AN APPROACH TO SUPPORT INTERDISCIPLINARY VARIANT
DIVERSITY OPTIMIZATION
Planning Variant Diversity – Beyond Complexity Reduction
Reiner Anderl, Sebastian Maltzahn and Daniel Spieß
Fachgebiet Datenverarbeitung in der Konstruktion (Computer Integrated Design), Technische Universität Darmstadt
Petersenstraße 30, 64287 Darmstadt, Germany
Keywords: Variant diversity, Variant decision, Planning diversity, Decision support.
Abstract: The increasing number of variants in manufacturing companies’ product ranges leads to rising costs due to
process and product complexity. The expected profit of higher diversity is often overrated while its costs are
underestimated because of missing methods and insufficient process transparency. This paper introduces a
methodical approach to identify the optimal diversity considering available capacities and the effects on
profit and costs for each variant to support variant decisions within the product and process planning.
Therefore a mathematical model of the described diversity planning problem is developed. This complex
decision problem is solved using a particle swarm algorithm, which is able to compute the optimal solution
within reasonable time. The found solutions can be discussed and evaluated by an interdisciplinary planning
team considering even qualitative aspects, leading to an increased transparency in the decision process.
1 INTRODUCTION
Manufacturing companies have to take great
challenges in a globalized competitive environment.
To face these challenges most European companies
follow the strategy of differentiation to improve their
competitive situation. This differentiation strategy
leads to greater variant diversity in the companies’
product ranges. Higher diversity causes higher
complexity in involved business and manufacturing
processes due to the increasing number of different
items which are to be handled. Furthermore national
norms, standards and laws, as well as differentiated
customer requirements enforce globally operating
companies to develop country-specific product
variants.
On the one hand companies benefit from variant
diversity because of increasing sales. On the other
hand increasing diversity means more complexity in
all business and manufacturing processes.
Complexity in turn leads to increasing costs because
the capacity of each involved department has to be
expanded. These costs rise exponentially with
increasing variant diversity. In contrast, benefits
have a concave development (Alders, 2006).
Figure 1: Optimum diversity regarding benefits and costs.
Figure 1 shows that the optimal diversity lies in
between the two extrema of very high and very low
variant diversity. In fact the optimum diversity is
characterized by the maximum difference between
benefits and costs. Finding this maximum resultant
value is a typical decision problem. In the following
we characterize this problem in the context of an
interdisciplinary product planning process. Our
approach is to support this decision process with the
methods of Operations Research. For this purpose
we describe the problem mathematically and will
show that solving this mathematical problem with
408
Anderl R., Maltzahn S. and Spieß D. (2009).
AN APPROACH TO SUPPORT INTERDISCIPLINARY VARIANT DIVERSITY OPTIMIZATION - Planning Variant Diversity – Beyond Complexity
Reduction.
In Proceedings of the International Conference on Knowledge Engineering and Ontology Development, pages 408-411
DOI: 10.5220/0002295404080411
Copyright
c
SciTePress
the help of a particle swarm algorithm promotes the
optimal decision under given constraints.
2 PROBLEM DESCRIPTION
Variant decisions are the result of a multilevel
problem solving process (Heina, 1999). First of all
the sales department performs a market analysis to
identify customer needs. Taking into account the
sales volume of previous products and forecasts for
the new product, the sales department proposes
different “variant scenarios” (Alders, 2006). Though
these scenarios imply a combination of different
product variants they often have the same diversity.
These scenarios are then analysed and evaluated by
an interdisciplinary team in terms of profits and
costs. This process may take up to one week for only
one part or assembly. It is assumed that most of the
time is wasted with recurring discussions about
capacities and costs (Alders, 2006).
The variant decision process is often dominated by
the sales department because of their knowledge
about markets and customer demands. The sales
department benefits from higher product diversity
through increasing volumes but does not bear the
costs of the increasing process complexity, like for
example the departments of production and logistics.
This is the reason why benefits of additional variants
are often overrated while their impact on process
complexity and costs is underestimated
(Rathnow, 1993).
Moreover, as human capacity is limited, only a
few alternative scenarios can be analysed. It is
unlikely that the optimal solution is one of these.As
a result, this process tends to expand production
capacities and human resources instead of
questioning the demand for a variant.
In the following we introduce an approach to
solve these problems with the help of a decision
support system.
3 SUPPORTING
INTERDISCIPLINARY
VARIANT DECISIONS
Our approach is based on the variant decision
process described in section 2. To avoid recurring
discussions about capacities and costs we propose to
support this decision process by a decision support
system (DSS). This system analyses and evaluates
the whole solution space of the variant decision
problem simultaneously, instead of discussing three
or four “scenarios” sequentially. The required data,
profits and costs are still forecasted by the experts of
each department (cf. section 2). Based on this data
we introduce the Interdisciplinary Variant
Optimization Model IVOM. This mathematical
description of the variant decision problem allows
computing the optimal diversity considering all
effects on business profits and given capacity
constraints.
Decision problems are represented
mathematically by optimization models. They
consist of an objective function
which has to
be minimized or maximized and one or more
constraints which define the possible solution
space of that particular problem either by equations
or inequations.
(1)
,
,
;
(2)
Based on this general optimization model we
define the Interdisciplinary Variant Optimization
Model IVOM as a specialized knapsack problem.
3.1 The Interdisciplinary Variant
Optimization Model (IVOM)
IVOM represents the variant decision problem
described in section 2. The objective of the variant
decision problem is the identification of the
optimum diversity given by the maximum difference
of profits and costs. According to formula (1) the
objective function of IVOM is
(3)
Where x is a binary variable to decide whether
variant j=1,...,n is selected or not. The resultant
value of a variant is given by the difference of its
profit n and its costs c (cf. Figure 1):
; (4)
The indices i and j specify that variant j causes
costs in the departments i=1,...,m.
At first, we want to define the optimum diversity
for the given capacities. In a second step one could
discuss the expansion of specific capacities
AN APPROACH TO SUPPORT INTERDISCIPLINARY VARIANT DIVERSITY OPTIMIZATION - Planning Variant
Diversity - Beyond Complexity Reduction
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considering this method’s results. The given
capacities of the involved departments are
represented by constraints in the form of
inequations. In general, a constraint for a capacity
l=1,...,u is defined as shown in formula (5).
(5)
K is the limit of capacity l. The variant j exploits
units of capacity l. We call the capacity driver
of variant j. This inequation assures that the chosen
variants (x=1) do not exceed the capacity limit.
Inequations can be defined by the experts of each
department for all kinds of limited capacity
(e.g. storage capacity, machine time). To enhance
transparency, the data and the capacity constraints
should be published. The constraint that affects all
involved business processes is human ressource.
Hence, we introduce the manpower-constraint
exemplarily.
Increasing diversity strains human resources.
That is why the given manpower resources are a
very important constraint.
The mathematical definition of the manpower-
constraint is defined as follows:
_
_
(6)
For human resources both, time and transaction
drivers can be taken into account:
and
.
Normally a work step is characterized by the time
that is needed to accomplish it. Sometimes,
especially for administrative tasks, this cannot be
detected separately. A time lump-sum per
transaction is needed. Potential units for the capacity
drivers as well as the capacity limit K are man-day,
man-month or man-year.
In the same manner we defined transaction and
stock constraints for the purchasing and logistics
department. A special stock constraint for the
production area considers the limited space for
different variants in an assembly area to avoid
special picking areas:
·
(7)
For assembling, variant j is provided in a
standard box that occupies the space d. In
conjunction with the number of boxes (z) that have
to be provided for variant j and the total space
available K, this constraint assures that the
production area does not need cost-intensive picking
areas.
And finally we defined a production constraint to
take machine hours and set-up time into account.
Many more are imaginable for different problems.
3.2 Solving IVOM
At this stage the variant decision problem is split and
formulated in the objective function and the
constraining inequations. In the next step the
described model of the variant decision problem has
to be solved by an applicable algorithm.
Algorithms were developed for different types of
problems. First of all we have to characterize IVOM
as a specific problem type. Secondly we select one
of the possible algorithms for this type of problem
that promises the best and efficient solution.
The variant decision problem as it is represented
by IVOM is a special knapsack problem. It has more
than one constraint; strictly it might have multiple
constraints for every department and all kinds of
capacities. This type of problem is called a
multidimensional knapsack problem
(Kellerer, 2004).
Concerning its computing time, a study by
Kennedy and Spears (Kennedy, 1998) came to the
conclusion that particle swarm algorithms are most
suitable for complex multidimensional binary
problems. Hence, to find the optimum solution of
IVOM we used a particle swarm algorithm.
3.3 Qualitative Aspects of the Variant
Decision
After IVOM is properly defined for a given variant
decision problem the swarm algorithm is able to
identify its optimal solution. The found quantitative
optimal solution might be in conflict with qualitative
constraints, e.g. the brand image.
The proceeding of the particle swarm algorithm
allows saving several very good solutions, delivering
optimal valid solutions within the defined constrains.
In every step of the algorithm the best position of
each particle is saved. This arises the opportunity to
add a qualitative analysis made by the
interdisciplinary team after the algorithm identified a
set of the best solutions, giving optimal decision
support.
3.4 Decision Support through IVOM
The result of the IVOM approach is a list, consisting
of all valid, optimum solutions found by the particle
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swarm algorithm. Every solution is described by its
values for the parameters and the objective function,
which were calculated by the swarm particle at its
position in the solution space. For each solution the
consequences for the company, explicit the benefits,
the costs and needed resources in general can be
calculated. The list can be used to discuss all options
by the decision team, to consider undefined
constraints like e.g. corporate strategy.
4 CONCLUSIONS
Current strategies of complexity reduction and
complexity control are time consuming, recurring
and often do not take all major constraints into
account. Especially in interdisciplinary teams the
team members trade for their own account with their
own perception of possible solutions (e.g. the sales
department). Finding the optimal diversity is a key
factor for success for manufacturing companies in
today’s globalized competitive market. We achieve
this by substituting sales department’s perception by
an impartial algorithm, based on interdisciplinary
expert knowledge. The optimal solution for a
company as a whole can be identified. Preventing
complexity by planning variant diversity in early
development phases of a product has the potential to
design future product lifecycles much more efficient.
It allows concentrating on the optimal variants,
rather then spending much time and assets in the
development and sale of barely demanded variants.
In this paper we presented the mathematical
concept, we called “Interdisciplinary Variant
Optimization Model” (IVOM), to define given
constraints in diversity problem discussions, as well
as the definition of an objective function which
allows computing the optimal diversity considering
all effects on business profits and costs. The
proposed particle swarm algorithm is capable not
only to find the best solution, but even computes and
stores local optima and delivers multiple very good
solutions. These can be discussed in interdisciplinary
decision teams, concerning even qualitative aspects.
IVOM has a major impact on decision making
processes to find optimal diversity and thus reducing
complexity within the whole product lifecycle. It
deliveres qualitative solutions within the solution
space in reasonable time and highly supports
decision discussions, allowing to elaborate the
consequences of the expansion of capacities or the
cancellation of a product variant.
REFERENCES
Alders, K., 2006. Komplexitäts- und
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Produkte - Komplexität beherrschen in Entwicklung
und Produktion. Springer Berlin et al.
Rathnow, P., 1993. Integriertes Variantenmanagement:
Bestimmung, Realisierung und Sicherung der
optimalen Produktvielfalt. Vandenhoek und Ruprecht
Göttingen.
Heina, J., 1999. Variantenmanagement - Kosten-Nutzen-
Bewertung zur Optimierung der Variantenvielfalt.
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Kellerer, H., Pferschy, U., Pisinger, D., 2004. Knapsack
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Kennedy, J., Spears, W. M., 1998. Matching algorithms to
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Diversity - Beyond Complexity Reduction
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