Balancing storage cost and customization time in product platform design: a bi-objective optimization model

Abstract

In the modern market scenario governed by the Mass Customization paradigm, the so-called delayed product differentiation (DPD) rose as a production strategy best balancing traditional Make-to-Stock (MTS) and Make-to-Order (MTO), potentially reducing storage cost and customization time. In industry, DPD uses product platforms, defined as a set of components forming a common structure, from which a stream of derivative variants is produced. Early-stage platforms, made of few components, limit their storage cost, increasing the time to customize and turn them into final variants. The literature widely discusses the product platform design problem, asking to explore quantitatively the trade-off between platform storage cost and customization time. This paper contributes to applied research in mass customization, proposing and applying a bi-objective optimization model able to assign the most suitable production strategy to each product variant among MTS, MTO, and DPD. In the case of DPD selection, the model designs the product platforms best balancing storage cost and customization time as the target metrics to optimize, subject to industrial constraints to produce and store them, matching each variant to the most suitable platform. A case study adapted from the electronic components sector exemplifies the use of the bi-objective model, supporting companies in managing high-variety mixes.

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The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
https://doi.org/10.1007/s00170-025-15081-1
ORIGINAL ARTICLE
Balancing storage cost andcustomization time inproduct platform
design: abi‑objective optimization model
LudovicaDilettaNaldi1· FrancescoGabrieleGalizia1 · MarcoBortolini1
Received: 9 April 2024 / Accepted: 16 January 2025 / Published online: 5 February 2025
© The Author(s) 2025
Abstract
In the modern market scenario governed by the Mass Customization paradigm, the so-called delayed product differentiation
(DPD) rose as a production strategy best balancing traditional Make-to-Stock (MTS) and Make-to-Order (MTO), potentially
reducing storage cost and customization time. In industry, DPD uses product platforms, defined as a set of components
forming a common structure, from which a stream of derivative variants is produced. Early-stage platforms, made of few
components, limit their storage cost, increasing the time to customize and turn them into final variants. The literature widely
discusses the product platform design problem, asking to explore quantitatively the trade-off between platform storage
cost and customization time. This paper contributes to applied research in mass customization, proposing and applying a
bi-objective optimization model able to assign the most suitable production strategy to each product variant among MTS,
MTO, and DPD. In the case of DPD selection, the model designs the product platforms best balancing storage cost and
customization time as the target metrics to optimize, subject to industrial constraints to produce and store them, matching
each variant to the most suitable platform. A case study adapted from the electronic components sector exemplifies the use
of the bi-objective model, supporting companies in managing high-variety mixes.
Keywords Delayed product differentiation· Product platform· Mass customization· Variety· Bi-objective optimization·
SDG 9: Industry, innovation and infrastructure
1 Introduction
The current industrial and market scenario, governed by
Mass Customization (MC), asks for wide product mixes to
meet the customer’s personalized needs [6, 28], [42]; [24].
To this purpose, the MC production paradigm aims to cope
with the increasing product variety guaranteeing production
efficiency, by providing products to customers with the same
quality and prices of the mass-produced ones [1, 11, 16]. In
such a scenario governed by MC, the focus is on custom-
ers and their purchasing experience, with their personalized
needs affecting the whole manufacturing process. Customers
are involved from the product design phase, participating
in the design of their preferred product by selecting from
a range of pre-defined sub-units which are then combined
into the customized product [3]. As the current market has to
best face the peculiar needs and specifications of customers’
demand to remain competitive, MC paradigm is receiving
rising attention from both academia and industry all over
the world, proposing and adopting different approaches.
The technological advancements stimulated by Industry 4.0
allow the adoption of product-service systems, taking advan-
tage of expandable and changeable supply chain networks to
grant additional value for the customers and high possibility
of customization [4] [49],). In this context, traditional pro-
duction strategies such as Make-to-Stock (MTS) and Make-
to-Order (MTO) overcome their limits. MTS satisfies cus-
tomer orders in a short customer lead time, generating stock
and storage costs, while MTO limits such costs, but with the
customer lead times increase [37]. The delayed product dif-
ferentiation (DPD) is a hybrid strategy born to join the pros
of MTS and MTO and uses the so-called product platforms
to reach this goal [18]. Literature defines product platforms
in various ways, either narrowly or broadly. [36] focused
on the exploitation of the core shared physical architecture
among product variants, defining a platform as “a set of
* Francesco Gabriele Galizia
francesco.galizia3@unibo.it
1 Department ofIndustrial Engineering, Alma Mater
Studiorum - University ofBologna, Viale del Risorgimento
2, 40136Bologna, Italy
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4934 The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
subsystems forming a common structure, from which a set
of derivative variants can be efficiently produced and devel-
oped.” McGrath [32] defined a platform as “a collection of
the common elements, especially the underlying core tech-
nology, implemented across a range of products,” includ-
ing technology and process dimensions, while Robertson
and Ulrich [47] further broadened the concept, considering
an abstract platform structure formed by “the collection of
assets i.e., components, processes, knowledge, people and
relationships that are shared by a set of products.” Product
platforms are produced according to MTS strategy and then
differentiated into different final variants after the arrival
of the customer orders, according to MTO strategy [18].
Authors Erens and Verhulst [15] introduced the modular
product platform concept as the entity able to produce differ-
ent variants by varying modular components in commonly
shared components. The product platform concept is exem-
plified in Fig.1. Product variant 1, variant 2, and variant
3 share common components, i.e., F1, F2, and F4, consti-
tuting the product platform, that is produced and stocked
in advance. After the order arrival, several customization
components are assembled to the platform to finalize each
product variant. As an example, if the final customer asks for
variant 1, the product platform is customized by assembling
component F3.
In many industries, the design of product families based
on the platform concept allows to take benefit of econo-
mies of scale and scope while satisfying a variety of market
segments [51]. Muffatto and Roveda [41] analyzed how the
product architecture influences the applicability of product
platforms, concluding that the product platform concept is
not applicable in both full modular and full integral product
architectures. While Simpson etal. [51] highlighted the need
of cohesive and flexible product architecture and common
subsystems and components for a successful implementation
of a platform-based strategy.
In addition, this last study showcased the application of
platforms in automotive, aerospace, and telecommunication
industries, while [56] evaluated additional different indus-
trial environment, discussing the life cycle of platforms also
in industrial machinery and product software industries.
Overall, among the most important and mentioned com-
panies adopting platforms, Hewlett-Packard, Kodak, Black
and Decker, Volkswagen, and Sony deserve to be mentioned
[48, 50, 51, 51], characterized by assembled product variants
belonging to families sharing the same basic structure and
differentiated along the manufacturing cycle by customized
finishing and details.
How to design and develop product platforms still con-
stitutes an important research stream attracting interests
from the academic community [58] proposing a wide set
of models and methods based on both optimal and heu-
ristic approaches, collected in reviews as Jiao etal. [29],
Pirmoradi etal. [45], and Zhang [58]. A further stream of
research focuses on the customer order decoupling point
(CODP) concept, identified as the breaking point between
productions for stock based on forecast, produced according
to MTS strategy, and customization driven by real customer
order demand, produced according to MTO strategy [12]. As
the position of CODP affects the platform structure, optimi-
zation models and heuristics approaches for CODP position-
ing are further explored by [12], Guo etal. [17], and James
and Mondal [26]. Generic product platform design models
are, usually, single objective, optimizing, as the main driver,
the economic cost in terms of product platform manufactur-
ing and management [16, 20]. By minimizing the manufac-
turing cost, product platforms are made of few components,
increasing the required customization time because of the
higher number of components to assemble and disassem-
ble to get the final variants. A relevant trade-off between
platform storage cost and customization time exists, which
still needs to be explored. This paper contributes to applied
research in mass customization management defining and
solving a bi-objective optimization model for the product
platform design, minimizing storage cost and the platform’s
customization time. To the authors’ knowledge, this problem
Fig. 1 Reference example of a
product platform
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4935The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
is novel and not explored so far by the literature. Further, the
proposed model returns the assignment of the most suitable
production strategy to each variant among MTS, MTO, and
DPD, and, in the case of DPD selection, the optimal mix of
product platforms, their structure, the assignment of each
product variant to the most suitable platform to minimize
the storage cost on one side, and the customization time on
the other side. In the case of variants managed through the
MTS strategy, platforms identical to such variants will be
generated, while in the case of variants managed through the
MTO strategy, empty platforms will be created and assigned
to those variants. The concept of “empty” platform refers
to dummy platforms, formed by zero components, and thus
to the formation of product variants from scratch after the
arrival of a customer order, i.e., according to the MTO logic.
According to this background and goal, the remainder
of this paper is organized as follows: Section2 reviews the
relevant literature on the topic. Section3 describes the bi-
objective model formulation for product platform design,
while Section4 applies the model to a case study repre-
sentative of an operative industrial environment discussing
some results and outcomes. Finally, Section5 concludes this
paper with final remarks and a set of tentative future research
opportunities.
2 Literature review
The ability of a manufacturing system to offer a wide pro-
duction mix in short lead times is a strong competitive factor
[16]. DPD is able to meet such trend using product plat-
forms. The goal is to best manage the high variety, delaying
the point in which the different variants take on their unique
features [22, 27, 57]. In this way, manufacturing and assem-
bly processes are common up to the so-called differentiation
point, and then, final tasks are performed to take platforms
into the final variants [23]. Despite assembly tasks are tradi-
tionally used to get final variants from product platforms, the
recent literature introduced the idea of implementing both
assembly and disassembly tasks [5, 19, 20, 24, 33]. This
option is introduced to increase the number of components
in each platform, and, consequently, the MTS production of
a larger product segment, i.e., the platform.
The literature proposed a wide set of studies focusing
on the product platform design and management. Among
the most representative, Martin and Ishii [31] introduced
a step-by-step method to support companies in developing
product platforms. Two relevant indices are developed using
the Design for Variety (DfV) method to measure a product’s
architecture, i.e., the generational variety index, which is a
measure of the amount of redesign effort for future product
design, and the coupling index, which is a measure of the
coupling among the product components. To jointly design
cost-effective product families and product platforms, Park
and Simpson [43] presented a production cost estimation
framework. The authors improved their framework in a prac-
tical way through an activity-based costing (ABC) system
in which activity costs are mapped to individual parts in the
product family, and the activity costs affected by product
family design decisions are restructured to make the costs
relevant to these decisions. Ben-Arieh etal. [5] proposed
a mathematical optimization model to select multiple plat-
forms for a given product family to minimize the overall
production cost, considering the market demand and the
structure of each variant. The decision variables included
in the model refer to the optimal number of platforms and
their configuration as well as the assignment of the variants
to the platforms. Hanafy and ElMaraghy [19] proposed the
Modular Product Multi-Platform (MPMP) model to design
optimal product platforms using the new concept of assem-
bly/disassembly instead of assembly, only. The objective
function minimizes the cost of platform component mass
assembly, platform customization by component assembly
and disassembly, and the labor training cost for each plat-
form. Hanafy and ElMaraghy [20] propose a platform net-
work model using the Median Joining Phylogenetic Network
(MJPN) algorithm to determine the required number and
composition of a product platform and to define the prod-
uct differentiation points. The MJPN methodology is also
used in the decision support system for product platform
design and selection in high-variety manufacturing proposed
by Galizia etal. [16], which allows platform customization
through combined assembly and disassembly tasks, and by
the bio-inspired phylogenetics methodology proposed by
Moussa and ElMaraghy [39]. Pruning analysis and attribute
matching are used in Zhang etal. [60] method for prod-
uct platform planning. Then, novel metrics are proposed
to evaluate the platform customization effort. Longo etal.
[30] proposed a two-step platform design process to support
apparel brands best coping with mass customization, deter-
mining the best number of product platforms and developing
an evolutionary-based decision support model to balance the
trade-off between the demand of garments that fit well and
the percentage of the population that is satisfied with the
proposed product family. Moussa and ElMaraghy [38] and
Moussa and ElMaraghy [40] developed cost-based models to
design multiple platforms, which can be customized through
additive and subtractive manufacturing, conceptually similar
to assembly and disassembly tasks. Recently, a preliminary
indicator to assess the production cycle similarity among a
set of product variants is proposed by Bortolini etal. [8],
acting as a first criterion to assess the feasibility of imple-
menting the DPD strategy.
The literature review on the topic highlights the pres-
ence of optimization models addressing economic goals.
A benchmark analysis between the proposed paper and the
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4936 The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
other existing optimization models in literature address-
ing product platform design is proposed in Table1, to
highlight the main differences in the models’ objective
functions and general structure. Table1 reports the target
of each optimization model and classifies their formulation
as single- or bi-objective, the considered platform strategy
as single- or multi-platform, and the final output provided
by the model application.
Hence, in such a cost-driven scenario, this paper con-
tributes to applied research in mass customization manage-
ment, proposing and applying an innovative bi-objective
optimization model to best balance the platform storage
cost and the platform customization time. The proposed
model adopts a multi-platform strategy, getting as output
their number, configuration, and the association of each
final variant to the obtained platforms. A further output
is the assignment of the most suitable production strat-
egy to each variant among MTS, MTO, and DPD. The
bi-objective formulation and the panel of information, i.e.,
output, provided by the model are elements of innovation
compared to the already existing optimization models on
product platform design, as highlighted in Table1. The
problem statement and the model formulation are in the
next Section3.
3 Problem statement andanalytic model
formulation
The use of product platforms allows to split the customer-
dependent customization activities, managed through a
MTO strategy, from the standard platform production phase
performed using an MTS strategy. Because the platforms
are stocked and, finally, customized after the arrival of the
customer order, an industry adopting this hybrid strategy
takes benefits from both MTS and MTO. Compared to MTS,
the storage of semi-finished products allows the company to
reduce the fixed economic value of the stocked items and the
risk of obsolescence, and to save space, thus resulting in a
lower overall management and storage cost. In the same way,
the use of platforms brings benefits compared to a MTO
strategy because it allows to respond quickly to the custom-
ers’ requirements through the customization of an already
available standard item, i.e., the platform, for the product
variants.
The structure of the platforms has a great impact on
the above-mentioned costs and times, bringing the DPD
closer to MTS or MTO. In fact, “small” platforms com-
posed by few components generate lower storage costs
with the drawback of a longer customization time, typical
Table 1 Literature contribution classification (SOO, single-objective optimization; BOO, bi-objective optimization)
Paper Model target Problem
formulation
Platform type Model output
SOO BOO Single-platform Multi-platform Platform
number
Platform
configura-
tion
Platform-var-
iant assign-
ment
Variant
produc-
tion
strategy
Zhang etal. [59] Development cost,
sourcing cost
✓ ✓ ✓ -
Ben-Arieh etal. [5] Platform production
cost, platform cus-
tomization cost
✓ ✓ ✓ ✓ ✓ -
Hanafy and
ElMaraghy [19]
Platform production
cost, platform cus-
tomization cost
✓ ✓ ✓ ✓ ✓ -
Hanafy and
ElMaraghy [21]
Assembly station
number
✓ ✓ ✓ ✓ -
Wang etal. [54] Carbon performance
platform configura-
tion
✓ ✓ ✓ -
ElMaraghy and
Moussa [14]
Platform production
cost, platform cus-
tomization cost
✓ ✓ ✓ ✓ -
Zheng etal. [61] Platform production
cost
✓ ✓ ✓ -
This paper Platform storage cost,
platform customiza-
tion time
✓ ✓ ✓ ✓ ✓ DPD/
MTS/
MTO
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4937The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
of a MTO strategy. On the other side, “big” platforms have
structures close to final products resulting in higher stor-
age costs but shorter customer response time, similarly
to MTS. In this context, this paper proposes a novel bi-
objective optimization model to best manage the trade-off
between the platform storage cost and the platform cus-
tomization time to get the final variants.
The starting point of the model is the analysis of the work-
ing cycles of a range of product variants given their market
demand. Each product variant is obtained through assembly
tasks of its specific set of components following the mount-
ing cycle and the precedence constraints. Due to its defini-
tion, the creation of a product platform involves the initial part
of the product working cycles containing standard interfaces
and modules [9]. Therefore, product variants can be derived
only from product platforms whose working cycle involves the
same components and precedence relations from the begin-
ning. Moreover, product variants sharing the initial part of
their working cycle are good candidates to be obtained by the
same platform. The customization phase is performed through
assembly and/or disassembly tasks of components according
to the variant-specific precedence relations. Considering both
assembly and disassembly tasks provides a greater flexibility in
the customization of the platforms and facilitates the associa-
tion among platforms and the derived product variants [19, 20]
Following the DPD strategy, the product platforms are
produced and stocked to be available for customization at
the customer order arrival, i.e., MTS. The stock coverage
method is used to define the target quantity of platforms
to store satisfying the product variants demand during the
reference timespan [25, 46], [52]. This method allows to esti-
mate the period during which the company will be able to
fulfil orders without producing or purchasing new products
or, conversely, to estimate the quantity of stock to held in the
company warehouse to fulfil orders for a specific period, i.e.,
the coverage time.
The proposed model returns the assignment of the most
suitable production strategy to each variant among MTS,
MTO, and DPD strategies. In the case of DPD selection, the
model specifies the optimal mix of product platforms, their
structure, the assignment of each product variant to the most
suitable platform to minimize the storage cost on one side,
and the customization time on the other side. Otherwise, in
the case of variants managed through the MTS strategy, plat-
forms identical to such variants will be generated, while in the
case of variants managed through the MTO strategy, empty
platforms will be created and assigned to those variants.
According to the literature and the industrial practice, the
proposed model lies on the following assumptions, validated
by previous studies [5, 9, 13, 16, 19, 20, 39]:
• The production mix is known, as well as the working
cycles of each product variant.
• The demand of each product variant in the reference
timespan is known and deterministic.
• The customization of a product platform is obtained
through both assembly and disassembly tasks.
• Assembly and disassembly times for customization are
known and deterministic.
• Components’ purchasing cost and the cost for the assem-
bly tasks to create a platform are known and deterministic.
• The upper limit to the number of platform types is equal
to the production mix size.
• Product platforms are produced and stocked following
the MTS strategy, while the customization components
are managed according to the MTO strategy; the custom-
ization components are assumed to be always available
when needed, following a Just in Time (JIT) strategy,
with no stock presence.
• The warehouse capacity is assumed to be large enough
to host all the platform storage quantities.
About the assumptions, input data used to feed the
model can be collected directly from the field, e.g., cus-
tomer forecast database, product Bill-of-Materials (BOM),
and company Material Requirement Planning (MRP), while
assumptions about product platform management policy are
validated by both previous literature studies and by several
real industrial company applications presented in Section1,
justifying their validity from the practical point of view.
The model explores the trade-off between the platform
storage cost and their customization time to get the final
variants. Since a product variant is manufactured through
assembly operations and the customization components
are managed following a JIT strategy with no stock, the
adoption of a DPD or MTS strategy to produce a variant
results in a storage cost due to the need to keep in stock the
associated platform or the finished variant. The production
costs are not included in the economic objective function,
because they coincide for the three considered production
strategies, i.e., MTS, MTO, and DPD, as well as different
costs and benefits derived from the use of platforms (Van
den [53]).
The following notations are introduced:
Indices
Product platform index p=1, ... V
Component index c,d=1 ..., C
Product variant index v=1, ..., V
Parameters
ACc
Assembly cost of component c to create a platform
(€/pc)
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4938 The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
AT c
Assembly time of component c for the customiza-
tion activities (s/pc)
BOMcv
⎧
⎪
⎨
⎪
⎩
1
if variant v includes component c in the
BOM,
0otherwise

Cc
Cost of component c (€/pc)
Dv
Demand of variant v (pcs/month)
DT c
Disassembly time of component c for the customi-
zation activities (s/pc)
I Stock cost rate (%)
Pvcd
⎧
⎪
⎨
⎪
⎩
1
if component d immediatly follows
component c in variantv,
0otherwise 
SCv
Stock coverage time of variant v (days)
wd Working days per month (days/month)
Decisional variables
aspcv
⎧
⎪
⎨
⎪
⎩
1
if component c has to be assembled to
platform p to produce variantv,
0otherwise

dspcv
1if component c has to be disassembled from
platform p to produce variantv,
0otherwise

qcp
⎧
⎪
⎨
⎪
⎩
1
if component c is already assembled in
platform p,
0otherwise

upv
{
1if variant v uses platform p
,
0otherwise 
3.1 Objective functions
The first objective function minimizes the customization
time. The first term considers the assembly time of customi-
zation components to the platforms, while the second term
considers the disassembly time.
The second (non-linear) objective function minimizes the
storage cost. The unitary platform storage cost is obtained by
(1)
𝜓
T=
V
∑
v=1
P
∑
p=1
C
∑
c=1
ATc⋅aspcv ⋅Dv+
V
∑
v=1
P
∑
p=1
C
∑
c=1
DTc⋅dspcv ⋅D
v
multiplying the stock cost rate and the platform manufacturing
cost that includes the purchase cost of the platform compo-
nents and the assembly cost to create the platform. Following
the stock coverage method [2, 25, 46, 52], the coverage time,
i.e., the amount of time the warehouse can meet customer
requests by using the available parts,
SCv
, is multiplied by
the consumption rate estimated through the variant demand.
The model is subject to the following feasibility constraints:
Equation(3) assigns each variant v to one and only one
platform p.
Equation(4) admits the assembly of a component c to a
platform p only if variant v is assigned to the platform.
Equation(5) admits the disassembly of component c from
a platform p only if the variant v is assigned to the platform.
Equation(6) manages the platforms customization activi-
ties through assembly. It forces the assembly of a component
c to a platform p to get the variant v, assigned to the platform
and requiring c according to its BOM, if it is not already
included in the platform.
Equation(7) manages the platform customization activi-
ties through disassembly. It forces the disassembly of a com-
ponent c from a platform p to get the variant v, assigned to
the platform and not requiring c according to its BOM, if it
is included in the platform.
Equation(8) ensures the manufacturing of a platform
according to the precedence constraints among components.
In particular, it allows the assembly in a platform of a compo-
nent d that follows a component c according to the BOM of a
variant v, only if c is already included in the platform.
(2)
𝜓
C=
V

v=1
P

p=1
C

c=1
I⋅

Cc+ACc

⋅qcp ⋅upv ⋅Dv
wd
⋅SCv

(3)
P
∑
p
=
1
upv =1∀
v
(4)
aspcv
≤
upv ∀p,∀,∀v
(5)
dspcv
≤
upv ∀p,∀c,∀v
(6)
aspcv
≥
upv +BOMcv −qcp −1∀p,∀c,∀v
(7)
dspcv
≥
upv +qcp −BOMcv −1∀p,∀c,∀v
(8)
qcp ≥Pvcd
⋅
upv +qdp −1∀p,∀v,∀c,d=1, …,C
(9)
V
∑
v=1
upv ≥qcp ∀p,∀
c
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4939The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
Equation(9) prevents the manufacturing of an empty plat-
form that is not associated to any product.
Finally, Eq. (10) gives consistency to the decisional
variables.
To get a linear optimization model,
𝜓C
is linearized using
the linearization scheme proposed by Watters [55] and Peter-
son [44]. The linearization procedure is summarized in the
Appendix. In the next Section4, the introduced bi-objective
model is applied to a reference case study representative of
an operative context showcasing its use in industry.
4 Case study
A case study inspired by the electronic components sector is
used to exemplify the use of the bi-objective model. The rep-
resentative company supplies different buyers with a wide
variety of products, adopting an MTS strategy to keep a high
service level. However, due to the introduction of custom-
ized variants and to the increased unpredictability of the
market demand, the company is experiencing some difficul-
ties in the warehouse management. Exploratory interviews
with production and logistics managers revealed a con-
gested warehouse, where the storage space on the shelves is
exhausted, and the company is starting to use the floor. This
issue affects the variant searching and picking time, hence
the overall customer lead time. Thus, the company is con-
sidering the adoption of hybrid production strategies such
as the DPD, using product platforms to manage in a better
cost- and time-efficient way the range of product variants
offered to customers. Without loss of generality, a scaled
version of the production mix is considered, for simplicity,
gathering data from company’s ERP and omitting further
details that are confidential.
The production mix includes 15 product variants
(
V=15
), assembled through a different combination of 12
available components (
C=12
). The BOMs of the variants,
named from V1 to V15, with precedence constraints, are in
Fig.2. The components are indicated by letters from A to N.
The precedence constraints involve components at differ-
ent assembly levels. As an example, in product variant V1,
the assembly of components H, I, and N can start only if
component C is already present, regardless on the presence
of components D and E. Moreover, there are no constraints
among components H, I, and N. The introduced parameter
Pvcd
models this input data.
The other input data used to feed the model are as follows:
– The stock coverage time
SCv
is of 3 days for all the prod-
uct variants.
(10)
qcp,aspcv ,dspcv,upv binary ∀p,∀c,∀v
– The assembly cost
ACc
of component c to a generic plat-
form is assumed equal to 2 € on average for each compo-
nent.
– The assembly time
AT c
of component c for the customi-
zation activities is, on average, 50 s for each component.
– The disassembly time
DT c
of component c for the cus-
tomization activities is estimated as a share of
AT c
, i.e.,
28 s for each component.
– The stock cost rate is assumed to be 20% of the total cost
of the related item, i.e., a product variant or a platform.
Finally, the monthly demand for each product variant and
the purchasing cost of each component are in Tables2 and
3, respectively.
The model and the case study data are coded in AMPL
language and processed adopting Gurobi Optimizer© v.5.5
solver over an Intel® Core™ i7-3770 CPU @ 3.40GHz
and 16.0GB RAM workstation. Within the set of existing
methodologies and approaches in the field of Multi-objective
Optimization (MOO), the Normalized Normal Constraint
Method (NNCM) proposed by Messac etal. [35] is used to
define the Pareto frontier. This curve is the locus of points,
within the solution space, that are not dominated by any
other point. For any point of the frontier, improving an
objective function without worsening the performance of
the other is not possible. The coordinates of each point of
the Pareto frontier include the values of the customization
time, i.e., Eq.(1), and the storage cost, i.e., Eq.(2), objective
functions. The solving time to get each Pareto point ranges
between 30 and 50s.
4.1 Pareto frontier
Figure3 presents the obtained Pareto frontier. The red points
of the curve are the so-called anchor points, i.e., the single
objective function optima, while the other non-dominated
points are in blue, representing the efficient solutions for the
considered case study.
AP1 is obtained by solving the model, using the objective
function
𝜓C
. The minimum storage cost for this solution is
0 €, while the customization time takes 449.5h. AP2 mini-
mizes the platform customization time objective function
𝜓T
, obtaining 0h and generating a storage cost of about
795 €.
The coordinates of the 21 non-dominated points defin-
ing the Pareto frontier, listed from S1, i.e., AP1, to S21,
i.e., AP2, are calculated. These points represent efficient
solutions best balancing the time and the cost objective
functions.
According to the existing literature on the topic [7, 35],
the choice of the final solution along the Pareto frontier fol-
lows an informal approach. In this paper, the adopted cri-
terion is the minimum normalized Euclidean distance from
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4940 The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
the Utopia Point, i.e., the point with time and cost optima
as coordinates [10]. The time and cost objective functions’
values for the Pareto points, together with the corresponding
Fig. 2 Set of precedence relations for the considered product variants
Table 2 Monthly demand Product vari-
ant v
Dv
(pc/month)
V1 500
V2 420
V3 650
V4 390
V5 700
V6 620
V7 360
V8 100
V9 265
V10 170
V11 80
V12 65
V13 300
V14 195
V15 250
Table 3 Purchasing cost for
each component Component c
Cc
(€/pc)
A 12
B 9
C 8
D 4.5
E 5.5
F 10
G 6
H 6
I 9
L 8
M 3
N 4
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4941The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
normalized Euclidean distances from the Utopia Point, i.e.,
in this reference case the origin of axes, are reported in
Table4.
According to this criterion, the final selected point is S11
(in green in Fig.2), rising as the point characterized by the
minimum normalized Euclidean distance from the origin of
axes, thus, the point best balancing the opposite trend of the
two divergent objective functions. Compared to AP2, the
selected point allows a cost reduction of about 52%, accept-
ing, at the same time, a time increase from 0h, i.e., the time
AP, to about 214h.
4.2 Discussion
As explained in Section3, the model assigns a product vari-
ant to a platform, jointly determining the platform struc-
ture and the components that have to be assembled and/or
disassembled to/from the platform for the customization
activities.
The solution associated to AP1 refers to the minimiza-
tion of the economic objective function. To minimize the
costs associated to the platform storage, the model does not
assign any components to the platforms, resulting in empty
platforms with all the product variant-related components
that have to be assembled after the arrival of the customer
order. This solution corresponds to the implementation of a
full MTO strategy, where no platforms are mass-produced
and stocked in advance and the production of the product
variants starts when needed, assembling all the related
components.
On the opposite, the solution associated to AP2 corre-
sponds to the adoption of a full MTS strategy. The minimi-
zation of the customization time leads to the configuration
of platforms containing all the components needed to get
Fig. 3 Case study, Pareto frontier
Table 4 List of the non-dominated Pareto point coordinates with nor-
malized Euclidean distance from the Utopia Point
Pareto point Time objective
function (h)
Cost objective
function (€)
Normalized
Euclidean
distance
AP1, S1 449.47 0 1
S2 419.86 26.43 0.9253
S3 394.90 62.42 0.8750
S4 372.47 102.98 0.8299
S5 349.72 141.34 0.7935
S6 327.60 181.30 0.7526
S7 303.45 218.49 0.7227
S8 281.40 258.83 0.6964
S9 258.44 298.05 0.6768
S10 236.31 338.41 0.6670
S11 213.92 378.51 0.6647
S12 190.02 419.08 0.6684
S13 169.47 458.88 0.6823
S14 147.56 499.54 0.7036
S15 127.08 542.88 0.7263
S16 103.95 581.46 0.7582
S17 80.50 619.50 0.7971
S18 59.43 662.00 0.8391
S19 41.72 709.55 0.8898
S20 18.55 749.00 0.9378
AP2, S21 0 795.34 1
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4942 The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
the assigned product variant, removing the second time-
involving phase of component customization by assembly
and/or disassembly. According to the above-mentioned
model assumptions, such complete platforms are produced
and stocked before the arrival of the customer order, which
corresponds to mass-produce final product variants using
an MTS strategy.
Intermediate Pareto points correspond to balanced solu-
tions, where the production mix is manufactured using a
combination of the three considered strategies, i.e., DPD,
MTS, and MTO. Figure4 presents the trend of the assign-
ment of the production strategies to the product variants in
each Pareto point, i.e., in each point, the number of variants
in the production mix managed by MTS, by MTO, and by
DPD. Moving from AP1 to AP2, the number of variants
managed through the MTO strategy decreases, from the
whole production mix in AP to 0 from S19. On the other
hand, the adoption of the MTS strategy follows a reverse
trend, starting with 2 variants in S8 up to 15 variants in AP2
solution. The number of variants adopting the DPD strategy
follows an erratic trend, varying from 0 in the AP, due to the
reasons already discussed above, to the maximum of 11 in
S16 solution.
Focusing on the selected trade-off point, i.e., S11, Table5
shows the platform structure, while Table6 shows the plat-
form-variant association as well as details about the customi-
zation activities to perform to get the final variants.
As a point located in the central part of the frontier, S11
refers to the adoption of a multiple production strategy
involving at the same time empty, complete, and custom-
izable platforms corresponding to the adoption of MTO,
MTS, and DPD production strategies, respectively. Prod-
uct platform PL7 rises as an empty platform, associated to
five product variants (V2, V3, V9, V10, V13). Hence, its
production is managed through an MTO strategy, assem-
bling all the components according to the variant BOMs
after the arrival of the customer order. The MTS strategy is
adopted to manage V8, stocking platform PL4 without any
further customization activities to perform. The remaining
nine product variants are managed through the DPD strategy,
assembling from 1 to 6 additional components to eight dif-
ferent platforms to get the final product variants. Following
Fig. 4 Product strategy assignment
Table 5 Platform configuration
for the selected Pareto point Platform Platform
components
(
qcp
)
PL1 A C D E N
PL2 C G H N
PL3 B E F L N
PL4 A D E
PL5 B D E F L N
PL6 B F H N M
PL7 -
PL8 A E M
PL9 E F
PL10 E F N M
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4943The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
the definition of product platform, different variants can be
obtained from the same platform, adapting the common
base, i.e., the platform, by assembling specific customiza-
tion components. This possibility is evident in platform PL8.
According to their BOM in Fig.1, the personalization for V4
requires the assembly of H, I, and N components while V12
is obtained by adding just H and N. As a recap, compared
to the initial situation in which the company stored, i.e.,
fully MTS, 15 variant types, in this new configuration, the
company stores eight platform types managing nine variants,
while one variant is produced through MTS and five through
MTO. Globally, nine-item types (eight platforms + one final
MTS variant) are stocked, getting a variety reduction com-
pared to the initial situation of about 40%. This is a relevant
result in the company under consideration, since it allowed
to keep stock under control, to reduce storage space utiliza-
tion, providing, at the same time, better results in terms of
customer lead time reduction.
A further consideration concerns the lack of disassembly
customization activities, as highlighted in Table5. Given the
parameter values of the considered case study, the model
does not use customization by disassembly to avoid the high
costs generated by the storage of platforms with unnecessary
components. According to [19, 20], the industry-specific
conditions promoting the use of disassembly tasks are the
low cost of components and the high cost of the assembly
activities. In addition, decreasing the number of feasible
platforms, set equal to the number of product variants in
this case study, could lead the model to assign more variants
to a platform, resulting in an increased use of disassembly to
derive the final product variants.
A limitation of this study deals with the possibility to
use disassembly operations for platform customization.
To be able to disassemble a component, it is implicitly
assumed that specific kinds of processes like welding, braz-
ing, or gluing are not required for the platform and product
manufacturing. Excluding similar kind of processes leads
to non-destructive disassembles that do not reduce prod-
uct functionality and aesthetic appearance as well as do not
damage the disassembled components that, in this way, can
be re-used as new for other variants, avoiding additional pur-
chasing costs. However, this assumption limits the applica-
bility of the model to products belonging to different sectors.
Other possible limitations arose from the deterministic
assumptions of assembly and disassembly times and compo-
nents and assembly operations costs. Economies of scale and
scope resulting from the adoption of a production strategy
could affect the value of these parameters.
5 Conclusions andfurther research
Dynamic market demands and variable customer require-
ments increase the company product variety. Derived from
the introduction of the delayed product differentiation (DPD)
strategy, product platforms are adopted by several indus-
trial companies to face product variety management. The
literature widely discusses product platform design from a
primarily cost-driven perspective, hence asking to explore
quantitatively the trade-off between platform storage cost
and customization time.
This paper contributes to applied research in mass cus-
tomization management, proposing and applying a bi-objec-
tive model to optimize the platform storage cost and the time
to customize a platform into a final variant. A case study
from the electronic components sector exemplifies the use
of the proposed model supporting companies in managing
variety. Compared to the customization time anchor point,
i.e., AP2, the selected trade-off point allows a cost reduction
of about 52%, accepting, at the same time, a time increase
from 0h, i.e., AP2, to about 214h. At the same time, the
company experienced a variety reduction compared to the
initial situation of about 40%. This is a relevant result in the
company under consideration, since it allowed to keep stock
Table 6 Platform association to
variants, required customization
tasks, and strategy definition
Platform Associated product variant (
upv
) Components to
assemble (
aspcv
)
Components to dis-
assemble (
dspcv
)
Produc-
tion
strategy
PL1 V1 H I - DPD
PL2 V15 I - DPD
PL3 V6 C G - DPD
PL4 V8 - - MTS
PL5 V5 H I - DPD
PL6 V7 I L - DPD
PL7 V2, V3, V9, V10, V13 A C E G I N H M - MTO
PL8 V4, V12 H I N - DPD
PL9 V11 F L E - DPD
PL10 V14 F L E H N I - DPD
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4944 The International Journal of Advanced Manufacturing Technology (2025) 136:4933–4946
under control, to reduce storage space utilization, providing,
at the same time, better results in terms of customer lead
time reduction.
Future research deals with the inclusion of relevant issues
not considered at this stage as limitations in the number of
feasible platforms to analyze the effect on their structure and
on the product variant assignment. Moreover, the impact of
disassembly tasks for final customization on reverse logistics
activities needs to be analyzed.
Appendix
According to Peterson [44] and Watters [55], given two mul-
tiplied linear variables z and x, with z being non-negative
and upper bounded by M, then their product can be replaced
by a linear variable y subject to the following additional
constraints:
This scheme is applied to the presented model, replac-
ing the couple of multiplied variables
qcp
and
upv
in Eq.(2)
with a new single variable
xpcv
and three sets of related con-
straints, with upper bound M value equals to 1 due to the
binary nature of the decision variables. The introduced vari-
able and the linearized cost-related objective function that
replaces the original one are reported below:
The following list of constraints, required for the cost
objective function linearization, completes the model
formulation.
(11)
Mx ≥y
(12)
y
≥
z+M(x−1)
(13)
z≥y
(14)
x binary
(15)
xpcv
=qcp
⋅
upv
(16)
V

v=1
P

p=1
C

c=1
I⋅

Cc+ACc

⋅xpcv ⋅Dv
wd
⋅SCv

(17)
qcp ≥xpcv ∀p,∀c,∀v
(18)
xpcv ≥qcp +upv −1∀p,∀c,∀v
(19)
upv
≥
xpcv ∀p,∀c,∀v
(20)
xpcv binary
∀
p,
∀
c,
∀
v
Funding Open access funding provided by Alma Mater Studiorum -
Università di Bologna within the CRUI-CARE Agreement.
Data availability The authors confirm that the data supporting the find-
ings of this study are available within the article and its supplementary
materials.
Declarations
Conflict of interest The authors declare no competing interests.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
included in the article’s Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in
the article’s Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will
need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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