics
of the transferred soldier. Soldiers have some
preferences for career paths, which are sequences of
job positions. Most soldiers would rather follow a
career path requiring their main skill. Although these
preferences are considered in the planning of
transfers, they cannot be always respected due to job
positions which are not on preferred career paths but
the organization needs to fulfill them.
On the whole, the military personnel have low
attrition rates except during basic training. During
basic training, there is a considerable rate of
attrition. This attrition can be voluntary (i.e. trainee
decision), or involuntary (because of health issues,
academic failures).
The main challenge is to model the military
manpower system in a way that permits for human
resource managers to incorporate both strategic and
operational policies. The model should be able to
simulate the effect of different policies on the
manpower distribution on statutory and competence
levels. Moreover, it has to provide an opportunity
for a simultaneous optimization of the solutions for
the statutory logic and the competence logic.
3 RELATED WORKS
Military human resources management consists of
two aspects, statutory logic with strategic goals and
competence logic with operational goals. This
section focuses on appropriate modeling methods for
both logics.
Wang (2005) expressed in his review that
effective military workforce planning means "there
will continue to be sufficient people with the
required competencies to deliver the capability
output required by the Government at affordable
cost". According to Wang, the mainly used
approaches in workforce planning are: Markov chain
models, computer simulation models, optimization
models and supply chain management through
system dynamics.
The statutory logic was mostly approached using
Markov chain models, computer simulation models
and system dynamics. Guerry and De Feyter (2009)
present a review of Markov manpower planning.
They illustrate different applications of Markov
chains in general manpower planning problems. In a
military context, Škulj et al. (2008) tackle statutory
logic problems within the Slovenian armed forces
using Markov chains. The manpower system is
modeled as a Markov chain and the transition matrix
is estimated from data on previous year’s transitions.
Based on available personnel data, Zais and Zhang
(2016) build a Markov model to simulate US army
Military Manpower Planning - Towards Simultaneous Optimization of Statutory and Competence Logics using Population based
Approaches
179
personnel in order to meet the strategic goals. They
exploit the estimated parameters to predict the
individual stay/leave decision using dynamic
programming. The literature review of An et al.
(2007) illustrates the use of system dynamics in
manpower planning for the statutory logic.
Furthermore, optimization models were also used
in the statutory manpower planning. A manpower
system modeling is proposed by Thompson G. L.
(1979) based on transshipment model. This model is
used to compute optimal promotions, retirements
and attrition. The officers’ recruitment problem is
modeled by Henry and Ravindran (2005) with a goal
programming approach.
However, optimization techniques were the main
approaches used for competence logic. Cai et al.
(2013) use a minimum cost flow model to approach
the manpower allocation problem with several
workers doing a set of tasks requiring different
skills. Hall and Fu (2015) classify the military
manpower based on military rank and rank seniority.
They use this classification in a network model.
They employ linear programming to generate an
optimal manpower distribution. A linear weighted
goal programming is used for manpower planning in
the army medical department by Bastian et al.
(2015).
Although the statutory logic and the competence
logic were tackled by these works, the consideration
of interdependency between the two logics was
neglected. Gass S. I. (1991) attempts to consider
both logics at the same time. He uses a classification
based on rank, skill, function and hired time. He
employs a Markov model to tackle the statutory
logic and he approaches competence logic problems
with network flows. However, this work puts a clear
separation between the two logics.
In this article, we merge both logics in the same
integrated model to have a simultaneous simulation
of the two logics at the same time. The simultaneous
representation of the logics permits the optimization
of the solution for both logics. The obtained solution
could be not optimal for any of the logics but it is
optimal for the combination of the two logics. The
presented model provides manpower managers with
a better tool to measure the impact of their policies
on both the statutory and the competence levels.
4 FLOW NETWORK MODEL
AND SOLVING APPROACHES
4.1 Flow Network Model
In order to fulfill the organization’s demand and
requirement, we have to find the optimal workforce
transitions able to direct the manpower distribution
to a steady state of the required distribution. The
required distribution should respect the strategic and
the operational goals of the organization. In previous
studies, the manpower system was modeled using
flow networks for both statutory logic (Thompson,
1979) and competence logic (Cai et al., 2013) (Hall
and Fu, 2015), thus there is an opportunity to
consider the same approach to model both logics at
the same time.
We model the military manpower system as a
flow network. We consider the military manpower
as the flow passing through the network. The
network has nodes representing homogenous
personnel groups and arcs representing the possible
personnel transitions. A homogenous group is a
yearly cluster of personnel having the same
characteristics and occupying job positions sharing
identical requirements or following the same
training. The personnel transitions are recruitment,
promotion, job transfer, towards training and
retirement. Each arc is a possible transition
respecting the eligibility to this represented
transition. Nodes are grouped in layers to form
annual distributions, where each layer represents all
possible groups for one year. These nodes are
transshipment nodes except for the first layer’s
nodes, which are source nodes supplying with the
initial flow representing manpower available in the
organization, and the last layer’s nodes, which are
sink nodes. The arcs are going from one layer to the
other to denote that transitions are performed once
per year. For each layer, we add two special nodes, a
source node and a sink node. The source node
supplies the basic training with new recruits and the
sink node receives the disappearing flow
representing personnel going into retirement. The
arcs coming from the source node and going to the
sink node have limited capacities. The recruitment
flow depends on the organization’s recruitment
capacity and the retirement flow depends on the
policy of the organization and the number it had
recruited.
Training nodes represent a homogenous group
going through the same training to preserve the
characteristics on the trainees. Typically, training
can be followed even at advanced stages of a career,
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180
therefore we find for the same training multiple
training nodes. Training can be for a competence or
a basic skill, as a new knowledge or as improving an
already acquired skill or competence.
The organization’s requirements are expressed
by the need for a certain distribution. We group job
positions based on their requirements which are a
combination of rank and skill/competence. These
groupings appear in the model as sub-groups of
nodes. The flow running to nodes inside one of these
sub-groups represents personnel occupying the
considered job position and having only the required
characteristics or having additional
skill/competences.
In this model, we will consider attrition only for
the basic training as it has a considerable rate
comparing to the other stages of the career which
present a very low rate of attrition. However, the
retirement depends generally on the number of years
spent in the organization. We can determine the
number of retirees each year using initial manpower
data as long as the initial manpower did not fully
retire. For the manpower generated by the model, we
can use the number of recruits each year.
We illustrate a representation of the model using
a virtual simplified example. The example is a
military organization with 910 job positions.
Personnel in this organization can have one of the
three ranks: rank1, rank2 and rank3. This
organization requires two skills (skill1 and skill2)
and one competence. The optimal distribution based
on job positions requirements is illustrated in the
table 1.
In this example, we have two types of
promotions. We onsider the first promotion (rank1
to rank2) as a push promotion and the second one
(rank2 to rank3) as a pull promotion. The first
promotion is acquired after three years of service in
rank1, and the second promotion is possible after
two years of service in rank2. Each soldier is trained
for one and only one skill at the beginning of his
career, and the competence can be trained while in
rank1 or rank2 only. When a soldier is promoted to
rank3, he has to work at least two years, imposing
that promotion to rank3 is granted only for soldiers
who still have at least two years left in their careers.
We consider that a career in this organization lasts
10 years i.e. soldiers go to retirement 10 years after
their recruitment.
Table 1: The optimal competence distribution of the
example.
Rank1
Rank2
Rank3
Skill1
150
100
70
Skill2
150
100
70
Competence
200
70
Total
910
We denote skill1, skill2 and competence
respectively as “S1”, “S2”, and “C”. The modeling
of this organization is shown in figure 1 (for a better
illustration we consider only two years). Figure 2
illustrates the superposition of those layers to see the
possible movements of the manpower. The
requirement sub-groups are marked by dash ellipses.
Note that nodes concerned with pull promotion have
a loop arc to ensure that soldiers who did not get a
promotion can stay on the same job position for the
next year. This loop arc is not available on the nodes
concerned with a push promotion to force the
personnel for the next rank.
Figure 1: Flow network representation of the example.
Military Manpower Planning - Towards Simultaneous Optimization of Statutory and Competence Logics using Population based
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181
Figure 2 : Superposition of the flow network layers.
4.2 Integer Programming Solution
Generally, flow network problems can be solved by
simplex algorithms using linear programming such
as illustrated in (Bazaraa and al., 2009) for
minimum cost flow networks. Our model has human
resources management policies to consider.
Additionally, the problem is not always balanced
(demand and supply are different). Therefore, a
modification of this solution approach is mandatory.
4.2.1 Integer Programming using Two
Virtual Nodes
First, we associate with each arc of the graph a cost
of the flow passing through this arc. This cost
expresses the transition difficulty and desirability for
the organization. Thus we need a human resources
manager to determine the costs. Having defined the
arcs’ costs, the objective function of our integer
program is the total cost of the flows running
through the network that has to be minimized.
In order to solve a flow network problem, the
available flow has to be equal to the demand. This
condition is not always satisfied for the military
organization. Therefore, we use two virtual nodes, a
virtual source node and a virtual sink node, so as to
equilibrate the demand and the available supply.
These virtual nodes, which have infinite capacities,
are connected to all nodes representing homogenous
groups of personnel working in the organization (i.e.
not training nodes). The role of these nodes is to
supply the organization with virtual workforce in
case of personnel lack and to receive the surplus in
case of personnel excess. The use of the virtual
workforce out of these nodes has to be a last
solution, so the costs of the arcs going to a virtual
sink or coming from a virtual source have to be
higher than the costs of all the other arcs.
The costs of the virtual arcs define the relative
severity of having a vacancy or a surplus on a
certain job position. A higher arc cost means that
using this arc is difficult and the vacancy or the
surplus should be pushed to another node with an arc
of lower virtual cost.
Our integer program has the objective to
minimize the total cost of the flows running through
the network, which is subject to some constraints.
Some of the constraints regard only the flow model
we developed and others depend on the
organizations’ policies.
The constraints related to the model are the
initial manpower conditions and the transshipment
conditions. The initial manpower conditions express
that the manpower present on the first layer must
move to the next layer. The transshipment
conditions ensure that the flow arriving to a layer
must leave it, unless it is a disappearing flow
(retirement flow).
The most important constraints concerning the
organizations’ policies are the expressions regarding
the requirements and the retirement. We include
constraints imposing the number of personnel
arriving each year to a subset of nodes equal to the
required demand. Also the number of personnel on
nodes of the same rank should be equal to the
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targeted amount by the organization. If these
constraints cannot be satisfied the solver uses the
virtual node to balance them. The retirement
condition concerns the disappearing flow which
must be equal to the allowed yearly retirement.
Additionally, we consider the recruitment conditions
which depend on the organization’s capacity of
training new recruits.
4.2.2 Integer Programming using Multiple
Virtual Nodes
The approach with two virtual nodes considers a
linear severity of vacancies and surpluses i.e. x
vacancies (surpluses respectively) inside the same
sub-group have the same severity as x times the
severity of one vacancy (surplus respectively) inside
this sub-group. However, this assumption is not
totally coherent with real life applications. In fact, if
the surpluses or vacancies inside the same grouping
reach a certain level, some military organizations
would rather push them to other job positions
groupings which were more important initially. In
order to add this possibility to the model, we use
multiple virtual nodes. The one virtual nodes couple
is replaced with several virtual nodes couples, which
creates severity steps for vacancies and surpluses.
We define for each arc connecting a node to a virtual
node a maximum flow capacity which denotes the
limit of the concerned severity step. Figure 3 shows
how three virtual nodes couples are connected to one
node. The virtual costs imposed on the arcs
determine the order of virtual nodes use. If we set
cost1<cost2 < cost3, then virtual source 1 is the first
virtual node to supply our organization subsequently
we move to virtual source 2 when we reach the
maximum flow capacity of the arc out of virtual
source 1 to supply this node.
Figure 4 illustrates the connection of three virtual
sources to two different nodes. We assume that
node2 represents a more important job position than
node1, therefore, C11 < C12. We consider that this
relative importance is true until a certain defined
limit. This limit is used for the flow capacity of the
arc from virtual source1 to node1. In order to flip the
importance between nodes beyond this limit, we set
C12 < C21. This will push the solver to supply the
organization from virtual source1 towards node2.
We can switch again the importance between the
nodes by defining a maximum flow capacity for the
arc going from virtual source1 to node2 and putting
C21<C22. The same case applies to virtual source3.
For the integer program, we need extra
inequalities to define the flow capacities of the arcs
connected to virtual nodes.
Figure 3 : The connection of three virtual nodes couples to
one node.
Figure 4 : The connection of three virtual sources to two
nodes.
4.3 Goal Programming Solution
The main challenge of the integer programming
solution is to define all the costs which influence the
optimal solution. Another solution approach is the
use of a goal programming approach with different
goals that express the different targets of the
organization. The goal programming approach
defines for every objective a numeric goal, and then
it targets the minimization of the deviations from
these goals (Hillier, 2010).
For our case, some of the constraints are rigid
constraints and cannot be deviated from, for instance
the constraints related to the model. Additionally, we
have other constraints which are soft constraint and
they can be considered as goals for the organization.
The constraints which are considered as rigid ones
are the models’ constraints (initial workforce
conditions, the transshipment conditions) and the
recruitment capacity, because it is impossible for the
organization to afford extra training. On the other
hand, the soft constraints or the goals are the
requirements, both statutory demand and
competence demand. Also, we add to these the goal
Military Manpower Planning - Towards Simultaneous Optimization of Statutory and Competence Logics using Population based
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183
of reducing the undesirable movements.
Each goal constraint generates deviation
variables which are used in the objective function
with different priorities. These priorities have to be
determined by a human resources manager.
4.4 Illustration
To study the different reactions of the model, we
perform simulations. In this article we illustrate a
simulation scenario for the previously defined
example in table 1 using the goal programming
solution. The simulation involves an initial
workforce sized 880 soldiers distributed over the
different ranks and job position of the organization
as illustrated in table 2. The organization has a
defined statutory logic target as shown in table 3 and
a competence logic target as in table 1. We perform
a 30-year simulation in order to see the evolution of
our organization both on the statutory level and the
competence level.
Table 2: Available initial manpower in the organization.
Job Position
Recruit
R1
R2
R3
Total
Skill 1
-
120
75
50
710
Skill 2
-
120
75
50
Competence
-
90
80
50
Training
30
90
50
-
170
Total
30
420
280
150
880
Table 3: Statutory logic demand of the simulated example.
Rank
Rank 1
Rank 2
Rank 3
Demand
390
350
210
Figure 5 shows the statutory view of the obtained
results. The graph illustrates the number of
personnel in each rank through the 30 years of
simulation. The dashed lines represent the targeted
number by the organization. The competence view
of the results is represented in figure 6. It shows for
every year of the simulation the total number of
active personnel (i.e. personnel number on a job
position and not on training). It shows also the
required number of active personnel and the
personnel number on training.
The results show that the model could converge
to a solution where both statutory and competence
logics are satisfied. Figure 5 demonstrates that the
statutory goal is attained after 11 years of
simulation. The required statutory goal is maintained
after that until the end of the simulation which
demonstrates that we have a steady state situation.
As for the competence goal, the total number of
active personnel is met after 7 years of simulation.
However, the fact that the total number is met, does
not guarantee that the optimal competence
distribution is met. Therefore, we illustrate in figure
7 the detailed distribution of the manpower on a
competence level. We present the personnel number
in each requirement. The graph shows that we could
fulfill the competence distribution within 7 years and
keep this optimal distribution until the end of the
simulation.
Figure 5: Statutory view of the obtained results out of the
simulation.
Figure 6: Competence view of the obtained results out of
the simulation.
Figure 7: Detailed competence view of the obtained results
out of the simulation.
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This illustration shows that our model is able to
mimic the manpower behavior on both statutory and
competence levels. It allows us the prediction of the
feasibility of our goals. Having attained and
maintained the statutory objective and fulfilled the
required operational distribution, our goals are
feasible within 11 years.
5 CONCLUSIONS
This article gives a brief description of the military
manpower system and its specificities. It tackles the
problem faced by military human resources
managers to strike the balance between the statutory
and the competence logics when they are modeled
separately. Therefore, we develop a way to model
the military manpower system for both logics
simultaneously. In order to find the optimal solution,
we illustrate the use of mathematical programming
methods, namely integer programming and goal
programming.
The developed model permits the military human
resources managers to study the impact of the used
policies on the strategic level as well as the
operational level. Used in a military human resource
management department, the model gives detailed
plans for the future actions to be taken. The provided
actions are linked to job transfers, promotions, the
yearly recruitment and the retirement policy.
As future works, we will use the developed
model in a real study case scenario in collaboration
with the human resources management department
to have a better idea of the impact of their policies
on the manpower structure in the future.
Furthermore, due to the shortcoming of population
based methods which is the non-consideration of
soldiers’ preferences and satisfaction each soldier
can express, a future modeling approach for the
military manpower system is to consider a fully
entity based model. Such modeling approach allows
the computation and incorporation of individual
attrition probabilities depending on the individual
satisfaction. Entity based model permits the
consideration of additional information about the
manpower, for example age and preferred
geographic region.
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