Additive Manufacturing Impacts on a Two-Level Supply Chain

Abstract

Additive Manufacturing (AM) is a recent and rapidly developing technology, which has brought about significant disruptions in manufacturing arena. To capture the full spectrum of changes resulting from AM’s introduction into industry, it is not sufficient to look at it just as a disruptive set of technologies but, rather, take a system’s approach. It must be noted that the investigation of AM’s impacts cannot be limited to an individual actor, but should encompass the whole supply chain to fully consider relevant changes in strategic as well as tactical decision-making and operations. This paper presents an analytic approach based on Joint Economic Lot Sizing (JELS) model, and aims at capturing the most significant impacts resulting from the implementation of AM concept on a two-level supply chain. This assessment of AM from inventory and logistics standpoints is targeted at providing insights into how manufacturers could adapt their supply chains’ planning to accommodate new paradigms introduced by AM. A numerical example followed by sensitivity analysis of a real industrial case study is presented to provide evidence for the main findings and further generalize them.

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Additive manufacturing impacts on a two-level
supply chain
Milad Ashour Pour, Simone Zanoni, Andrea Bacchetti, Massimo Zanardini &
Marco Perona
To cite this article: Milad Ashour Pour, Simone Zanoni, Andrea Bacchetti, Massimo Zanardini &
Marco Perona (2017): Additive manufacturing impacts on a two-level supply chain, International
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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS, 
https://doi.org/./..
Additive manufacturing impacts on a two-level supply chain
Milad Ashour Pour, Simone Zanoni, Andrea Bacchetti, Massimo Zanardini and Marco Perona
Department of Mechanical and Industrial Engineering, University of Brescia, Brescia, Italy
ARTICLE HISTORY
Received  January 
Accepted  May 
KEYWORDS
Additive manufacturing;
traditional manufacturing;
supply chain management;
joint economic lot sizing
ABSTRACT
Additive Manufacturing (AM) is a recent and rapidly developing technology, which has brought about
signicant disruptions in the manufacturing arena. To capture the full spectrum of changes resulting
from AM’s introduction into the industry, it is not sucient to look at it just as a disruptive set of
technologies but, rather, take a system’s approach. It must be noted that the investigation of AM’s
impacts cannot be limited to an individual actor, but should encompass the whole supply chain to
fully consider the relevant changes in strategic as well as tactical decision-making and operations.
This paper presents an analytic approach based on Joint Economic Lot Sizing model, and aims at
capturing the most signicant impacts resulting from the implementation of the AM concept on a
two-level supply chain. This assessment of AM from inventory and logistics standpoints is targeted at
providing insights into how manufacturers could adapt their supply chains’ planning to accommo-
date new paradigms introduced by AM. A numerical example followed by sensitivity analysis of a real
industrial case study is presented to provide evidence for the main ndings and further generalise
them.
1. Introduction
Additive Manufacturing (AM) technologies have been
around in the industry for almost 30 years, and there
are a proliferating number of academic researches that
build upon the industrial appeals of AM. However, most
of them focus on the technological aspects, without pro-
viding insights about AM’s economic and managerial fea-
sibility. Consequently, the status quo on the acceptance
level of this set of technologies and their penetration rate
are still at a challenging level.
Most of the literature developed in the past 20 years
concerningAMfocusesonthisnewparadigm’sgen-
eral principles: according to Costabile, Fera, Fruggiero,
Lambiase, and Pham (2016), roughly 50% of the liter-
ature contributions can be classied as ‘AM overview’
or ‘AM technology’ and another 20% focus on techno-
logical parameters, describing the impacts of variables
such as materials and AM machines’ hardware upon the
mechanical and physical properties of products. Con-
versely, less than 10% of AM literature investigates AM’s
impactsonsupplychaincoststructuresandperfor-
mances. In accordance with the scarcity of literature in
these areas, this work considers economic peculiarities
of AM technology by comparing traditional and addi-
tive lot sizing decisions in order to deepen the extent to
which a technological choice can impact the supply chain
performances.
CONTACT Simone Zanoni zanoni@ing.unibs.it
This scarcity of literature entails that on one side
manufacturers are struggling to balance o high capi-
tal and production costs, while on the other side, they
are still lacking incentives robust enough to guarantee
a secure move towards productions based on AM. For
instance, one of the general claims reported in literature
is that the implementation of AM would increase costs
and not full desirable expectations (e.g. improving or
even keeping the same level of quality as in more con-
ventional technologies). This has added to the perception
that shifting towards AM might be too risky for man-
ufacturers. Apart from the obvious cost-benets trade-
o, the reasons behind the hesitation to adopt AM, espe-
cially among small and medium-sized enterprises (SMEs)
require to be investigated at a more practical level to
account for a broader range of concerns around these
technologies. Therefore, a dierent approach to study the
industrial capabilities of AM might be necessary, since it
does appear it could take a while for the technology to
master diculties and disadvantages that are currently
discouraging SMEs from investing in AM.
While inherent independence of AM from economies
of scale provides manufacturers with the cost-eective
capability of producing parts in small batch sizes, the
Original Equipment Manufacturers can exploit the AM
machinery to produce on demand legacy spare parts for
their phased-out products. Also, customers do not need
to be concerned about the number of orders to be put,
©  Informa UK Limited, trading as Taylor & Francis Group

2M. ASHOUR POUR ET AL.
while manufacturers can conveniently go on with making
the parts in an even more eective way, since AM pro-
vides the capability to prioritise functionality over design
diculties, a feature which would be otherwise sacriced
in a conventional machine such as Computer Numeri-
cal Control (CNC). Another important feature to con-
sider while assessing AM productions is the exibility of
productionmachinesandthehighlevelofcustomisa-
tion that can be achieved as a result of their applications.
This is particularly appealing to industries where com-
petitiveness relies heavily on the customisation of prod-
ucts. The AM features are not however limited only to
the operational point of view. From a tactical standpoint,
an over-stretching supply chain which is a common char-
acteristic of conventional technologies due to the entan-
gled web of supply, manufacturing and logistics activities
would gradually result in high accumulation of costs, and
managerial complexity, so much so that any improvement
to reduce the size of the chain and lower diculties of
management activities would be rewarding. One way in
which AM can achieve this goal is by the elimination of
high resource-demanding warehouses and correspond-
ing inventory-holding activities. Not only will this sim-
plify the supply chain, it would also shorten lead-times
throughout the chain. So, it can be contemplated that
warehouses in AM facilities are rather virtual databases of
CAD designs whose technical properties can be simulta-
neously reviewed, modied, optimised and shared among
dierent partners of the chain in a matter of seconds.
However, based on the observations made in the lit-
erature, there seems to be a gap between the capabilities
provided by AM, and a practical approach to analyse and
measure the performances achieved through these capa-
bilities in the industry. This paper aims at resolving this
gap by identifying and quantitatively evaluating supply
chain eects caused by switching from a Traditional Man-
ufacturing (TM) system towards AM. We believe it would
simply be an underestimation of AM to merely consider
it as an alternative manufacturing technology to produce
limited volumes of complex parts. Rather, the authors’
perception is that AM could have profound eects on
the supply chain’s dynamics and its conguration. The
terms conventional/traditional in this text are only used
to describe the set of technologies and systems (e.g. sub-
tractive or forming technologies) which come in contrast
with those enabled by AM. To the best of our knowledge,
this study is the rst that presents an analytical investiga-
tion of AM’s impact on supply chains with the scope of
tactical decision-making.
The remainder of this paper is organised as follows:
Section 2 provides a background of the mainstream stud-
ies that are available in the literature on separate subjects
of AM and JELS model. Section 3 introduces notations
andassumptionsusedindevelopingandelaboratingcost
components in AM and TM based on a JELS model.
Section 4 delivers a numerical example to illustrate the
performance of the proposed model. Section 5 provides
a set of sensitivity analyses over the main elements of the
model. Section 6 presents an overall discussion and fur-
ther elaborates on managerial implications of the study.
Finally, Section 7 concludes the paper by proposing some
ideas for improvement of the study and future research.
2. Literature review
2.1. Background in AM
On top of the limited academic attention dedicated to
AM’s manufacturing performance, the literature falls
short of making weighty links between on-going opera-
tionsandthewaystheycouldbeadaptedtohouseAM
within their technological portfolio. In fact, most man-
agerial contributions on AM issued before 2012 base their
approaches towards AM in terms of Rapid Prototyping
concept (Atzeni, Iuliano, Minetola, Salmi, & Atzeni,2010;
Hopkinson & Dickens, 2003;Ruo&Hague,2007;Ruo,
Tuck, & H a gue, 2006), while the recent technology evolu-
tion and the birth of new additive techniques (e.g. Con-
tinuous Liquid Interface Production) led the technol-
ogy beyond its limits, making it applicable and feasible
even in direct production of small to medium sized series
(Rapid Manufacturing). Yet, as it was mentioned earlier,
it accounts for a sharp underestimation of AM’s potential
to merely simplify it as an alternative technology for mak-
ing prototypes, or a means to produce limited quantities
of complex designs.
For instance, it must be noted that to fully exploit AM
capabilities, it is required to revise and adapt the parts’
design accordingly. Sticking to the same old designs of
parts which were originally designed to be manufactured
through TM methods would not result in full exploita-
tion of AM points of strength e.g. the ability to make
lattice structures (Vayre, Vignat, & Villeneuve, 2012). A
redesigned part that accommodates the concepts of AM
in its core would enable both the designers and manufac-
turers to focus on functionality rather than design com-
plexity. A direct consequence of this would be the oppor-
tunity to make rapid design modications that could be
required within the nal stages of pre-launch into the
market. This aspect of AM entails Design For AM as pro-
posedbyDoubrovski,Verlinden,andGeraedts(2011)
and Gao et al. (2015).
Another important aspect of AM is related to its
increasedexibilityascomparedwithconventionalman-
ufacturing methods. This is a broad concept whose
dimensions relate to a greater exibility in production

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 3
volume, mix and the product itself. As a direct con-
sequence of using AM technologies, the AM machines
allow for elimination of machine set-ups, coolants, tools,
jigs, xtures and mould changeovers (Huang, Liu, Mokas-
dar, & Hou, 2013). To this regard, all AM’s technological
variations have more or less the same overall characteris-
tics,andthegeneralprocedurewhichisrequiredtobefol-
lowedinanAMprocesssequenceadherestomuchofthe
same steps (Mellor, Hao, & Zhang, 2014). This means that
regardless of their input raw materials and the mechanism
by which they form each layer of material, all they need is
aCADoftheparttobeuploadedtotheAMmachineby
either a software or as an output of the three-dimensional
(3D) scan of an actual part (Kim, Witherell, Lipman, &
Feng, 2015). The AM processes’ tool freedom, plus the
possibilitytoproduceuniformobjectswithoutassembly
operations would enable manufacturers to shorten sup-
ply chains and to build complex parts whose productions
with conventional methods would be cumbersome and in
some cases even impossible (Achillas, Aidonis, Iakovou,
Thymianidis, & Tzetzis, 2015).
Sustainability is another fundamental aspect which is
enhanced as a result of implementing AM technologies.
Since consumption of raw materials in the processes is
under control and they are only used selectively for pro-
duction of specic layers, there can be signicant savings
where unused powder-form materials on the substrate
can be returned to the process and then recycled (Cozmei
&Caloian,2012) for the next production run.
This fast overview shows how AM is not just another
manufacturing method, but a game-changing paradigm,
in that it allows for production of parts with new
and enhanced characteristics through a fundamentally
shorter and more exible process, with the opportunity
to customise them to each individual customer’s require-
ments, all with a lower environmental impact. As a con-
sequence, any evaluation of AM’s economic and manage-
rial impacts should start by considering AM’s most rel-
evant characteristics, such as lower levels of inventory,
lower order quantities and production volumes, shorter
lead times, etc. There are several motivations behind the
pertinence of a supply chain model in this study: the
small number of manufacturers who have actually imple-
mented AM in their productions thus far, and conse-
quently the limited amount of available data with respect
to AM performance, lack of standard frameworks in the
literature which can base their approaches on the grounds
of operational performance of a supply chain rather than
strategic and managerial issues, as well as missing links
between multiple economic studies dedicated to AM and
their implications over performance of related manufac-
turing companies are the main reasons why a specic sup-
ply chain model is required to improve AM assessments.
2.2. Background in JELS
One of the classic models which can be considered to
reect upon the performance of a supply chain is the well-
known Economic Order Quantity model (Harris, 1990).
While this model includes buyer’s inventory-holding cost
andorderingcostinitsevaluationtocalculateanopti-
mal order size for the buyer, it fails to take the other
side of the equilibrium i.e. the vendor into considera-
tion and thus, it oers a one-sided approach. The other
classic model of Economic Production Quantity does the
analysis over the performance of manufacturer’s side by
including its inventory-holding cost and set-up cost into
thestudy.Bothmodelshowever,considertheannual
demandandannualproductionratebymakingassump-
tionsaboutthem.ThisstudybenetsfromtheJointEco-
nomic Lot Sizing (JELS) model to consider the buyer and
vendor simultaneously, and it aims at comparing the per-
formances of a TM-based system with those of an AM
system. In other words, this model tries to capture the
overall performance of the system through a joint opti-
misation process.
The purpose of JELS models is to nd a more protable
joint production and inventory policy, as compared to
the policy resulting from independent decision-making.
Goyal (1977a,1977b) is believed to be the rst to intro-
duce the idea of a joint total cost for a single-vendor
single-buyer system, assuming an instantaneous produc-
tion for the vendor using a lot-for-lot (LFL) shipment
policy to the buyer. His work was extended by Baner-
jee (1986) who assumed a nite rather than an instan-
taneous production rate, and later by Banerjee (1986)
who assumed that the vendor’s inventory is accumulated
(not LFL) and is delivered to the buyer in shipments of
equal sizes. Following the works of Goyal and Baner-
jee, the basic JELS model has been extended in many
dierent directions. One relevant extension is the inclu-
sion of transportation costs and nite capacity by Top-
tal, Çetinkaya, and Lee (2003) and Ertogral, Darwish, and
Ben-Daya (2007). A recent and very exhaustive review of
this stream of research was provided by Glock (2012).
Latest additions to this research stream were proposed
by Zanoni, Mazzoldi, Zavanella, and Jaber (2014), who
presented a joint economic lot size model with price
and environmentally sensitive demand; Sadjadi, Zokaee,
and Dabiri (2014) who studied a single-vendor single-
buyer joint economic lot size model subject to bud-
getconstraints;GlockandKim(2015)whoproposed
a joint economic lot size model with returnable trans-
port items; Marchi, Ries, Zanoni, and Glock (2016)who
considered nancial collaboration between members of
the supply chain in a single-vendor single-buyer forma-
tion to invest in increasing the production rate; Jauhari,

4M. ASHOUR POUR ET AL.
Fitriyani, and Aisyati (2016)withanintegratedinventory
model for single-vendor single-buyer system with freight
rate discount and stochastic demand; and nally, Ferretti,
Mazzoldi, Zanoni, and Zavanella (2017)whoproposeda
joint economic lot size model with a third-party external
manufacturer.
3. Methodology – the model and cost structures
This section elaborates on the proposal of forming a para-
metric modelling of a supply chain that exploits AM
in its production processes. The scenario consists of a
single vendor directly supplying its products to a single
buyer. A numerical example inspired from an industrial
case is used to show the impacts of AM on the supply
chain. Initially, a basic JELS model with its parameters is
introduced from the literature. Following that, the spe-
cic relationships which are going to be considered in
the formulations and their actual translations in the real
worldareintroducedandthen,thecostcomponentsand
the overall structures of AM and TM consistent with the
basic formulation of JELS are shaped and discussed into
detail.
3.1. JELS base model
The JELS model in this paper considers a single vendor
and a single buyer who keep inventories of their own. In
each shipment, only one type of product is delivered from
the vendor to the buyer. Each time the buyer issues an
order for the product, it incurs a constant ordering cost
whichisindependentofthesizeoftheorder,whilethe
vendor incurs an equally constant production set-up cost
each time it launches a production order for the same
item.Boththebuyerandthevendorincurinventory-
holding cost.
All the main notations that are going to be used in
the formulas in the text are listed in Tab le 1. Since these
notations are identical for both AM and TM systems, the
superscripts denoting the corresponding system are used
whereneeded.Forinstance,whileAvdenotes the produc-
tion set-up cost of vendor for both systems, ATM
vrefers to
this cost in the TM system and AAM
visthesamecostin
the AM system.
The model considers the following assumptions,
according to the greater part of the models in the liter-
ature related to joint economic lot size. For more details,
please see Glock (2012):
rProduction and demand rate are considered to be
known and constant (Goyal, 1977a,1977b);
rIf Pis lower than D, then the demand would not be
satised, and so this would result in the infeasibility
Tab le  . Notations used in the formulas.
Symbol Description Unit
AbOrdering cost of the buyer per order €/order
AvProduction set-up cost of the
vendor
€/set-up
cpProduction variable cost €/unit
hvUnit holding cost for the vendor €/unit·year
hbUnit holding cost for the buyer €/unit·year
pbSelling price to the buyer €/unit
qShipment lot size Units
QProduction lot size Units
nNumber of shipments Shipments/year
PProduction rate Units/year
DDemand rate Units/year
ctUnit transportation cost €/unit
iInterest rate %/year
rProfit margin of the vendor %
TI Total inventory cost €/ year
TC Total transportation cost €/ year
TT Totalcostofinventoryand
transportation
€/ year
TTotal cost of the system €/year
Figure . Inventory levels for buyer, vendor and system.
of the problem. Thus, the production rate is always
more than the demand rate (P>D);
rHolding cost of the buyer is larger than that of the
vendor (hb>hv),accordingtoHill(1999), since it
isassumedthattheproductincreasesitsvaluealong
the supply chain;
rThe production batch sizes are dispatched in
n(n∈Z,n≥1)shipments of equal qsizes. Prod-
uct of these two parameters constitutes the batch size
(Figure 1), i.e. Q=nq;
rThe transportation cost is based on step-discounting
(Ertogral et al., 2007)approach.Thiswouldputthe
unit cost of transportation in a decreasing trend,
meaningthatthehighertheshipmentsize,thelower
the unit cost of transportation;
rOrdering cost of the buyer is constant and indepen-
dent of the order size;
rThe interest rate which is an interpretation of the
stock-carrying cost is equal for both the vendor and
buyer;

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 5
rThere are no stock-outs and so its associated cost is
zero.
The inventory trend at the buyer’s and vendor’s ware-
houses is illustrated in Figure 1. As it can be seen, dierent
levels of inventory are available for the system, buyer and
vendor at each time instant. The cycle duration is Q/D,
while nrepresents the number of shipments for each pro-
duction batch. As it can be seen, nin Figure 1 equals ve.
The parametric relationships (1)and(2) between the
ordering cost of the buyer and the production set-up cost
of the vendor will be considered:
AAM
b=ATM
b·α1(1)
AAM
v=ATM
v·α2(2)
Where α1and α2are multiplier factors assumed to be
0<α
1≤1and0<α
2≤1. The real-world translation
of the multiplier factors in the formulas (1)and(2)can
be found within the inherent characteristics of both sys-
tems. For instance, assume a customer order of size x
has been received by a manufacturer. While commenc-
ing a production run in TM generally requires coordi-
nation tasks between multiple departments in the system
to plan, schedule and assign jobs to the production line,
an AM system can rapidly process the order, recall the
part’sCADandassignamachineforimmediatelaunch
of production. Regardless of all administrative and oper-
ation management tasks [which would result in costs], the
exibility of TM machinery has certain limits which can-
not be ignored. Even if there are empty machines that can
be assigned to full the order, they should still undergo
a specic sequence of set-ups and provisions including
moulds and tooling congurations, as well as raw mate-
rials preparations and processing that would eventually
increase the lead-time and add costs. Although the cur-
rent maturity of AM technologies is not sucient to pro-
cess any quantity of xpromptly, there are still reassuring
signs – including the main arguments discussed through-
outthecurrenttext–whichoutlinecertaincircumstances
in which opting for AM rather than TM could be a supe-
rior alternative method for making products.
3.2. Model development
In the JELS model, studying the cost components and
their optimisations are performed based on a centralised
optimisation, i.e. one single entity has access to all the
available data on dierent interactions of actors within
the system. Thus, by setting all the data in the best
possible trade-o to either reduce the cost or increase
the prot, the decision variables are optimised in a way
that benet of all actors are guaranteed. In this paper, the
study is based on minimisation of the total cost (T), which
includes the total cost of inventory (TI), the total cost of
transportation (TC) as well as the total cost of production.
Thecostcomponentsintheformulathatmakeupthe
total inventory cost (3) of the system are the vendor’s set-
up cost, vendor’s average inventory-holding cost, buyer’s
ordering cost and buyer’s average inventory-holding cost
(Ertogral et al., 2007):
TI q,n=(Av+nAb)·D
nq
+hv·Dq
P+(P−D)nq
2P+(hb−hv)·q
2
(3)
The transportation cost (4) is specically considered
as a function of the shipment size (q), and it is taken to be
in a discounted format to account for dierent shipment
sizes with respect to the demand (Ertogral et al., 2007):
TC q=⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
c0D,q∈[0,M1)
c1D,q∈[M1,M2)
c2D,q∈[M2,M3)
..., ...
cmD,q∈[Mm,∞)
(4)
The unit cost of transportation (ct) is taken as a factor
of the ordering cost of the buyer (Ab)forbothAMand
TM (5), since this cost would eventually be paid by the
buyer in the current conguration of the supply chain:
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
U1Aj
b,q∈[1,M1)
U2Aj
b,q∈[M1,M2)
U3Aj
b,q∈[M2,M3)
..., ...
UmAj
b,q≥Mm
λ1<λ
2<λ
3< ... < λ
m
θ1<θ
2<θ
3<... < θ
m
if j=TM ⇒Ui=λi
if j=AM ⇒Ui=θi
θi≤λi
0<λ
i≤1
0<θ
i≤1
i=1,...,m(5)
where:
rjisthesystemalternativebetweenAMandTM,
rλisthefactormultiplierforTM,
rθis the factor multiplier for AM.
Again, using the multipliers of λand θis to account
for inherent properties of the systems. Since productions
basedonAMarenotlabourintensive,theycouldbe
located within the proximities of customers or points of
use. When put in comparison with highly complex and

6M. ASHOUR POUR ET AL.
costly logistic operations in TM systems, AM can be cred-
ited as a simple system which can rapidly make the prod-
ucts and deliver them to the points of use with very low
costs of transportation. The total cost of the system (6)
is made up of the system’s inventory and transportation
costsaswellasthoseofproductions:
Tq,n=TI q,n+TC q+Dcp(6)
In the following, the cost components of AM and TM
systems are presented: it must be noted that the main dif-
ference between the cost components in these systems is
not due to dierent cost structures but rather, the values
that they assume.
3.3. TM cost components
The following describes details of various cost compo-
nents in the TM model:
rUnitholdingcostforthevendorisaproductofthe
unit cost of production and the interest rate,
rUnit holding cost for the buyer is a product of unit
holding cost for the vendor and a prot margin,
rThe unit cost of production is calculated from a ref-
erence by cost components summation of raw mate-
rials, processing, post-processing and set-up,
rThe unit cost of transportation, as explained ear-
lier in the text, is a function of the shipment size
(through a discounted model).
cTM
p=rTM
m+pTM
r+pTM
p+tTM
p(7)
hTM
v=cTM
p·i(8)
hTM
b=hTM
v·(1+r)(9)
where:
rrTM
mis the raw material cost in TM,
rpTM
ristheprocessingcostinTM,
rpTM
pis the post-processing cost in TM,
rtTM
pis the tooling cost in TM.
3.4. AM cost components
In the following, details of the various cost components
in the AM model are described:
rThe unit cost of production is calculated from
a reference by cost components summation of
raw materials, pre-processing, processing and post-
processing,
rUnitholdingcostforthevendorisaproductofthe
unit cost of production and the interest rate,
rUnit holding cost for the buyer is similar to that of
TM; a product of unit holding cost for the vendor
and a prot margin,
rThe unit cost of transportation is a function of the
ordering cost (through a discounted model).
cAM
p=rAM
m+pAM
r+pAM
p+tAM
p(10)
hAM
v=cAM
p·i(11)
hAM
b=hAM
v·(1+r)(12)
where:
rrAM
mis the raw material cost in AM,
rpAM
ris the processing cost in AM,
rpAM
pis the post-processing cost in AM,
rtAM
pis the pre-processing cost in AM.
3.5. Solution procedure
The optimisation algorithm is identical for both AM and
TM since the analytic formulation of the objective func-
tionisthesame.Therstoptimisationisrelatedtothe
minimisation of production inventory-related costs com-
ponents for (3).
According to Zanoni and Grubbstrom (2004), the fol-
lowing procedure can be done for the joint optimisation
of qand n.Todoso,TI(q,n)is formed in a way to match
with the following format:
f(x)=ax +b/x+c=(a/x)·x−b/a2
+2√ab +c(13)
The optimal value of shipment size for minimisation
of the total cost of inventory ˆ
qaccording to the above for-
mula would be b/a.Havingdonetheprocedure,thefol-
lowing formula (14)isobtained:
ˆ
q=2DP (nAb+Av)
nicp(nP +(1+r)P−nD −P+2D)(14)
Then, by replacing ˆ
qand getting TI(ˆ
q,n),thefor-
mula is again adapted so that (TI(ˆ
q,n))2follows the same

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 7
form, but this time according to n.Havingdonethepro-
cedure,thefollowingclosedformula(15)isobtained:
ˆ
n=Av(P(1+r)−P+2D)
Ab(P−D)(15)
Recalling the main assumptions of the model, nis an
integer parameter, and for given values of 
q,ˆ
n:ˆ
n=
ˆ
nif TI(ˆ
q,ˆ
n)<TI(ˆ
q,ˆ
n), ˆ
n=ˆ
n.
The following condition holds:
ˆ
nˆ
n−1≤Av(P(1+r)−P+2D)
Ab(P−D)≤ˆ
nˆ
n+1
(16)
The values of ˆ
qand ˆ
nwith the closed formulas given
in (14)and(15) would then be used to calculate the min-
imum cost of inventory in the system. It must be noted
that ˆ
qand ˆ
nare not the optimal values for shipment size
and number of shipments, since the optimisation needs to
be done for the total cost of the system and not the total
cost of inventory in the system.
The second optimisation is related to the joint optimi-
sation of inventory and transportation costs.
Having obtained the value of the batch size ( ˆ
Q=ˆ
q·
ˆ
n), the cost of transportation is then enforced through
a discounted model according to the ranges which are
introduced based on the shipment size (ˆ
q). By doing so, it
wouldbepossibletocalculatethetotalcostsofinventory
and transportation (TT) from (17):
TT ˆ
q,ˆ
n=TI ˆ
q,ˆ
n+TC ˆ
q(17)
The same procedure by Ertogral et al. (2007)canbe
done for this part. The third optimisation is related to the
minimisation of the total cost of the system as expressed
in (6).Inthisstep,thetotalcostofproduction(i.e.Dcp,
with cpexpressed by (7)and(10), respectively for the TM
case and for the AM case) is added up to TT, as expressed
in (17), to calculate the total cost of the system (T). Since
this value may not be the minimum value of the total
cost,aniterativeapproachistakeninawaythatstarting
from an initial (..
n=1), the algorithm xes ..
qand tests
thetotalcostofthesystembyincrementalincreasingof
..
n.Oncethebest ..
nis found, the algorithm is repeated by
xing ..
n=n∗and incremental increase of ..
qand calculat-
ing the total cost of the system until nding ..
q=q∗for
which the TI(q∗,n∗)is minimum. This is a procedure
similar to Jaber and Goyal (2009)whichisusedtond
the optimal nand q. This procedure is implemented via
a nested loop algorithm using Visual Basic for Appli-
cations (VBA) that is programmed in Microsoft Excel.
For more information regarding common optimisation
procedures, readers are encouraged to take a look at
Kazemi, Abdul-Rashid, Shekarian, Bottani, and Monta-
nari (2016), Kazemi, Olugu, Abdul-Rashid, and Ghazilla
(2016), Kazemi, Shekarian, Cárdenas-Barrón, and Olugu
(2015).
4. Numerical example
4.1. An industrial case study
An operational level cost analysis taken from a separate
studythatdetailsthecostcomponentsoftwomanufac-
turing technologies which can interchangeably be used
to produce a single part is exploited as a guide to keep
the model parameters in check, and further enhance the
comparison drawn between the AM and TM systems.
The numerical example in this paper is mainly taken
from the paper by Atzeni and Salmi (2012). In their paper,
the breakeven point analysis of cost per assembly between
two dierent processes for a main landing gear of a scale
1:5 model of an aircraft (P180 Avant II by Piaggio Aero
Industries S.p.A) is performed. The status quo of the
productionprocessisthroughtheassemblyofvedif-
ferent major components linked together by small link-
age parts. The study investigates the redesign of the part
based on an AM process, and according to a set of impor-
tant design rules to abide by the principles of AM and
exploit their capabilities. These rules include reducing
the number of assemblies by functional integration, opti-
mising strength and weight by saving raw materials and
energy consumption and using hollow structures where
possible. According to Atzeni and Salmi (2012), the status
quo process and the redesign based on AM have dierent
trends in terms of the total cost, which can be seen in
Figure 2.
While in the conventional process of High-Pressure
Die Cast (HPDC), the cost per part for smaller volumes
Figure . Breakeven point of the total cost in an additive manufac-
turing process compared with that of traditional manufacturing.

8M. ASHOUR POUR ET AL.
Tab le  . Data of numerical analysis for one iteration.
Parameter TM AM Unit
D Units/year
P Units/year
Av. . €/set-up
Ab. . €/order
cp. . €/unit
rm. . €/unit
pr.  €/unit
pp.  €/unit
tp . €/unit
i% %/year
r% %
of production starts signicantly higher than the ini-
tial price in Selective Laser Sintering (SLS) process, by
increasing the production volume, a reduction of assem-
bly costs through a downward curve is observed. This
could potentially be the result of costs proration through
economies of scale in TM (HPDC). This eect however
is non-existent in the AM process (SLS), and so the cost
trend is constant over dierent production volumes. This
kind of research which takes the economic implications
of AM into its core has been studied in multiple practices
among which Hopkinson and Dickens (2003), Ruo et al.
(2006), Ruo and Hague (2007), Weller, Kleer, and Piller
(2015) provide the most important insights on the AM
economic performances. To test the model for an indus-
trialscenario,thefollowingsetofdata(Tabl e 2 )isusedto
calculate the optimal number of shipments and shipment
size.
Inthisnumericalexample,thereareafewadaptations
compared with the values presented by Atzeni and Salmi
(2012) to adjust the two systems into comparable alterna-
tives for the supply chain performance analysis. For the
number of parts produced per job on the SLS machine,
thebuildchamberisassumedtoaccommodate10parts
(andnotfourasintheoriginalmodel)perjob.Thiswould
help create more consistency in the calculations by dis-
carding the eect of disproportionate comparisons which
are partly caused by the annual demand rate. The produc-
tion volume of HPDC machine has been consequently
modied to 200 parts.
For calculating the production set-up cost of the ven-
dor in TM, the costs associated with machine set-up for
thersttimeinthebeginningofworkingshiftaretaken
andthensummedup.ThiscostintheAMmodelpre-
sented by Atzeni and Salmi (2012) includes only the costs
associated with pre-processing, and it does not account
for other important costs that the vendor incurs, e.g. ini-
tial CAD drawing, design optimisation, support struc-
tures preparation, etc. In this paper, however, discarding
this eect is performed by proportionate evaluation of the
same cost in TM to present a more realistic situation. This
Tab le  . Results of the optimal decision variables and objective
function for the iteration.
Supply
chain
based
on q∗n∗Q∗TI TT T∗
TM    € ,. € ,. € ,.
AM    € . € ,. € ,.
is done by considering a coecient of α2related to the
production set-up cost in TM.
The buyer’s ordering cost in TM is assumed to take the
same value as the production set-up cost of the vendor,
while a coecient of α1is considered into the calcula-
tions of this parameter in the AM system. In the sensi-
tivity analysis, however, these parameters as well as their
impacts on the dierent costs of the system are going to
be discussed further in detail. It must be noted that the
calculation of the rest of the parameters depending on the
production volume in TM, and number of parts produced
per job in AM are still based on the relationships of the
original model and these adjustments are all performed
proportionately.
4.2. Results
The total cost function is optimised by the number of
shipments (n)andtheshipmentsize(q)intheequation
both for AM and TM. They have been registered in Table
3.
Looking at the total inventory cost in Figure 3,aphe-
nomenon which has rarely been discussed in literature
canbeobserved.Contrarytothecommonnotionthatthe
unit cost of production in AM always remains constant
irrespective of the production volume, the latter’s eect
Figure . Total inventory cost of the system for AM and TM.

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 9
Figure . Total cost of inventory and transportation for AM and
TM.
canbeobservedintheAMsystemaswellwhichcould
signal the potential presence of some type of economies of
scale locally conned for such systems; the signicant dif-
ference being on AM having a higher sensitivity towards
changes in the batch size of production. In other words,
the TM system is believed to be more exible in dealing
withdisruptionsofproduction.AsitcanbeseeninFigure
4, the total costs of inventory and transportation (TT) in
the optimal batch size in AM are signicantly lower com-
pared with that of TM. This is consistent with the charac-
teristics of AM systems in literature.
As it can be seen in Figure 5,theoptimalshipment
size for AM is 200, which is smaller than the calculated
optimal size for TM that puts it on 400. It must be noted
thatthesevalueshavebeenoptimisedforthetotalcost
(T) function. For optimisation of the transportation cost
TC(q),thesameapproachwhichhasbeenperformedby
Ertogral et al. (2007) can be used to test the optimal value
of the transportation cost with respect to the q∗and n∗
Figure  . Total cost of the system based on AM and TM for different
batch sizes.
Figure . Total cost of the system for AM and TM for different val-
ues of n∗.
according to the ranges which are introduced based on
thebatchsize.Forthesakeofsimplicity,therangesof
unit transportation costs (aecting the graph in jagged
shape)areonlyintroducedforthebatchsizesthatarein
the locality of optimality.
A further elaboration of this example regarding the
numbers of shipment can be discussed for dierent val-
ues of n∗.AsitcanbeseeninFigure 6,AM’ssuperior-
ity in total cost of the system applies to lower numbers of
shipment, while by increasing n∗,TMbecomesmorecost
ecient.
The corresponding behaviour of the total inventory
cost of both systems for dierent values of n∗canalsobe
seen in Figure 7.
5. Sensitivity analysis
5.1. Demand rate (D)
A set of sensitivity analyses on the performance of both
systems by varying the demand rates over the production
Figure . Total inventory cost of AM and TM systems for different
values of n∗.

10 M. ASHOUR POUR ET AL.
Figure . Changes in optimal batch size on various demand rates.
rate while keeping the rest of the parameters at their orig-
inal values illustrate how AM and TM would react to this
variation. This set includes major performance indicators
ofthemodeli.e.optimalbatchsize,totalcostofinven-
tory,aswellasthetotalcostofthesystem.Asitcanbe
seen in Figure 8, by increasing the demand rate towards
the value of production rate (with the condition of P>D,
changesinoptimalbatchinAMinsteadofTMaremuch
larger with higher capacity utilisation. More precisely,
with capacity utilisation of the base case D/P=8%, the
ratiobetweentheoptimalbatchsizeofAMandTMis
Q∗AM /Q∗TM =50%, while increasing the capacity utilisa-
tion to D/P=92%wouldreduceratiooftheoptimal
batch size to Q∗AM/Q∗TM =8%.
AsitcanbeseeninFigure 9,byincreasingthedemand
rate, the total cost of inventory also increases in both AM
and TM, while the dierence in costs becomes more sig-
nicant in favour of AM for higher demand rates. The
interesting aspect nevertheless is the amount of cost sav-
ing, particularly in higher demand rates that could be
achieved due to the lower overall costs of inventory and
transportation in the AM system in comparison with the
same values coming from TM. Corresponding with the
absolute values, the cost saving that can be obtained by
AM becomes more remarkable in higher demand rates.
Figure . Total costs of inventory for the AM and TM systems.
Figure . Total cost for the AM and TM system.
One of the most interesting investigations is to look
atthebehaviourofthetotalcostofthesystem.Asitcan
be seen in Figure 10, provided the annual demand rate
issmallenough,theAMsystemcouldprovideanactual
cost-saving opportunity which can be exploited under the
right circumstances (e.g. annual production rates), but
this opportunity would soon fade away as the demand
rate gets closer to the annual production rate. However,
the actual dierence between AM and TM in terms of
total system cost even for higher demand rates is illus-
trative; leaving the nal option of either AM or TM a
strategic decision-making task which requires taking into
account multiple aspects of performance.
5.2. Ordering cost (α1)and production set - up cost
(α2)
The following analysis investigates the eect of vary-
ing the ordering cost of the buyer (Ab)and the pro-
duction set-up cost of the vendor (Av),andmonitor-
ing their impacts on the total cost of inventory as well
asthetotalcostofthesysteminasolutionbasedon
AM. According to the main characteristics of AM, the
machines which use this type of technology have low set-
ups, while the online-based mechanism of putting the
orders and modifying them (hypothetically through a
web-based platform) as well as the corresponding costs
associated with proximity of buyer and vendor would
help reduce inventory costs even further. This would con-
sequentlyreducethetotalcostofthesystem.Thus,itis
once again emphasised that it would be a logical assump-
tion to limit the upper range of the two coecients
to one, since the corresponding costs in TM seem to
dene the maximum value which could be given to these
parameters.
In Figure 11, the impacts of increasing the costs asso-
ciat e d with ve n d or’s pr o ducti o n s et-up a n d buye r ’s orde r -
ing on the total cost of inventory are illustrated. Although

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 11
Figure . Total inventory cost saving by AM system for different
values of α1and α2.
adding up to the original values of these costs would result
in aggregating the overall inventory cost of the AM sys-
tem, the cost savings that could be achieved compared
with the results given by TM are still meaningful.
As shown in Figure 12, with the ordering cost of buyer
in AM getting closer to the same value assumed by TM,
thetotalcostoftheAMsystemincreaseslinearly,with
minor cost saving expectable only in small ratios of α1.
This increase could be linked to the impact of (Ab)on
the unit transportation cost. Increasing the production
set-up cost of vendor would not have signicant impacts
on the total cost of the system, and its impact is almost
always constant in its slight accumulation over the total
cost of the system. When it comes to the absolute val-
ues, increasing the ordering cost of the buyer would
always result in increasing the total cost of the system,
while increasing the production set-up cost of the ven-
dor would have negligible impacts on the total cost of the
system.
Figure . Total cost saving of the system by AM solution for dif-
ferent values of α1and α2.
Figure . Total inventory cost saving of the AM system with
respect to various costs of raw materials.
5.3. Cost of raw materials (rm)
Since the behaviour of this change in AM is the main
focusofthispart,theanalysisisonlyperformedinthis
system by decreasing the cost of AM raw materials and
bringingitclosertothelevelsatwhichtheTMrawmate-
rials originally cost. As it can be seen in Figure 13,reduc-
tion of raw materials cost would result in further cost sav-
ing of system’s inventory in an AM system. From another
viewpoint, high costs of raw materials in an AM system
areafactorwhichmustbecloselywatched,sincethereis
a ‘decoupling point’ after which, the total inventory cost
is no longer advantageous compared with that of TM.
AsitcanbeseeninFigure 14,theamountofcostsav-
ing that can be attained by decreasing the unit cost of raw
material is an inuential factor only for small ratios of
rAM
m/rTM
mand in a specic range. Beyond that range, how-
ever, the total cost of the system in AM would be higher
than that of TM under the inuence of the cost of raw
materials.
Figure . Total system cost saving of AM with respect to various
costs of raw materials.

12 M. ASHOUR POUR ET AL.
The sensitivity analyses on parameters of the indus-
trialcaseshowhowchangingparametersinthemodel
could aect the total cost of the system, the total cost of
inventory and transportation as well as the optimal batch
sizes. Changes in some parameters such as the cost of
raw materials or variations in demand could have signi-
cant implications on protability of AM as compared with
TM.However,theresultscomingfromchangestaking
place over values of other parameters such as the produc-
tion set-up cost of the vendor are not robust enough to
provide conclusive outcomes. Finally, the analysis shows
that investigation of the results for system’s inventory is
not necessarily in line with the results coming from the
system’s total cost, meaning that under certain circum-
stances (investigated in the industrial case in this paper),
AM could almost always prove to be more economical
than TM with respect to the total cost of inventory in the
system, but this better performance loses its leverage once
it is put together with other costs, i.e. the costs of trans-
portation and production.
6. Discussion and managerial implications
The context analysed and modelled in this rst attempt to
evaluate the performance of JELS over the dierent tech-
nologies is by default skewed towards adoption of TM.
Several supply chain drivers which directly depend on the
choice of implementing AM or continuing the use of tra-
ditional technologies can be considered for future contri-
butions in order to underline the full potential of additive
technologies. These drivers may include: (1) supply chain
performance as exibility and responsiveness, (2) nature
of products realised in terms of demand predictability
and (3) risk of products’ obsolescence.
Adopting AM technologies leads to a higher level
of exibility in production processes. To make this
eect visible, the developed model should consider
dierent product families. In such conguration, AM
will unleash all its potential thanks to the (almost)
zero setup costs. In other words, increasing the range
of products managed along the supply chain and
the level of demand fragmentation could enhance
feasibility of AM for production purposes. Introducing
another relevant aspect such as demand predictability
would further clarify the overall supply chain benets.
Recent contributions in the literature provide insights
about how additive technologies can help spare parts sup-
ply chain management (Li et al., 2016)) which are char-
acterised by high unpredictability of demand pattern. In
general, a supply chain which manages a large number
of products with less predictable demand is more pre-
pared to implement AM. Then, a nal extension of the
implemented model will consider another product char-
acteristic which is related to the life cycle and obsoles-
cencerisk.Infact,forproductsaectedbyhighriskof
obsolescence (e.g. electronics products such as notebook
and smartphone), AM can support the service supply
chain by reducing the batch size. This would decrease
inventory holding concerns and consequently, result in
reduction of the costs associated with obsolete products.
The authors strongly believe that introduction of these
supplychainfeaturesintheanalyticalmodelwillallowfor
identication of preferable contexts in which AM tech-
nologies can unleash their potential and thus, generating
economic benets which can be compared to those of tra-
ditional technologies.
7. Conclusions
This paper is an analytic study to investigate AM’s impacts
in supply chain management. To do so, a lot sizing com-
parison between AM and TM are separately implemented
over a two-level supply chain. The study applies a JELS
modeltobothAMandTMsystems,andthenbyintro-
ducing identical analytic parameters, it tries to develop
a comparative analysis over the total cost of each system.
The total cost includes inventory, transportation and pro-
duction costs. A contemplation of this analysis could be
further extended to overcome its current limitations and
include analysis of more inuential factors such as the
eect of capital investment costs, machines’ depreciation
costs, overhead costs, etc. This could be achieved through
more complex models or further breakdown of the cost
components to address the capabilities and limitations of
the AM system in response to supply chain dynamics.
These dynamics could be elaborated on an extension of
the current model to include multiple vendors supply-
ing dierent products to multiple buyers (e.g. along the
line of Zavanella and Zanoni (2009)), situations where
the vendor and buyer are characterised by dierent credit
condition and thus with dierent interest rate (e.g. along
the line of Marchi et al. (2016)) or analysis of decision-
making scenarios in which a hybrid solution of AM and
TM is also an option besides the individual ones.
Disclosure statement
No potential conict of interest was reported by the authors.
Notes on contributors
Miland Ashour Pour is 3rd year Ph.D. student in the Mechan-
ical & Industrial Engineering Department at the University of
Brescia, Italy. He graduated in Management Engineering M.Sc.
from the Polytechnic University of Milan. His main research

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 13
interests are: Additive Manufacturing, Advanced Manufactur-
ing Systems, and Supply Chain Management.
Simone Zanoni is associate professor in the Mechanical &
Industrial Engineering Department at the University of Bres-
cia (Italy). Hegraduated (with distinction) in Mechanical Engi-
neering and took his Doctorate at the University of Brescia
(Italy). His main research interests are: Layout Design, Inven-
tory Management and Closed-loop Supply Chain, Environ-
mental and Sustainable aspects in Supply Chain Management.
Andre a Bacch etti is research associate at the Mechanical &
Industrial Engineering Department of the University of Brescia
(Italy). He graduated in Industrial Engineering at the Univer-
sity of Brescia (Italy) and took his Doctorate at the University of
Brescia (Italy) in 2010. He is involved in RISE Laboratory, devel-
oping activities concerning Supply Chain Management, Inven-
tory Management and Digital Innovation.
Massimo Zanardini is research fellow at the Mechanical &
Industrial Engineering Department of the University of Bres-
cia (Italy). He graduated in Industrial Engineering at the Uni-
versity of Brescia (Italy) and took his Doctorate at the Univer-
sity of Brescia (Italy) in 2016. He is involved in RISE Labora-
tory, developing activities concerning Supply Chain Manage-
ment and Digital Innovation.
Marco Perona is full professor of Industrial Logistics at the
Mechanical & Industrial Engineering Department at the Uni-
versity of Brescia (Italy). He is scientic director of the Research
and Innovation for Smart Enterprises (RISE) Laboratory of the
University of Brescia. He does research, teaching and trans-
fer activities on operations management, supply chain manage-
ment and service management.
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