DTIC ADA440392: Congruence of Human Organizations and Missions: Theory versus Data

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Title:
Congruence of Human Organizations and Missions: Theory versus Data*
Student paper: yes

(Sessions on Adaptive Architectures for Command and Control (A2C2))

Authors:
Georgiy M. Levchuk
Aptima Inc.,
12 Gill Street, Suite 1400
Woburn, MA 01801
Fax: [phone]
Phone: [phone]x267
e-mail: [email protected]

David L. Kleinman
Professor, Naval Postgraduate School
589 Dyer Road, Room 200A
Monterrey, CA
Fax: [phone]
Phone: [phone]
e-mail: [email protected]

Sui Ruan
Graduate Student, ECE Dept., UCONN
Storrs, CT
Fax: [phone]
Phone: [phone]
e-mail: [email protected]

Krishna R. Pattipati
Professor, ECE Dept., UCONN
Storrs, CT
Fax: [phone]
Phone: [phone]
e-mail: [email protected]
Correspondence:
Prof. Krishna R. Pattipati
Dept. of ECE, The University of Connecticut
260 Glenbrook Road
Storrs, CT 06269-2157
Phone: [phone]
Fax: [phone]
e-mail: [email protected]

* This work was supported by the Office of Naval Research under contract # N00014-00-1-0101.

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14. ABSTRACT
In this paper, we present a methodology for quantifying the degree of fit between a mission and an
organization based on the closeness between the task structure (i.e., resource requirements and task
interdependence) and the DM-asset allocation across the organization (i.e., amount and distribution of
resource capabilities among DMs, and organizational processes). This closeness is based on three main
characteristics of organizational performance: workload balance, communication requirements, and
DM-DM dependence. These characteristics are affected, in turn, by the interactions and interdependencies
of the organizational processes and the demands of the mission scenario. Invariably, coordination is
essential to achieve good performance because the information required for decisionmaking is often
distributed. However, excessive DM-DM communication and coordination are harmful to performance,
since they increase the processing workload/overhead that delays task execution. Performance
improvements can be obtained by changing the structure and processes of an organization to decrease the
requisite coordination, while balancing the levels of workload across the organization and reducing inter
DM dependence.
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ABSTRACT OF PAGES RESPONSIBLE PERSON

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Standard Form 298 (Rev. 8-98)
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Congruence of Human Organizations and Missions: Theory versus Data*

Georgiy M. Levchuk1,2, David L. Kleinman1,3, Sui Ruan1, and Krishna R. Pattipati1

1University of Connecticut, Dept. of Electrical and Computer Engineering, Storrs, CT 06269
2Aptima, Inc. 12 Gill Street, Suite 1400, Burlington, MA 01801
3Naval Postgraduate School, Information Sciences Dept., 589 Dyer Road, Monterey, CA 93943

ABSTRACT

In this paper, we present a methodology for quantifying the degree of fit between a mission and an
organization based on the closeness between the task structure (i.e., resource requirements and task
interdependence) and the DM-asset allocation across the organization (i.e., amount and distribution
of resource capabilities among DMs, and organizational processes). This closeness is based on
three main characteristics of organizational performance: workload balance, communication
requirements, and DM-DM dependence. These characteristics are affected, in turn, by the
interactions and interdependencies of the organizational processes and the demands of the mission
scenario. Invariably, coordination is essential to achieve good performance because the
information required for decisionmaking is often distributed. However, excessive DM-DM
communication and coordination are harmful to performance, since they increase the processing
workload/overhead that delays task execution. Performance improvements can be obtained by
changing the structure and processes of an organization to decrease the requisite coordination,
while balancing the levels of workload across the organization and reducing inter DM dependence.

in uncertain and dynamic environments, where the effort
1. Introduction*
to achieve dynamic congruence forces organizations to
An organization is said to be congruent with its mission adapt, while they continue to operate [11]. In situations
if its structure and processes are matched to the involving dynamic and uncertain environments, we turn
environmental parameters [1], [10]. The degree of to the concept of structure-based congruence measures.
“match” (“fit”) between an organization and a mission
In this paper, we argue and provide evidence that
can be quantified based on its performance or structure.
structure-based congruence is a multi-dimensional
The concept of performance-based congruence is
concept involving resources, task structure and
relative: the degree to which an organization is
organizational processes (e.g., workload balance). We
congruent to a mission is obtained by comparing its
define structure-based congruence measures by
performance to that of an “optimal” organization for the
evaluating the closeness of task parameters with the
same mission. However, finding this optimal
organizational structure and processes. Based on
organization is computationally prohibitive for real-time
substantial evidence in the management literature [1],
mission monitoring, re-planning and decision support.
[10], [5], and our normative organizational design
On the other hand, human-in-the-loop simulations,
process [8,9] developed as part of the Adaptive
needed for performance evaluation, present a challenge
Architectures for Command and Control (A2C2)
program, we hypothesize that the better an organization
* This work was supported by the Office of Naval Research under is matched to its mission, the better will that
contract # N00014-00-1-0101. organization perform. In order to validate the normative

2
predictions, namely that structure-based congruence The rest of the paper is organized as follows. Section 2
leads to performance-based congruence, we designed describes how we represent missions and organizations.
and conducted a team-in-the-loop A2C2 experiment Section 3 formalizes organizational processes and
using two different organizational structures and two measures for evaluating the degree of congruence.
different missions. The first organizational structure was Section 4 discusses the task execution model to evaluate
to be congruent (matched) with the first mission, but the delays associated with task processing and
highly mismatched (i.e., exhibit low congruence) to the communication. Section 5 distinguishes among the three
second mission. The reverse is true for the second dimensions of congruence: resource, task network, and
organizational structure. The experiment – number 8 on workload balance congruence. Sections 6 & 7 describe
the list of A2C2 empirical milestones – was conducted at the application of our congruence hypotheses in the
NPS in August and November 2002. The objective of design of Experiment 8. Section 8 concludes with the
this experiment was to compare theoretically predicted summary and future extensions.
and experimentally observed measures of congruence
2. Representing Missions and Organizations
between the missions and the organizations. In this
paper, we describe how we reverse synthesized missions 2.1. Tasks and Task Graphs
to generate mismatches with organizations, and how we
A fundamental question underlying a distributed
modeled the specific structural mismatches and matches
organizational design - ‘who should do which part of the
among the corresponding elements of organizations and
mission?’ - implies that the mission must be
missions. The model serves as the basis of our structure-
decomposable into a set of entities. These entities are
based congruence framework.
generally referred to as tasks. A Task is an activity that
In our work, the congruence between an organization entails the use of relevant resources (provided by
and a mission is measured by the structural interaction organization’s assets) and is carried out by an individual
between the organization and its environment. DM or a group of DMs to accomplish the mission
Informally, the incongruence between the organization objectives. Every task in itself represents a “small
and a mission can be perceived as the structural fit mission”, and can oftentimes be further decomposed into
depicted in Fig. 1.1. more elementary tasks.
In our model, we characterize a task T (i =1,...,N ,
i
Mission Mission where N is the number of tasks) by specifying the
following basic attributes:
• Task release time b (time at which the task appears
i
Organization Organization in the mission scenario);
• Task processing time window, tˆ (maximal time
Incongruent Congruent ai

available from the start of task execution to its
Figure 1.1. Informal visualization of (mis)match between a finish; this time window is used to synchronize
mission and an organization assets assigned to this task: it indicates the time
window during which these assets must be “applied”
A congruent organization minimizes the levels of
to execute the task);
workload imbalance, communication requirements, and
DM-DM dependence. Our methodology is based on
• Task processing time t (the interval between the
identifying these three characteristics via a fit of specific i
time the first asset starts executing the task and the
structural parameters of organizations and missions. The
time at which the last asset finishes the task; the task
parameters include:
processing time must not exceed the task processing
• Organization: DM-asset allocation and time window: t ≤tˆ );
i ai
organizational structure (authority and
communication). • Task accuracy α;
i
• Mission: task density, locations, information flow, • Task start time s (corresponding to the time that a
i
task precedence, and resource requirements.
task execution is started, and obtained during
mission execution);
3
• Geographical location of task (x ,y ) in a state As a consequence of decentralization in large-scale
i i
systems, each DM only has access to a portion of
space. The location parameters can be used to
organization’s resources and, possibly, to the
compute the “distance” d between tasks T and T ;
ij i j information available to the team. The distribution of
• Resource requirement vector [R ,R ,...,R ], where resources among DMs and their assignment for task
i1 i2 iL
processing are among the key elements defining an
R is the number of units of resource l required for
il organizational design. Team members must
successful processing of task T (l =1,...,L, where L dynamically coordinate their resources to process their
i
is the number of resource types); individual tasks, while assuring that team performance
goals are met. The critical issues in team resource
• Task value ω (task value reflects the importance of
i allocation are: who should own which resource, who
individual tasks – either on a relative or absolute
should use which resource to do what, and when? An
basis – and is taken as an indicator of the
organization is therefore characterized by DM-asset
commander’s intent or priority; all tasks are not
allocation that provides DMs with resources to execute
equally important).
tasks. The allocation is formally defined by:
A Task Graph is a dependency diagram that details the
 1, if asset P is allocated to DM
following interrelationships among tasks: a =  j m , (2.1)
mj  0, otherwise
• task precedence;
for j =1,...,K , m=1,...,D, where D is the number of
• inter-task information flow; and
DMs in the organization. We assume that each asset is
• input-output relationships between tasks. assigned to a single decision-maker, and cannot be
D
A directed acyclic task-precedence graph represents the shared during the mission: ∑a =1.
mj
plan to execute a mission.
m=1
2.2. Assets 3. Organizational Processes and Measures
An Asset is a physical entity of an organization that 3.1. Mission Execution
provides resource capabilities and is used to process
The critical issues in team task processing are: what
tasks. For each asset P (m =1,...,K , where K is the
m should be done, who should do what, and when? The
number of assets), we define its maximal velocity v processing of a mission by an organization is identified
m
and its resource capability vector [r ,r ,...,r ], where by specifying asset-to-task assignment, and the
m1 m2 mL
corresponding DM-task allocation:
r specifies the number of units of resource type l
ml
available on asset P . Assets must be routed among  1, if asset P is assigned to task T
m y =  j i (3.1)
task locations to execute the assigned tasks. Assets can ij  0, otherwise
begin to process the same task at different times, but
must be synchronized to complete a task in a specified u =1, if DMm is assigned to task Ti
task processing window. For each asset-task pair, the mi 0, otherwise
(3.2)
asset-task engagement time e is specified. 1, if ∃ asset P such that a =1, y =1
m,i = j mj ij
0, otherwise
2.3. Decision-makers and Organizations
The asset-task assignment specifies the necessary
A Decision-maker (DM) is an entity with information-
interaction among assets when processing a task. This
processing, decision-making, and operational
interaction necessitates coordination among DMs that
capabilities that can control the necessary resources to
have ownership of these assets; the DMs serve as
execute mission tasks, provided that such an execution
information/decision/action carriers. Specifically, to
will not violate the concomitant capability thresholds.
model coordination-related overhead in an organization,
An Organization is a team of human decision-makers, we define two types of coordination: internal and
who coordinate their information, resources, and external. Internal coordination accounts for the need to
activities in order to achieve their common goal in a coordinate among assets assigned to the same DM.
complex, dynamic, and uncertain mission environment. External coordination is the inter-DM dependence that
4
results from cooperative processing of a task by multiple may be similar, their performance is distinguished by the
DMs. distribution of this workload among team members. We
define the main performance measure of an organization
3.2. Internal Coordination
as the root-mean-square of workloads of DMs in this
The workload associated with operating an asset must be organization:
determined from the specifics of asset’s operation and its
involvement in task processing. We define an asset Pj’s Θ= 1 ∑D CW2(m) . (3.8)
D
operational workload as the aggregated load of tasks m=1
executed by this asset:
This measure accounts for both the mean and the
N variance of workloads, and, consequently, provides a
w(j)=∑y w , (3.3)
ij ij measure of balance of the aggregated workloads of DMs.
i=1 Given that two organizations O and O have the same
1 2
where w is the workload associated with executing mission completion time or task gain on a mission M,
ij
we say that organization O is more congruent with this
task T using asset P . Here, we assume that w 1
i j ij mission than O , if Θ(O ,M)<Θ(O ,M). That is, the
parameters are known, and, without loss of generality, 2 1 2
better an organization is matched to its mission, the
w =1.
ij better will be its workload balance among the DMs.
The internal coordination workload of a DM is 3.5. Task Accuracy
m
defined as the aggregated workload of operating assets
When all resources required by task T are met, that is
assigned to this DM: i
K
I(m)=∑K a w(j). (3.4) ∑yim⋅rml ≥Ril, (3.9)
mj
m=1
j=1
then the accuracy of task completion is equal to 100%.
3.3. External Coordination
However, in realistic applications where the resources
A direct DM-DM coordination between two decision- are scarce, an organization may wish to reduce the task
makers DM and DM is the aggregated time execution accuracy in order to achieve better timeliness.
m n
In order to accommodate timeliness-accuracy trade-off, a
associated with simultaneous processing of the same set
model of accuracy has been defined within the DDD-III
of tasks:
simulator for scoring the DMs [6] as the average of
N N squared ratios of the resource used to the resource
D(m,n)=∑u u t =∑min(u ,u )⋅t . (3.5)
mi ni i mi ni i required over all resource types:
i=1 i=1
The external coordination workload of a DM is the 1 L Rˆ 2
m α = ∑ il  , (3.10)
sum of its direct coordination with other DMs: i Lˆ R 
 l=1 il 
D
E(m)= ∑D(m,n). (3.6) where Lˆ is the number of non-zero resource requirement
n=1,n≠m types of task T : Lˆ =|{l:R ≠0}|, and Rˆ is the
i il il
3.4. DM Workload and Team Load Balance resources of type l used to process task T :
i
Workload of a DM is defined as a weighted sum of the
m K
internal and external coordination workload of this DM: Rˆ =min{R ,∑y ⋅r }. (3.11)
il il im ml
m=1
CW(m)=WI ⋅I(m)+WE ⋅E(m). (3.7)
The ratio of the resource used to the resource required
identifies the percentage of satisfied resource for the
The weights for internal (WI ) and external (WE)
corresponding resource type. The squaring of this ratio
coordination specify their impact on the aggregated DM
penalizes significant resource allocation mismatches.
workload. While the total aggregated workloads of
organizations with the same mission completion time
5
3.6. Task Latency G(O ,M;t) rising at a faster rate than G(O ,M;t). On
1 2
the other hand, the final values of gain functions for both
The latency of a task T is defined as the time from the
i
organizations might be the same, since the total
appearance of a task to the time when its execution
achievable mission gain is the same for any organization
starts:
N
τi =si −bi (3.12) and equal to Gmax =∑ωi (and it will be achieved in
i=1
The average task latency is given by: case the organization completes all tasks with 100%
accuracy). Hence, the ultimate measure of performance
1 N
τ= ∑τ⋅δ[i], (3.13) of an organization on a mission is the normalized area
N i under the accrued gain function curve for this
i=1
organization (see Fig. 3.1):
where δ[i]=1 if the task has been executed by the
s
organization, and = 0 otherwise. The speed of command 1
A(s)= ∫G(t)dt, s≥0. (3.16)
that can be achieved by the organization is inversely s
related to its task processing latencies. That is, the better 0
an organization is matched to its mission, the smaller nn
will be its task latencies and higher will be its speed of aiai
gg
command. d d TTaasskk ggaaiinn
ee
uu
3.7. Task Gain crcr
cc gain area
AA
In the presence of time-critical tasks, an organization
may trade-off task accuracy versus timeliness. For an ttiimmee
organization that is incongruent with its mission, such
TTaasskk ccoommpplleettiioonn ttiimmeess
engagement practices may result in the same levels of
task timeliness as for a congruent organization. Figure 3.1. Accrued Gain Metric
However, this timeliness is achieved at the cost of lower
We say that organization O with normalized gain area
accuracy. Therefore, a measure that reflects the task 1
( )
AO ,M;T on mission M (where T is the mission
accuracy and timeliness tradeoff can be combined into a 1 f f
single measure, called the task gain. The task gain of a end time – assumed the same for all organizations on the
task T is defined as the accuracy multiplied by its value: tested mission) is more congruent to this mission than
i
organization O with normalized gain area
2
g =α⋅ω. (3.14) ( ) ( ) ( )
i i i A O ,M;T , if AO ,M;T > AO ,M;T . The
2 f 1 f 2 f
In order to visualize the dynamic pattern of total gain
computation of accrued gain and gain area is
achieved by an organization over time, we define the
straightforward. If {i ,i ,...,i } (n≤ N ) is the sequence
accrued task gain G(t) [7] as an aggregate of task gains 1 2 n
of task completions, then f ≤ f ,k =1,...,n−1, where
achieved by time t. We increment the gain function ik ik+1
f =s +t is the time of completion of task T . Hence,
when each task T completes its execution (at time i i i i
i
the accrued gain at time t∈[f , f ) is equal to
s +t ) with a task gain of g . Therefore, the accrued
i i i ik ik+1
task gain is computed as follows: G(t) =G[k], where G[k]=G[k−1]+g , k =1,...,n,
i
k
N and G[0]=0. Therefore, the gain area is computed as
G(t)=∑g ⋅δ[i]⋅U(t−s −t ), (3.15)
i i i follows:
i=1
1 n
1, if x≥0 A(T )= ∑G[k]⋅(f − f )
where U(x)= . Thus, G(t) is a piece- f T ik+1 ik
0, otherwise f k=1 , (3.17)
1 n
wise constant (i.e., stair-case) function as shown in Fig. = ∑g ⋅(T − f )
3.1. An organization O that achieves better task latency T ik f ik
1 f k=1
and higher task accuracy than, say organization O , on
2 where f =T .
mission M is seen as having the accrued gain function in+1 f
6
4. Delay Models required to execute each subtask in the execution chain
of task T :
4.1. Task Execution i
In our simulations, we considered a simplified task (cid:131) ςI - time required to identify the task; this time
i
execution model (Fig. 4.1). Generally speaking, we
depends on the organization’s internal processes,
decompose the problem of task execution into several
locations of information sensors, etc.;
subtasks:
(cid:131) ςA - time required to determine the asset-to-task
1) identification (task must be identified with i
sensor resources available to the organization); allocation;
2) asset allocation (assets must be selected to (cid:131) ςP - time required to send/route the asset P to
i,j j
execute the task);
the task location, including any waiting needed for
3) task prosecution (assets must be synchronized asset synchronization; and
and routed to task location); and
(cid:131) ςE - time to attack the task (ςE =t ) – from the
i i i
4) attack (actual engagement/processing of a task
first asset attack to the last asset-task completion.
by assets).
Therefore, the start time of a task is determined as
I A P E follows:
task Identify task Allocate Prosecute Execute task
appears Platforms (Attack) completed s =b +ςI +ςA + minςP . (4.1)
i i i i i,j
j: yij=1
Figure 4.1. Task execution chain Also, note that task precedence constraints must be
satisfied (that is, task execution cannot start before all its
In this model, identification subtask (I) and allocation
predecessors are completed). The actual processing time
subtask (A) are executed sequentially, while prosecute
of a task is found as follows:
subtask (P) and execute subtask (E) are done in parallel
(in DDD experiments, the latter subtasks involve parallel
 ( )
communication among DMs owning the assets in order ti =mintˆai,bi +ςiI +ςiA −si + maxςiP,j +ej,i (4.2)
 j: y =1 
to synchronize the assets’ time-over-target to complete ij
the task in a specified processing time window). During From now on, we assume that the asset-to-task
the identification subtask (subtask I), the DM allocation variables { y } are such that
ij
responsible for task completion is specified. Efficient
asset-to-task allocation (subtask A) is essential to b +ςI +ςA −s + max(ςP +e )≤tˆ .
i i i i i,j j,i ai
effective mission execution, since it reduces the delay j: y =1
ij
associated with prosecution of the corresponding task
This assumption does not imply that there is no resource
(subtask P). If a single DM, responsible for executing
wastage, but rather that the variables are given according
the task, possesses the assets with the requisite resources
to the actual asset-task processing that occurred during
to complete this task with a high accuracy, the problem
the mission.
of selecting the most efficient asset package to execute a
task can be formulated and solved (note that the actual The subtask time parameters defined above implicitly
problem of resource-task allocation is NP-hard; see affect the values of task start times in human-in-the-loop
[8,9]). However, the problem becomes significantly experiments. In our simulation models, we assume that
more complex when a single DM does not possess the all tasks are identified immediately (ςI =0), and that
i
required resources. In this case, the allocation subtask
the time required to determine the asset-to-task
should be further decomposed into elementary subtasks
allocation is proportional to the number of DMs assigned
that involve asset prioritization, asset request,
to this task, but a single DM can assign the assets
communication, etc. Informally speaking, the
 D 
responsible DM would have to coordinate the actions without any delay, i.e.,ςA =ςA ⋅∑u −1. This
with other DMs, requesting the commitment of their i  mi 
m=1
resources and their direct participation in prosecuting the
implies that ςA can be viewed as the time required for
task. Given the model above, we identify the times i
coordination among DMs to determine the asset-to-task
7
allocation. The parameter ςA can be viewed as In order to normatively address the congruence
hypothesis, we first identify the elementary
coordination delay factor.
dependencies between the characteristics of mission
The routing time ςP depends on the distance traveled scenario and the processes of an organization. To do so,
i,j
we need to identify the features of the mission that create
by an asset and the asset’s velocity, and includes the
an incongruent situation for one organization, and a
time delay for asset synchronization (in our simulations,
congruent one for another. In the rest of this section, we
we assume that all assets assigned to a task must arrive
illustrate the effects of mission/task parameters on the
at the task location and begin its execution at the same
processes of various organizations (congruent and
time).
incongruent ones) using simplified examples. In all of
4.2. Asset Utilization the examples below, we assume that the coordination
The assets typically have diverse operational and delay factor ςA =1, asset-task processing time e =1,
j,i
execution characteristics. For example, a salient feature task processing time window tˆ =1, and task release
of single-hit weapons located on the same platform (e.g., ai
time b =0 (all tasks appear at the beginning of the
a carrier) is the “duty cycle”, which imposes constraints i
on utilization of weapons of this type. Consequently, in mission and are detected immediately, that is, ςI = 0).
i
our model, we specify a “duty cycle” time window ψ
j Hence, task duration is fixed at t =1, and the start time
i
for each asset P . During a duty cycle, no asset of the is found via:
j
same type can be committed from the same platform on
 D 
which asset P resides. s =∑u −1+ minςP . (5.1)
j i  mi  i,j
m=1  j: yij=1
5. Congruence Hypothesis
5.1. Resource Congruence
In order to formalize the effects of structural interactions
In this subsection, we quantify the effects of task-
between an organization and a mission, and to predict
resource requirements on the processes of two distinct
organizational performance, we utilize our 3-phase
organizations.
design methodology [8,9]. The performance of
organization is obtained using the scheduling step (Phase Table 5.I. Example of asset parameters
I) of the design methodology; this step defines the
Resource DM allocation
processes of an organization executing the mission. In Assets Velocity Locations
capabilities Organization A Organization B
the following, we consider the notion of structure-based
P1.1 [1,0] 1 (0,0) 1 1
congruence measure derived from the following P1.2 [1,0] 1 (1,1) 1 2
characteristics of the mission: P2.1 [0,1] 1 (0,0) 2 1
P2.2 [0,1] 1 (1,1) 2 2
o Task-resource requirements;
o Task precedence/dependence; and DM1 DM2 DM1 DM2
o Task load per resource type.
These parameters determine the (mis)match between a P1.1 P2.1 P1.1 P1.2
mission and an organization because they affect the
P1.2 P2.2 P2.1 P2.2
following four primary characteristics of organizational
performance:
Organization A Organization B
■ Accrued task gain;
Figure 5.1. Example of Organizations
■ Workload balance;
Assume that the organization consists of two decision-
■ Communication requirements; and
makers, with two platforms assigned to each (Fig. 5.1).
■ DM-DM dependence. We consider two resource types. Asset parameters
(resource capabilities, velocities, locations, DM-asset
The accrued task gain measure serves as the ultimate
allocation, etc.) are shown in Table 5.I. It is evident that
“congru-o-meter” for assessing the fit of an organization
the resource capabilities of DMs (according to resource
to a mission.
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capabilities of assigned assets) are distinct for the two start times are s =s =2. On the other hand,
1 2
organizations. We define the aggregated resource
Organization B can execute the mission with a lower
capability vector of a DM ,m=1,...,D as accuracy and with the same task latencies as
m
rˆ =[rˆ ,...,rˆ ], where Organization A. Assigning task T1 to asset P1.1
m m1 mL
(resources (1,0)) and task T2 to asset P2.2 (resources
K
rˆ =∑a ⋅r ,l =1,...,L. (5.2) (0,1)), Organization B achieves accuracy of 25% for
ml m,j jl
2
j=1 1
both tasks: α =α =  =.25 (equation (3.10)). The
In Organization A, DM1 has aggregated resource 1 2 2
capability vector of [2,0], while DM2 has aggregated task processing schedules for Organizations A and B are
resource capability vector of [0,2]. Thus, this shown in Fig. 5.2.
organization has DMs with non-overlapping resource Table 5.II. Example S1.A: task parameters
capabilities, and is termed Functional. In such
Tasks Resource requirements value Locations
organizations, the task execution capabilities of DMs are
distinct. The DMs need to have a global view of the T1 [2,0] 1 (0,1)
T2 [0,2] 1 (1,0)
mission in order to execute the mission successfully.
In Organization B, each decision-maker has aggregated Table 5.III. Example S1.A: task-asset-DM allocation;
accuracy 100%
resource capabilities vector equal to [1,1]. This
organization has DMs with maximally overlapping DM allocation
resource capabilities, and is termed Divisional. In this
Task-Asset Allocation Organization A Organization B
type of organizations, each DM has the same task
execution capability as any other DM. Consequently, tasks P1.1 P1.2 P2.1 P2.2 DM1 DM2 DM1 DM2
the mission must be divided into geographical areas, T1 1 1 0 0 1 0 1 1
delineating areas of responsibility for each DM in order T2 0 0 1 1 0 1 1 1
to minimize task execution conflicts.
The accrued gain function is depicted in Fig. 5.3. We can
In the following, we consider two missions that are see that Organization A has a higher gain, and a higher
congruent with each of the organizations, and gain area. The trade-off of accuracy versus timeliness by
significantly incongruent with the other. The desired organization B only decreased the gain measure. Given
mission completion time T is equal to 4 time units, i.e., the DM workload and gain area measures in Table 5.IV,
f
we conclude that the Organization A is more congruent
accrued task gain is measured from 0 to 4 time units
with scenario S1.A than Organization B.
only.
Table 5.IV. Example S1.A: Organizational Measures;
A. Example S1.A: tasks with resource requirements
workload weights WI =WE =1
of the same type
Consider a mission scenario (denoted by S1.A), organization I(m) E(m) CW(m) Θ gain area
consisting of two tasks, with task parameters as in Table
A,100% DM1 2 0 2
5.II. Each task requires the same number of resources 2 4
accuracy DM2 2 0 2
(2), but of different types. It is evident that this scenario
matches the functional Organization A. Indeed, this B,100% DM1 2 2 4
4 2
organization can execute both tasks with 100% accuracy accuracy DM2 2 2 4
without any communication delays by allocating (see
B, 25% DM1 1 0 1
Table 5.III) task T1 to assets P1.1 and P1.2 (and 1 1
therefore to a single decision-maker DM1 in accuracy DM2 1 0 1
organization A), and task T2 to assets P2.1 and P2.2
Table 5.V. Example S1.B: task parameters
(owned by a single decision-maker DM2 in A). The task
start times for Organization A are calculated as Tasks Resource requirements value Locations
s =s =1 (ςA =0; see equation 5.1). Organization B T1 [1,1] 1 (0,1)
1 2 i
T2 [1,1] 1 (1,0)
must have multi-DM task processing to achieve 100%
mission accuracy, with ςA =ςA =1. The resulting task
1 2
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