Military Manpower Planning

Towards Simultaneous Optimization of Statutory and Competence Logics using

Population based Approaches

Oussama Mazari Abdessameud

, Filip Van Utterbeeck

Johan Van Kerckhoven

and Marie-Anne Guerry

Royal Military Academy, Department of Mathematics, Avenue de la Renaissance, Brussels, Belgium

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

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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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

Skill2

150

100

Competence

200

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.

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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

Total

Skill 1

120

710

Skill 2

120

Competence

Training

170

Total

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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