InfraSmart: A Decision Guidance System for Investment in
Infrastructure Service Networks
Bedor Alyahya and Alexander Brodsky
Department of Computer Science, George Mason University Fairfax, VA 22030, U.S.A.
Service Network, Investment Model, Infrastructure, Optimization, Cost-effective.
Current approaches to infrastructure investment either (1) model the problem in high-level financial terms, but
do not accurately express the underlying system behavior and non-financial performance indicators, or (2) are
hard-wired to infrastructure silos, and do not take into account the complex interaction across these silos. This
paper proposes to bridge the gap by modeling interrelated infrastructures as a hierarchical service network
operating over a time horizon, as well as an extensible repository of infrastructure-specific component models.
The paper reports on formal modeling, the development and an initial experimental study of InfraSmart, a
decision guidance system for investment in interdependent infrastructure service networks.
Capital investment in interrelated infrastructures,
such as manufacturing, supply chain, renewable en-
ergy and smart grid, is vital for accomplishing orga-
nizational or societal long-term goals and enabling
future growth. Infrastructures often require multi-
billion dollar investments which are difficult to re-
verse or liquidate (Migliore and Mccracken, 2001).
Analyzing and making actionable recommenda-
tions on investment in infrastructures is challeng-
ing due to (1) complex interaction among differ-
ent network components such as supply, manufactur-
ing, transportation and energy; (2) trade-offs between
multiple objectives and performance metrics; and, (3)
uncertain patterns of supply and demand of resources.
As outlined by Hsieh and Liu (2004) multi-objectivity
in infrastructure decisions, numerous alternatives and
temporal resource constraints make the problem even
more complicated.
There has been extensive research in modeling
and optimizing the investment in infrastructures, e.g.,
see (Breen et al., 2019; Dey, 2019; Hsieh and Liu,
2004; Manca et al., 2010). However, as we explain
below, these models either (1) express the investment
model in a very generalized way that fails to accu-
rately express the underlying system behavior over
the investment time horizon, or (2) are hard-wired
to a silo domain-specific investment problem, which
does not take into account the often complex inter-
action with interrelated infrastructures across the si-
los. These limitations inhibit the wide-spread adop-
tion and reusability of these models.
The work (Hsieh and Liu, 2004) is an example of
category (1), in which the authors approach the invest-
ment allocation problem as resource scheduling us-
ing genetic algorithms. However, this approach does
not try to model the physical infrastructure systems
and their operational controls which may effect in-
vestment performance indicators.
Modeling techniques around critical interrelated
infrastructure protection and optimal performance un-
der disruption have also been studied, e.g., (Trucco
et al., 2012; Thacker et al., 2017; Zhang and Peeta,
2011). However, this work does not focus on infras-
tructure investment.
Works that attempted to model inter-dependencies
among infrastructure systems were discussed in the
review paper by Ouyang (2014). Among these mod-
els is the network flow, which represents a general
structure that can depict how units are transferred be-
tween different infrastructures. As stated by (Holden
et al., 2013)
”A major advantage of network flow models
is that a single mathematical formulation can
describe flows of commodities in different in-
frastructure systems”.
An initial step in this direction was made in de-
veloping a general financial optimization model by
Alyahya, B. and Brodsky, A.
InfraSmart: A Decision Guidance System for Investment in Infrastructure Service Networks.
DOI: 10.5220/0009398003700380
In Proceedings of the 22nd International Conference on Enterprise Information Systems (ICEIS 2020) - Volume 1, pages 370-380
ISBN: 978-989-758-423-7
2020 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
input:x output:AM(x)
objective function
Figure 1: Service Network Investment AM.
Golden et al. (1979) based on network flows. By
using network flows, the model increases its flex-
ibility on handling input and output data depen-
dencies between interdependent system components,
which makes it very expressive compared to other ap-
proaches. Righetto et al. (2016, 2019) extends the
above work by addressing uncertainty of the model.
However, these models only optimize the financial
management of the cash flow, but do not model un-
derlying network components to enable express non-
financial performance indicators, such as environ-
mental and safety metrics.
There also has been work on optimizing cash
flows in production networks using manually crafted
mathematical programming models. However, these
models are designed to optimize domain-specific
problems, such as water supply (Manca et al., 2010),
supply chain (Dey, 2019; Neiro and Pinto, 2004) and
energy (Home-Ortiz et al., 2019). All of the above
mentioned models are hard-wired to a specific domain
which makes it difficult to generalize and take into
account an often complex interaction among inter-
dependant infrastructures and their components.
The focus of this paper is on overcoming the
aforementioned limitations of investment decisions
made in silos, as opposed to accounting for the syn-
ergistic value of strongly interdependent infrastruc-
tures. More specifically, the contributions of this pa-
per are as follows. First, we develop a formal Analytic
Model (AM) for Service Network (SN) investment
over a time horizon, as well as an extensible repos-
itory of domain-specific component models, initially
including supply, contract manufacturing and trans-
The investment AM expresses, over the time
horizon, (1) financial, environmental and quality-of-
service metrics, and (2) capacity and demand con-
straints, as a function of investment and operation de-
cision variables, such as investment choices and net-
work planning and operational controls. The atomic
model repository is designed to be extensible, so that
additional component models can be added without
the need to modify the SN model or previously de-
fined components. For example, new component
models may include unit manufacturing processes,
elements of supply chain, transportation and logis-
tics, and power network components from generation
to transmission and distribution to renewable energy
sources and power storage. The SN investment AM
leverages our previous work on modeling the opera-
tion of (but not investment in) manufacturing service
networks (Brodsky et al., 2019; Brodsky et al., 2017;
Brodsky and Wang, 2008).
Second, we develop InfraSmart, a Decision Guid-
ance System (DGS) to enable stakeholders to de-
rive actionable recommendations on inter-dependent
SNs investment, based on optimization of perfor-
mance metrics under the assumption of optimal op-
eration controls. To develop InfraSmart, we im-
plement the formalized AM using Decision Guid-
ance Analytics Language (DGAL) (Brodsky and Luo,
2015), and perform optimization and analysis us-
ing Unity Decision Guidance Management System
(Unity DGMS) (Nachawati et al., 2017; Brodsky
and Wang, 2008). The technical uniqueness of In-
fraSmart lies in modularity and composability of
simulation-like AMs, yet without manually crafting
mathematical programming (MP) models, which are
instead machine-generated. This results in order-of-
magnitude productivity gain, as well as quality of re-
sults and computational efficiency of the best avail-
able MP algorithms, which significantly outperform
simulation black-box-based algorithms.
Third, we demonstrate the use of InfraSmart and
its methodology by providing an example of a ser-
vice network comprised of suppliers, transportation
providers, and Tier 1 and 2 manufacturers. Finally,
we conduct an initial experimental study on four prob-
lem instances of various computational complexity in
terms of a number of atomic services and added com-
binatorial constraints. The initial results demonstrate
computational feasibility of InfraSmart, at least on the
tested examples, although more experimentation will
be needed for different types and sizes of service net-
works and components.
The paper is organized as follows. Section 2 il-
lustrates how the investment model works by using
a simple supply chain example; Section 3 formalizes
the investment model; Section 4 gives an overview
of the InfraSmart architecture and methodology; and,
Section 5 discusses the results of an initial experimen-
tal study. Finally, Section 6 presents concluding re-
InfraSmart: A Decision Guidance System for Investment in Infrastructure Service Networks
marks and briefly outlines directions for future work.
The purpose of the investment model is not to rep-
resent the domain-specific optimization problem di-
rectly, but instead to represent it using a general
investment analytic model (AM), as shown in Fig-
ure 1. This AM uses a generic input structure that
describes the domain-specific problem and defines the
controlled parameters that need to be optimized. Us-
ing this input, the investment AM produces an output
that contains (1) aggregated periodical performance
metrics that are used to define the objective function
of the optimization problem and (2) feasibility that
serves as optimization constraints. This separation al-
lows the AM to be reused to optimize other invest-
ment problems.
To demonstrate how the investment model works,
we use a simple supply chain example that depicts, as
in Figure 2, the delivery of raw materials from suppli-
ers to manufacturing facilities through transportation
lines. To manufacture the final products, Tier 2 facil-
ities rely on supplying parts from Tier 1 facilities. As
can be observed in Figure 2, there are multiple deci-
sion paths in which these products can be produced
to meet the periodical demand. Some of these paths
require investing in infrastructures. In this example,
we consider transportation line 2 and manufacturing
facilities A2 and B2 to be investment opportunities.
To analyze if it is worthwhile to invest in these in-
frastructures, the investment model should optimize
performance metrics, such as cost, through these in-
vestment and operational decisions over a given time
horizon. To enable the investment model to aggre-
gate the performance metrics generated by these in-
frastructures over time, we use a generic structure
called a service network (SN). The SN, as described in
(Brodsky et al., 2017), represents a hierarchy of ser-
vices that are linked together to depict flow of com-
modity over the network. The services at the bottom
of the hierarchy, called atomic services, represent in-
frastructures that are either owned by the organiza-
tion or considered to be an investment opportunity. In
our example, the dotted boxes (e.g., combined sup-
ply) represent composite services which contain two
or more nested services. Within a composite service,
each nested service can be either composite (e.g., Tier
1 in combined manufacturer) or atomic (e.g., Supplier
1 and 2 in combined supplier). For each atomic ser-
vice, the SN defines the initial status of these infras-
tructures as well as other fixed and controlled param-
eters that are needed to define the capacity and de-
mand constraints and calculate the performance met-
rices. Also, each arrow in the figure represents the
flow of items through these infrastructures to produce
certain products.
The investment analytic model (AM) uses an in-
put structure that contain of (1) temporal parameters
that allow the user to define the time horizon in which
these investments are evaluated; (2) Service Network
which describes how these infrastructures are linked
together as well as the status of these infrastructures;
and, (3) repository of atomic analytic models (AMs)
that define how each infrastructure type generated its
performance metrics as well as the feasibility con-
straints at the infrastructure level (eg,. The level of
inventory in the supplier).
The proposed model uses this input to optimize
financial metrics that are generated bottom-up by in-
voking for each infrastructure the corresponding an-
alytic model type. This model type calculates some
financial metrics and determines feasibility to satisfy
periodical demands at both the network level and the
infrastructure level. The analytic model also updates
the state of some infrastructures that are needed to cal-
culate the next period performance metrics and con-
straints. For example, the supplier analytic model rep-
resents how Supplier 1 and 2 (1) calculated the sup-
plying cost as a function of item quantity and; (2)gen-
erated a new state reflecting the inventory reduction
after pulling items at a given period; and, (3) defines
whether it can provide this quantity, given the avail-
able supplier stock at a certain point in time. In the
next section, we formally define the service network
investment model (SNIM).
3.1 High-level Optimization Problem
As mentioned in section 2, the optimization model for
Service Network Investment is based on the concept
of the analytic performance model (AM), which de-
scribes the performance metrics such as net present
value (NPV) and internal rate of return (IRR) as well
as feasibility as a function of fixed and controlled per-
To formalize AM, the following notations are used
for the Service Network Investment Model (SNIM):
d A valid input instance to SNAM, which
contains fixed and controlled parameters.
DD The set of all valid inputs d.
ICEIS 2020 - 22nd International Conference on Enterprise Information Systems
Root Service
Combined TransportionCombined suppler
Combined Manufacturer
supplier 1
supplier 2
transport 1
transport 2
tier 1 tier 2
raw material 1
raw material 2
raw material 2
raw material 1
part 2
part 1
product 1
product 2
Figure 2: Service Network.
cd A valid output from the SNAM, which
contains performance metrics and feasi-
CD The set of all valid outputs cd.
D DD The set of all input alternatives, to be con-
sidered for optimization.
The analytic performance model AM (formalized in
Appendix A ) is a function:
AM : DD CD (1)
which forms a valid output cd CD of performance
metrics, such as NPV and IRR, from a valid input
d D of fixed and controlled investment parameters.
In the context of a particular investment optimiza-
tion, we assume as given in (2) an objective function,
which gives the real objective value in R given a valid
output of the AM.
Ob j : CD R (2)
Also, we assume C given a boolean constraint func-
C : CD {T, F} (3)
which gives True or False given a valid output cd
CD. Then, the investment optimization problem
x D
ob j(AM(x))
s.t. C(AM(x))
The reason we describe the objective and constraints
using the analytic model AM, as opposed to describ-
ing them directly from x D is modularity and flexi-
bility, so that some AM can be used to formulate mul-
tiple investment related optimization problems. Now
we need to describe all of the components above more
formally, starting with a valid service network invest-
ment model output instance cd in section 3.2, fol-
lowed by the input instance d in section 3.3, and fi-
nally, we describe the analytic model which is a func-
tion that computes an output instance from the input
instance in APPENDIX A.
3.2 Service Network Investment
Instance: The Model Output
A valid SN investment output instance cd is a tuple
hconfig, services, rootServiceID i
config is a tuple
hunitInterval, interestRate, noPeriods,
unitInterval represents the unit of temporal se-
quence (e.g. day); interestRate represents the
zero-risk investment rate for net present value cal-
culation; noPeriods is the number of periods, so
that investment decisions can be made over a set
of all of periods, P = {1, . . . , noPeriods}, in the
time horizon; periodDuration is a function
periodDuration : P Z
which gives the duration (in unitInterval, such as
days) for every period p P.
services is a set of services {s
. . . s
}, where each
service s is either a composite or an atomic ser-
vice instance. We begin describing common ele-
ments of these services in section 3.2.1 ; then in
sections 3.2.2 and 3.2.3, we describe the rest that
are unique for each service.
rootService is the id of a service in services des-
ignated as a root service.
InfraSmart: A Decision Guidance System for Investment in Infrastructure Service Networks
3.2.1 Common Service Instance
A common service instance is a tuple:
h id, type, inFlow, outFlow, metrics,
constraints i.
id S is a unique identifier of a service, where S
is the set of all service ids.
type is either composite or one of the specific
available atomic services (such as supplier, man-
ufacturer) described in section 2.
inFlow is a tuple:
h flowIDs, qtyPP ,totalQty i
flowIDs is a set of inflow unique identifiers.
qtyPP: P× flowIDs N , is a function that
gives the quantity of flow fidflowIDs in period
p P, where N , is a numerical domain (either
real numbers R or integers Z)
totalQty: flowIDs N , is a function that
aggregates all quantities of flow fidflowIDs
over all periods.
outFlow is a tuple that follows the same pattern as
in inFlow to describe the outFlows of a service.
metrics: is a tuple
h costPP, totalCost, NPVPP,
totalNPV , cashFlow i
costPP: P R
, is a function that gives the
cost of running this service at period p P.
totalCost: is the aggregated cost over all peri-
NPVPP: P R , is a function that gives the
net present value of cash flows at period p P.
totalNPV: S R , is the total NPV over all
cashFlow:{ f irstPay, . . . , lastPay} R,
is a function which gives the amount
of payment for every pay interval
i { f irstPay, . . . , lastPay}, where
{ f irstPay, . . . , lastPay} is the set of all
time intervals (e.g. days) with non-zero cash
flows. Note that negative payment means cash
constraints: true if the constraints of service in-
vestment are satisfied, and false otherwise (see
section A).
3.2.2 Composite Service Instance
A composite service instance is a tuple of the form
h . . . , subServices i.
. . . are composed of the common service instance
components (see section 3.2.1) and subServices is a
set {id
. . . id
} S , which defines the sub-service
ids of this composite service.
3.2.3 Atomic Service Instance
An atomic service instance is a tuple of the form
h . . . , onFlag, invested, investedAmt,
[State] i.
. . . are composed of the common service instance
components (see section 3.2.1).
onFlag: P {0, 1}, is a boolean function that
gives, for every period p P, ”1” if the service is
running (ON) and ”0” otherwise.
invested: P {0, 1}, is a boolean function that
gives, for every period p P, ”1” if investment
occurs at period p, and ”0” otherwise. By stating
that the investment ”occurs” at period p, we mean
that the service being invested in becomes avail-
able at the beginning of period p.
investedAmt: is the amount of the investment.
Some atomic services may have an optional element:
state: P dom(type), is a function that describes
the temporal state of atomic service type in pe-
riod p P, where dom(type) is the domain of this
atomic service type.
In the next section, we describe a valid input model
for the investment analytic model which contains
fixed and controlled investment parameters, necessary
to compute the output instance.
3.3 Service Network Investment
Instance: The Model Input
A valid SN investment input instance d is a tuple
h config, domainSpecific,
inputServices, rootServiceID i
config, rootServiceID: are defined previously in
the model output (section 3.3)
domainSpecific: defines shared elements that
are needed for a domain specific atomic analytic
model calculation.
ICEIS 2020 - 22nd International Conference on Enterprise Information Systems
graphical user interface (GUI)
Atomic models
   supplier
   transportation
   manufacturer
   ...
 Composite models
     SN investment
     ...
Analytics Engine:
input output
Figure 3: Decision Guidance System Architecture.
inputServices: is a set of service input instances,
where each service in model input follows the
same structure as in the model output. In the fol-
lowing, we only describe differences.
Atomic or Composite Service:
The service does not have metrics and constraints.
Every inFlow and outFlow is tuple
h flowIDs, lbPerPeriod,ubPerPeriod i
flowIDs: is a set of flow unique identifiers.
lbPP: P× flowIDs N is a function that rep-
resents the lower bound of a given flowIDs for
a given period p P.
ubPP: P× flowIDs N is a function that rep-
resents the upper bound of a given flowIDs for
a given period p P.
Atomic Service:
investedAmt: is replaced by investAmt which de-
fined as:
investAmt: P R
, is a function that gives a con-
ditional investment amount which depends on the
period p P in which the investment occurs.
additional elements are needed:
initAvailable: is a binary value {0,1} : ”1” if
the investment is made and the service is avail-
able at the beginning of the first period, and ”0”
typeSpecific: defines parameters that are
needed for a specific atomic-type analytic
model calculation.
[initState]: defines the initial state of this
atomic service type.
The user can determine the investment controlled pa-
rameters in the model input by annotating (1) the in-
vested at each infrastructure (i.e., atomic service) that
can be considered as an investment opportunity and
which periods P to look at in the time horizon.
(2) the onFlag and other domain specific parameters,
such as quantities of flow, that define how the services
network can ideally operate while these investments
take place.
A decision guidance system (DGS) is a system that
provides recommendations to guide its users in mak-
ing better decisions. Typical decision guidance sys-
tems are designed to solve domain-specific problems.
Therefore, building such systems requires major ef-
forts in modeling, designing and developing tightly
integrated components which discourage any attempt
to reuse or even to extend these systems to solve other
problems (Brodsky and Wang, 2008).
A different distinctive approach in building DGS
was proposed in (2008) and developed in (Nachawati
InfraSmart: A Decision Guidance System for Investment in Infrastructure Service Networks
Figure 4: CPLEX solution progress.
et al., 2017). The key idea is to build a decision guid-
ance management system (DGMS) that aids the user
in executing different analytical tasks using a repos-
itory of reusable, modular and composable models.
This architecture also provides an analytics language
that hides the complexity in dealing with external
tools to perform a variety of different tasks, such as
simulation, optimization and learning (Brodsky and
Luo, 2015).
In this paper, we develop InfraSmart - a decision
guidance investment system based on DGMS. The
architecture of this system is depicted in Figure 3.
The middleware contains the decision guidance man-
agement system (DGMS) which in turn consists of
a reusable, extensible and modular model repository
as well as the analytics engine that symbolically exe-
cutes and reduces the analytic models to perform an-
alytical tasks. These tasks may require a variety of
external tools that support the optimization and trade-
off analysis as shown in the bottom of figure 3. The
graphical user interface (GUI) in the top of the figure
aids to the decision maker in creating and combining
atomic models with the SN investment model, which
is located in the repository to perform analytical tasks
to solve the domain-specific problem.
We demonstrate how the user interacts with In-
fraSmart to solve a domain-specific problem as fol-
1. The user interacts with the GUI to create model
input that defines the domain-specific problem
through combining the atomic models in the
2. The user annotates the controlled parameters in
the model input that need to be optimized.
3. The user configures temporal and financial param-
eters that are needed to run the investment model.
4. The user defines the financial metric that needs to
be optimized.
5. The user runs the investment model to produce the
optimal investment and operational setting based
on the metrics defined in the previous step.
6. By instantiating the annotated controlled parame-
ters, the system provides a recommendation that
aids the user in determining which infrastructures
to invest in, as well as when these investment must
7. The user can adjust the input to compare different
investment alternatives.
For the purposes of evaluating InfraSmart, we con-
ducted an experiment that aimed to assess the fea-
sibility of this system in handling large-scale prob-
lems. We coded the SN investment model as well as
the atomic analytic models described in section A.4
using Unity Decision Guidance Management System
(DGMS). The experimentation was performed on a
machine with a 1.8 GHz Intel Core i5 processor and
ICEIS 2020 - 22nd International Conference on Enterprise Information Systems
8 GB of DDR3 memory executed at 1600 MHz. We
used CPLEX 12 as an optimization tool.
We generated four different instances of the sup-
ply chain example in section 2 by adjusting the num-
ber of periods in the time horizon, varying the num-
ber of atomic services, and altering the level of con-
straints in each problem. Table 1 summarizes the
main parameters we used to generate each problem.
For each instance as shown in Figure 4, we track the
progress of the solver while converging to the optimal
The first instance uses 48 atomic services, has 24
periods in the planning horizon, and is constrained by
periodical demand of the final products and the flow
of items along the supply chain. The first feasible
solution for this problem was found after 4 seconds
within the convergence bound of 0.01% and the opti-
mal solution was identified after 36 seconds.
By restricting the total number of suppliers and
transportation lines to deal with to 50% over the time
horizon, we created combinatorial constraints
that were added to the first instance to create the sec-
ond. By adding these constraints, the time it took the
solver to find the first feasible solution increased to 22
seconds within the convergence bound of 4.25% and
the optimal solution was found after 2.8 minutes.
The third instance uses 104 atomic services, has 8
periods in the planning horizon and is constrained by
periodical demand of the final products. The first fea-
sible solution for was found after 38 seconds within
the convergence bound of 27.62% and the optimal so-
lution was found after 3 minutes.
The last problem was generated by adding addi-
tional combinatorial constraints to the third problem.
The first feasible solution was found at 12 seconds
with a proven gap of 99.96%. After 2.8 minutes, the
gap had been reduced to 20%. After that the solution
gradually improved until it reached the optimal solu-
tion at 4 hours and 40 minutes.
We can see that all problems converged optimally
and all solutions except the last converged within sec-
onds to a near optimal solution. As an initial step, the
results look promising for solving realistic investment
We present in this paper a new generic infrastruc-
ture investment model that is based on reusable an-
alytic models. We described the model using a sim-
ple supply example where the model extracts and op-
timizes the domain-specific metrics to solve the in-
vestment problem. We also developed InfraSmart,
Table 1: Sample Dataset.
of binary
8 104 1664 low
8 104 1664 high
24 48 2304 low
24 48 2304 high
a Decision Guidance System (DGS) that helped the
investors meet their specified investment goals. The
initial experiment shows a promising result that the
model can be used to solve realistically-sized plan-
ning problems. Further work needs to be done in
extending the investment model and expanding the
repository by building more atomic analytic models
for complex infrastructures.
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A Analytic Model (AM)
A.1 Basic Notation
In this section, we use the following notations to for-
malize AM:
S a set of service ids in the inputSer-
vices model input.
C S S a set of composite service ids.
AS S a set of atomic service ids.
SAS S a set of atomic service ids with
inFIds(s) a set of infow ids for service s S .
outFIds(s) a set of outfow ids for service s
sub(s) a set of subService ids for service
s C S .
onFlag(s, p) is the onFlag(p) for a service with
id s AS for period p P, which
gives ”1” if the service is running
(ON) and ”0” otherwise. (see sec-
tion 3.2.3).
invested(s, p) is the invested(p) for a service with
id s AS for period p P, which
gives ”1” if investment occurs and
”0” otherwise. (see section 3.2.3).
investAmt(s, p) is the amount required to invest in
a service with id s AS in period
p P.
investedAmt(s) is the invested amount for a ser-
vice with id s AS .
lb(s, p, f ) is a lower bound lb of a service
with id s S for period p P and
flow id f inFIDs(s).
ub(s, p, f ) is an upper bound ub of a service
with id s S for period p P and
flow id f inFIDs(s).
inQtyPP(s, p, f ) is an inFlow quantity per period
(qtyPP) for a service with id s S ,
for period p P and flow id f
outQtyPP(s, p, f ) is an outFlow quantity per period
(qtyPP) for a service with id s S ,
for period p P and flow id f
totalQty(s, f ) is the total quantity (totalQty) for
inFlow with flow id f inFIDs(s)
or outFlow with flow id f
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outFIDs(s) of a service with id
s S.
costPP(s, p) is a cost per period costPP of a ser-
vice with id s S and for period
p P.
totalCost(s) is a total cost totalCost of a ser-
vice with id s S.
NPV PP(s, p) is a NPV per period NPV PP of a
service with id s S and for period
p P.
totalNPV (s) is a total NPV totalNPV of a ser-
vice with id s S.
cashFlow(i, s, p) is the amount of payment
(cashFlow) for pay interval
i { f irstPay, . . . , lastPay} of
a service with id s S and for
period p P.
constraints(s, p) true if the constraints of a service
with id s S and for period p P
are satisfied, and false otherwise.
state(s, p) is the state of a service with id s
AS at period p P.
initAvailable(s) ”1” if the investment is made and
the service is available at the be-
ginning of the first period of a ser-
vice with id s AS .
A.2 Computation for Composite and Generic
Atomic Services
Some of the notations above are associated with the
model input while others are associated with the
model output. We first describe how the ones that are
associated with output notation are computed from
those associated with model input. For composite
service, inQtyPP(s, p, f ) for s C S , p P and
f inFIds(s) is expressed, recursively as:
inQtyPP(s, p, f ) =
outQtyPP(s0, p, f ) inQtyPP(s0, p, f )
Similarly, outQtyPP(s, p, f ) for s C S , p P and
f outFIds(s) is expressed as:
outQtyPP(s, p, f ) =
inQtyPP(s0, p, f ) outQtyPP(s0, p, f )
For atomic service, inQtyPP(s, p, f ) and
outQtyPP(s, p, f ) are domain-specific. Section A.4
describes how some atomic analytical models (AMs)
formulate the input and output quantities.
Then, the totalQty(s,f) for s S, and
f (inFIds(s) inFIds(s)) is expressed as:
totalQty(s, f ) =
inQtyPP(s, p, f ),
if f
outQtyPP(s, p, f ),
if f
The metrics costPP(s, p) and npvPP(s, p) for
s C S and p P are expressed as:
costPP(s, p) =
costPP(s0, p)
npvPP(s, p) =
NPV PP(x, p)
Therefore, the totalCost(s) and totalNPV(s) for
s S are expressed as:
totalCost(s) =
costPP(s, p)
totalNPV (s) =
npvPP(s, p)
The cashFlow(i,s,p) for i { f irstPay, lastPay},s
C S) and p P is expressed recursively as:
cashFlow(i, s, p) =
cashFlow(i, s0, p)
For every composite service s C S and for ev-
ery period p P, the constraints(s,p) is expressed
as a conjunction of demandConstraint(s,p), bound-
Constraint(s,p) and subServiceConstraints(s,p). Each
constraint is expressed recursively as follows:
demandConstraint(s, p)
(s0 sub(s))
( f [inFIds(s0) outFIds(s0)
(inFIds(s) outFIds(s))])
inQtyPP(s0, p, f ) > outQtyPP(s0, p, f )
boundConstraint(s, p)
( f (inFIds(s) outFIds(s))
lb(s, p, f ) 6 inQtyPP(s, p, f ) 6 ub(s, p, f )
subServiceConstraints(s, p)
(s0 sub(s)) constraints(s0, p)
For every atomic service s AS and for every period
p P, the constraints(s,p) is expressed as a conjunc-
tion of boundConstraint(s,p), qtyConstraint(s,p), on-
FlagConstraint(s,p) and investedConstraint(s). The
InfraSmart: A Decision Guidance System for Investment in Infrastructure Service Networks
boundConstrant(s,p) is expressed as in the compos-
ite service boundConstrant(s,p) and the others is ex-
pressed as follows:
qtyConstraint(s, p)
( f inFIds(s))
(onFlag(s, p) = 0) (outQtyPP(s, p, f ) = 0)
onFlagConstraint(s, p)
onFlag(s, p) 6 initAvailable(s)+
p0∈{1... p}
invested(s, p0)
investedConstraint(s, p)
0 6 initAvailable(s) +
invested(s, p) 6 1
The investedAmt(s) for s AS is expressed as:
investedAmt(s) =
investAmt(s, p) invested(s, p)
The state(s,p) for s S AS and p P is expressed
state(s, p) =
newState(s, p, state(s, p 1)) if p > 1
initState if p = 0
where newState is a function that returns the new state
from a given state for a service with id s SAS , and
period p P.
A.3 Computation of Output from Input
To formalize the analytic model AM : DD CD,
where DD is the set of all valid inputs d and CD is
the set of all valid outputs cd, we need to describe
how a valid input instance cd CD is computed from
a valid output d DD .
cd = AM(d) = hconfig, services, rootServiceID i
where config and rootServiceID are taken from the in-
put d, and each service srv Services is computed as
follows. For composite service:
srv = h id, type, inFlow, outFlow, metrics,
constraints, subServices i
where id, type and subServices are taken from the
services in the inputServices. The inFlow,outFlow
and constraints are computed using the expressions
in section A.2. For atomic service:
srv = h id, type, inFlow, outFlow, metrics,
constraints, onFlag, invested, investedAmt, [state] i
where id, type, onFlag, outFlow and invested are
taken from the atomic services in the inputServices.
The investedAmt, constraints, and state are computed
using the expressions in sectionA.2. The other el-
ements are calculated by invoking the AM of the
atomic service type which can be found in the repos-
itory of atomic analytic models as described in sec-
tion 4.
A.4 Atomic Models Formulation
So far we have created three analytic models (AMs):
supplier, transportation and manufacturer. Due to
page limitation the formalization of the atomic ana-
lytic models (AMs) are omitted here.
We briefly describe how each atomic service s
AS that belong to these AM types produces in ev-
ery given period p P its performance metrics using
these atomic AMs.
The supplier AM generates no inFlows but for ev-
ery flowID in the supplier atomic service, the AM
simply takes the outflow quantity given in typeSpecific
elements under the same service in inputServices. By
knowing the inFlow quantity from each raw material,
the cost and NPV per period can be calculated us-
ing the cost per item of each flowID defined in the
typeSpecific and the interestRate located in the con-
fig in the input model. The supplier analytic model
also generate a newState that basically update atomic
service inventory level after pulling some items.
In the transportation AM, the inflow and the out-
flow quantities are calculated using the orders that
define the source, destination and the quantity from
each row material. Some general information that
are needed for calculating the cost, such as the dis-
tances between the suppliers and manufacturing fa-
cility as well as items’ weight are shared globally in
The manufacturer AM computes the inFlow quan-
tities for each item (raw material or part) from the
quantity of each outflow given in typeSpecific and the
number of units needed from each inflow to produce
one unit of each outflow. The cost is computed by us-
ing the quantity and the price per unit given in model
The cash flow for all these AMs is calculated us-
ing the cost payment due and the investment payment
due located in atomic service under the typeSpecific.
These values represent intervals(e.g., day) relative to
the beginning of the periods where the cost and the in-
vestment are due. For example, 2 means that it is due
on the second day of the period, while -3 means that
it is due 3 days before the beginning of the period.
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