=Paper=
{{Paper
|id=None
|storemode=property
|title=Integrated use of linear programming and multiple criteria methods in an engineering design process
|pdfUrl=https://ceur-ws.org/Vol-696/paper2.pdf
|volume=Vol-696
}}
==Integrated use of linear programming and multiple criteria methods in an engineering design process==
https://ceur-ws.org/Vol-696/paper2.pdf
CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011
Integrated use of linear programming and multiple criteria methods in an
engineering design process
Maria Franca Norese (mariafranca.norese@polito.it), Ersilia Liguigli (ersilia.liguigli@polito.it)
Chiara Novello (chiara.novello@polito.it)
Department of Production System and Economics – Politecnico di Torino
Corso Duca degli Abruzzi, 24 – 10129 Torino, Italy
Abstract a specific legacy aircraft has to be updated in relation to
these needs, or to understand what kind of aircraft has to
In an aeronautical sector company, where engineering be designed or (at least partially) re-designed, in order to
design process steps and activities are developed, a guarantee its integration in the new SoS that the client
decision aiding methodology was required to support the
perceives as possible or essential for the future.
processes.
We have proposed the integrated use of linear The client's involvement in the initial phase of the
programming and multiple criteria methods, which can be design process is analyzed in the literature in "front end"
used to orient the conceptual design of alternative models of the product development process (see, for
functional and physical solutions and to cope with instance, Smith & Reinertsen,1992; Reinertsen,1999).
complex design problems. Some authors have focused on the concept phase of the
Linear programming has been used in relation to some process where, through the involvement of the client, it is
case studies, to generate design alternatives that satisfy the possible to obtain meaningful improvements (Clark &
set of the initial requirements, while multiple criteria Fuijmoto, 1991) and to resolve ambiguity and
methods have been proposed to interact transparently with
uncertainties in the customer’s requirements that may
the client, in relation to some aspects that a linear
programming model cannot include, to evaluate, compare
cause orientation difficulties (Smith & Reinertsen,1998).
and select alternatives in order to identify and formalize In aeronautics, a partial and apparently limited re-
new expectations that the first solutions have not be able to design requires years of work (five years on average) and
resolve. The iterative use of the two approaches, in a cyclic therefore uncertainty concerning the evolving nature of
procedure of mutual learning, allows the requirements to the client’s requirements is normally present, with an
be defined more clearly and a final satisfying solution to evident impact on the engineering design process. The
be reached. MBDD asked our research group for suggestions and
methods, in order to improve the interaction with the
Introduction client (who has to understand every step of the process
and freely propose his point of view), to reduce time and
Engineering design is an iterative decision-making
guarantee quality of the results, which can be solutions
process which is developed to devise a component,
and/or a better definition of the needs, objectives,
product, process or system that meets the customer’s priorities and future scenarios of aircraft use.
needs (Eggert, 2005). A collaboration with the Marketing We proposed the integrated use of two kinds of
and Business Development Department (MBDD), of a Operation Research methods, in relation to some case
company that designs and produces aircraft for civil and studies, and the cyclic use of the method application
military use, has allowed us to understand their main outputs, as new inputs for the other method application
conceptual design activities (Norese et al., 2008a; Norese (Belton & Stewart, 2002). Linear programming (LP) can
& Liguigli, 2009) and to propose an integrated use of be used to analytically define the constraints and
linear programming and multiple criteria methods in aspirations of a client, generate the widest set of design
order to aid engineering designers (by means of a logical alternatives that satisfy the initial requirements
framework that was used also in Alenia Spazio, 2004 and (admissible solutions) and calculate optimal solutions, in
Norese et al., 2008). relation to specific objectives. Multiple Criteria Decision
An aircraft is a complex system, but it can also be seen Aid (MCDA)1 models can be developed and MCDA
as a component of an even more complex structure, a methods activated iteratively, in order to transparently
System of Systems (SoS), in which different systems interact with the client. Alternative solutions, produced
communicate and work together to achieve specific by means of the previous LP application, can be analysed
targets. In an SoS, integration and synergic work may and evaluated, in relation to aspects that an LP model
vary from a simple collaboration, in which the single cannot include, such as the perception of a risk (of using
components work alone, to a situation in which the single a too innovative technology, or to generate new
components are not able to work in an autonomous way, complexity in the future maintenance problems, and so
when extrapolated by the SoS. on) in relation to a specific solution. Some client’s
The MBDD supports product development by requirements can be identified and formalized when a
managing the relationship with the client in the initial
engineering design process phase. The client’s needs 1
have to be identified, in order to decide whether and how More details can be found on the Euro Working Group
MCDA website: www.cs.put.poznan.pl/ewgmcda/
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CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011
solution is not compatible with expectations that were not performed to verify and, when necessary, to modify the
clear enough before the MCDA analysis and therefore design.
not included in the LP model. At this point, new In the conceptual phase of the design process, it may be
functional and organization limits may be included in the necessary to go back to a previous step at any point in the
LP model and the consistency of each solution should process. The chosen solution may prove to be
also be tested for these new constraints, in the new cycle unworkable for different reasons and may require
that it started, and so on until an acceptable solution is specification redefinition, new solution generation, the
reached. collection of more information or, in the worst situation,
The first section of the paper focuses on the iterative redefining the problem. This is a continuous and iterative
nature of the engineering design process and offers a process.
synthetic overview of the methods, theories and tools that Several tools are commonly used to aid designers.
are used by designers. Methodologies and theories that have been proposed in
In the second section, the problem, as perceived by the the literature, usually offer a more analytically rigorous
MBDD, is presented and, in the third section, a set support for engineering designers. Concurrent
covering model is proposed for the generation of design engineering may be the most practical methodology to
alternatives. improve the design process. The approaches that are
In the fourth section, some multiple criteria approaches most frequently suggested to obtain input from
are described, in relation to the evaluation of design stakeholders in the design process are the Pugh Method
alternatives, and the integrated use of two methods is (Pugh, 1990), Quality Function Deployment (Akao,
proposed to support communication with the clients, in 1997) and the Analytical Hierarchy Process (Saaty 1980;
order to better define their needs and expectations. The 1994), which always incorporate subjective judgments.
possible development of the procedure, in relation to Others are used to generate alternatives for designers,
more complex projects and decision contexts, is analysed such as TRIZ (Altshuller, 1988) and the C-K Theory
in the conclusions. (Hatchuel & Weil, 2009).
Problem Statement
Engineering design process The problem definition step, in the engineering design
Several theories and various tools are proposed in process, is critical when the client has to face an evolving
engineering design to aid designers in different ways: to situation and cannot clearly communicate needs that are
understand stakeholders’ needs, improve quality, address no well defined. This criticality is often present in
variability and uncertainty in the design process or aeronautics, where many years are required to create a
generate alternatives for designers. new aircraft, but also to innovate some elements of a
The engineering design process, as described by Eggert legacy system.
(2005), is structured in five steps: definition of the The problem definition step is developed in the MBDD
problem, gathering pertinent information, generating by anticipating some activities that pertain to the
multiple solutions, analyzing and selecting a solution and, successful steps of the process (as described in Eggert,
2005) and using them to acquire essential, but latent or
finally, testing and implementing the solution. A
fragmented, knowledge elements.
procedure of identifying and formally listing the
Clearly understanding the point of view of the client, at
customer’s requirements is usually present in problem a functional level but also in organization terms, is
definition, in order to define product functions and essential to identify and structure the requirements that
features. These activities are included in the first step of orient the design. The MBDD arrives at a complete
the described process, but in some cases problem problem definition through a procedure that involves the
definition is complicated and can be completed only organization of a client in a comparative analysis of some
when pertinent information is gathered. And generating promising draft solutions. These solutions are elaborated
and analyzing multiple solutions, with the involvement of in the MBDD, in relation to general technical
the client and some areas of the enterprise, is a way to requirements, and then the strength and weakness
obtain relevant information on the product design and elements of the solutions are discussed with the client or,
functional specifications. more precisely, with some organization-client key actors
Once at least the structural components of the design (for example, a pilot or whoever is in charge of
have been identified, above all with inputs from testing, maintenance).
manufacturing and marketing teams, the design team Even if the innovation is related to a single aircraft
generates alternative conceptual solutions that are component, the future use of the aircraft in an integrated
oriented in different ways to achieve predefined goals SoS has to be analyzed. Various types of aircraft, but also
(i.e. requirements that have to be satisfied). satellites and maritime or ground systems can be
Considering costs, quality and risk, as the main involved, in order to achieve an assigned target in
selection criteria, the most promising alternatives are missions of various kinds (i.e. military, civil or a
selected for a further analysis (Dean & Unal, 1992), combination of the two situations). Innovation is often
which enables a complete study to be made of the required in order to specifically facilitate coordinated
work and communication in the SoS.
solutions and elaboration of the final design
The MBDD procedure includes two subsequent stages:
specifications that best fit the requirements. A prototype
in the first one, some “functionally acceptable” solutions
is therefore constructed and functional tests are
are identified or elaborated, in relation to the
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CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011
functionalities that are required. In the second stage, the integrated assets can be seen as an SoS and both the
client’s attention is focused on these solutions, in order to performances of the assets and the relationships between
evaluate the associated costs (which are not only them allow the missions to be performed.
monetary), their economic sustainability and specific The purpose of the analysis is to define a mathematical
benefits and risks, as proposed in (Office of Aerospace model in which the variables are the different assets that
Studies, 2002). This analysis orients the elaboration of a can be activated to accomplish a mission. The
better solution for the client, but at the same time defines functionalities that have to be guaranteed (or guaranteed
the overall problem and identifies pertinent information at a required level), in relation to the “nature” of the
and/or information sources. A representation of how the mission, can become the constraints of the model.
cyclic procedure develops is proposed in Figure 1,with The different objectives, in relation to a specific
indications on the main activities that are included. decisional problem, can be: minimize the costs, maximize
In the last few years, some clients have required the use the effectiveness, minimize the risks of a mission and so
of an Operations Research tool, in order to facilitate on. A combination of assets that is acceptable because it
comparisons of the solutions in a multiple criteria guarantees the Required Level of Performance (RLP) for
analysis. Having found the tool very interesting, the each functionality (i.e. for each constraint of the model)
MBDD asked to our research group for a method to help becomes an admissible solution, which is called
the generation of “interesting” and acceptable solutions, architecture (of the SoS). The optimal solution is an
in order to reduce time and guarantee the completeness of admissible solution that minimizes (or maximizes) the
the acceptable solution set. We analyzed their use of the objective. If a single admissible solution does not exist,
tool and the weak and strong points of their applications. the need for a technological innovation (i.e. at least a
We then proposed the integrated use of LP and MCDA partially new asset) is underlined. A new product, or an
models in a procedure that fits the MBDD approach to improvement in a legacy system, satisfies the client’s
the problem, but also improves the interaction with the needs if all the missions that the client had proposed to
client, who can propose his point of view (in terms of describe his needs can be faced with a minimum cost.
limits of the solutions and opportunities that have to be The problem can be represented by a linear
stressed), in a simple but formal language, and who can programming model, if all the constraints and the
almost immediately analyze all the new solutions that are objectives are linear functions. If there is only one
consistent with the new vision. objective, the oldest and most famous method of
Operations Research, the Simplex method (Dantzig,
1963), can be used to obtain the optimal solution. If there
is more than one objective, the multi-objective linear
programming methods (Ehrgott & Wiecek, 2005) can be
used.
At the start of the model setting, the assets that have to
be included in the model and a list of functionalities, i.e.
the constraints of the model, are defined in relation to the
(generic or specific) request of the client and above all
using the Universal Join Task List (UJTL) Report2.
A complete list of about 720 functionalities, in terms of
ability to perform a task, is proposed in the UJTL Report,
in relation to the strategic, operational and tactical level
of mission in a military context. The UJTL was
developed for the U.S. Armed Forces, but it has been
used by several other countries and international military
organizations, such as NATO. The MBDD has structured
and adapted the Report to facilitate its use with the
clients. The MBDD synthesizes all the coordination,
monitoring and controlling functionalities for military
Figure 1: Cyclic procedure
missions in the Mission Management macro functionality
and Find-Fix-Track is the code that is used to indicate the
Linear programming application set of functionalities which, at different levels of detail,
The request of a client can be very generic and the real allow the area of interest to be patrolled, in order to
needs are not always easy to understand. In order to indentify and trace the target. Using this framework, xx
reduce uncertainty, a request can be expressed in terms of main functionalities, that have to be guaranteed in a
mission types that the new system (or asset) has to face, military mission, are always present as model
as a component of an SoS. constraints. When the mission requires a specific and not
From a technical point of view, an asset is a system that usual functionality or for non military missions, the UJTL
guarantees specific functionalities. The assets may be Report is used directly as a check list.
component parts of a single aircraft that have to be If the adopted objective is to minimize the number of
integrated to complete a mission, or to be integrated with assets that have to be involved in the proposed missions,
other assets in other aircraft or in systems that operate on the mathematical problem can be re-formulated in terms
the ground. The assets may also be specific kinds of of a set covering problem, which consists in finding the
aircraft (or other resources) that have to be activated
together in a specific mission. In all these situations, the
2
Report available on the www.dtic.mil website
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CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011
minimum number of service centers (in our model, the
assets) so that the request for each service (the guarantee
of a required level of a specific functionality) is covered
(Tadei & Della Croce, 2001).
In this mathematical model, the performance pij of the j-
asset for the i-functionality is compared with Si, the
RLP that has to be guaranteed for the i-functionality, in
order to define the covering matrix [tij], in which the
elements tij are equal to 1, if pij≥ Si, or equal to 0
otherwise.
The set covering problem can be formulated in the
following way:
Figure 2: Cost/effectiveness analysis
Min ∑ xj j = 1,…, m
∑tijxj ≥ qi i = 1,..., n xj={0,1}
The MBDD adopted a different approach when a client
where xj has a value of 1 when the asset is included in suggested the use of a multiple criteria method for the
the solution (which in this case, is an SoS architecture), comparison of the alternatives. The first application was
otherwise it is equal to 0. not totally satisfactory. Some other experiments allowed
The value of the redundancy, for each functionality the MBDD to realize that the correct approach has to
with redundancy (i.e. a critical functionality that requires involve structuring the evaluation model in macro aspects
more than one asset that is able to satisfy this task, in an that can be analysed separately by the organisation actors
SoS architecture), is equal to qi. For the others, qi is equal in charge of each specific aspect. At the same time, the
to 1. MBDD elaborated a way of translating each personal
We used Xpress-MP, version 2007 (Mosel 2.0.0, IVE judgment into an analytical function.
1.18.01, Optimizer 18.00.01), produced by DASH When we analysed the procedure they were using, we
Optimization, to treat models with a single mission or noticed that the results were very interesting, in relation
multi scheduled missions that are included in the model. to the first aim (improve communication with the client
For a multi missions model with 18 variables and 210 in order to understand his point of view and adequately
constraints, the application has provided six admissible model his requirements), but very poor as far as the
and three optimal solutions in 0.15 seconds. second (transparently arrive at the decision and
The model structure and the linear programming analytically document the decision motivations) was
application to the problem were tested in relation to some concerned. In fact, their analytical functions did not
previous military cases, where the solutions and their result to be consistent with either the original judgements
characteristics were well known for the MBDD. We or with the logical structure of the method. At the same
spent a great deal of time defining and modifying the time, their need to artificially construct evaluation
constraints, in order to have a better fit of some specific functions, after the application of the method and in order
requirements, but the immediate calculation of the to explicitly document the process, was analysed together
solutions facilitated convergence towards a good model. with them, to show them that the wrong method had been
The same procedure was then applied to a new case, in adopted.
relation to the surveillance of a critical sea canal. The There are many multiple criteria methods that can be
model development and PL application were accepted by used to aid decision making (see for instance, Belton &
the MBDD as effective steps of a procedure that can Stewart, 2002). It is necessary to choose among the
support communication with the client. various methods in relation to the specific requests of the
At this point attention was focused on the tool that decisional problem. In this case, they essentially are:
should be used to understand why a solution is not transparency of the process that elaborates a conceptual
adequate enough. solution; an objective way of expressing each evaluation
and, finally, a treatment of the uncertainty that affects
Multiple criteria approaches data and judgments.
We proposed the analysis of two methods, Analytic
The U.S. Air Force Center of Expertise for Analyses of Hierarchy Process (AHP) (Saaty, 1980; 1994) and
Alternatives (Office of Aerospace Studies, 2002) ELECTRE III (Roy, 1978; 1990), which were tested in
suggested a multiple criteria approach in which all the relation to the examined case studies. AHP is the method
aspects that are related to the effectiveness have to be that is already used by the MBDD with its SW tool,
analyzed and then synthesized in an overall judgment, in Expert Choice, which supports model structuring by
a transparent way. The different costs (which are not means of an easily visualization of the organizational
necessary monetary) of each solution have to be aspects, scenarios, problem dimensions and model
identified and synthesized in an overall cost. Every criteria. A sensitivity analysis facilitates the identification
solution can be graphically shown in a two axe diagram of model weakness elements and the consequent
(see Figure 2) where, as is natural, the most effective improvement or re-structuring of the problem and/or the
solution is also the most expensive. One or more multiple criteria model. An analytical evaluation of the
acceptability thresholds can be introduced to facilitate a solutions is not required. Comparative judgments are
decision that is not easy to make. used both to assess the solutions and calculate weights for
the compensatory synthesis procedure.
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CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011
In the ELECTRE III method, unlike AHP, the relation to the defined problem, when a decision has to
alternatives have to be evaluated in relation to all the activate the subsequent design process phases.
criteria in an explicit and (as much as possible) objective In the examined cases, the aircraft and the other
way. Thresholds are introduced when uncertainty is systems were under production, or at least in the final
present in some evaluations, to limit the negative effect phases of the production process, and the nature of the
of the uncertainty on the results. Criteria can have missions was clear, since the MBDD knows the decision
different degrees of importance and, in this case, context very well. Therefore, the principal aspects of the
coefficients of relative importance of the criteria have to evaluation problem were easily identified (SoS
be introduced. performance in relation to the operational scenarios of the
ELECTRE III starts by comparing each solution with missions, technical effectiveness in relation to the
each of the other solutions. A fuzzy outranking relation, operational management process and life cycle costs) and
based on the two principles of concordance and their disaggregation into organizational and functional-
discordance, is modelled in phase I of the method economic components was visualized through the SW
through the computation of a concordance index, a Expert Choice and its multilevel decision tree.
discordance index and an outranking degree. The method In order to support interaction with the client, three
uses the latter result in the second fuzzy relation models were elaborated during some simulation sessions
exploitation phase, in order to construct two complete in the MBDD: an AHP-Expert Choice model that is
pre-orders through a descending and an ascending sufficiently general to be used in different decision
distillation procedure. Outranking relation modelling situations, with a decision tree that is articulated in five
offers some interesting advantages, in comparison to levels and twenty-six elementary components for the
other multiple criteria methods: each criterion can use a comparison of the solutions, and two models for
different ordinal or cardinal scale, since a unique specific ELECTRE III, with twelve criteria for the first case
scale (such as the cost-benefit analysis monetary scale or study and fifteen criteria for the second one. Different
the 0-1 utility scale of the multi attribute utility theory) is decisional scenarios were hypothesized, in order to
not necessary and the outranking relation is not analyze which impact could have on the result the
compensatory (or partially not compensatory). importance that the criteria assumed.
A weak point of ELECTRE III is its software package, The AHP-Expert Choice model and the results of some
which does not pay any attention to dialogue with the applications were then analyzed to understand their
decision maker, which is essential in model structuring potentiality to facilitate communication between the
and parameter definition and when the results require a MBDD and the different clients. The ELECTRE III
collective analysis. A new product, which is more results were examined in terms of robustness and
suitable and includes several multiple criteria methods, is reliability, and the models in terms of formal validity and
currently being developed in the Decision Deck project3. consistency with the internal procedures of the company.
This weak point is related to the original nature of the
method which was invented to be used when a problem
was well structured, i.e. when: Conclusions
· a set of solutions is identified, or elaborated, and A client's involvement in the initial phase of an
tested in terms of completeness, admissibility and engineering design process is always important and has
comparability, and to be carefully managed. The temporal horizon to
· a family of evaluation functions (i.e. criteria) produce an innovation in the aeronautic sector always
which has been created to represent all the different involves a difficult definition of the client’s needs and
aspects of the problem at hand contains a sufficiently some risks in translating the needs into formal
small number of criteria to be a basis for discussion requirements. The analysis and comparison of some draft
(legibility condition) and to be considered by all the solutions is an effective approach to understand the
actors as a sound basis for the continuation of the client’s point of view and the general structure of his/her
decision aid study; its coherence (exhaustiveness, preference system. However, this approach requires time
cohesiveness and redundancy) has to be verified by to elaborate understandable technical solutions, analyse
operational tests (Roy & Bouyssou, 1993; Roy, them with the client and elaborate new solutions for a
1996). new collective analysis, in a learning cycle.
For this reason, ELECTRE III is not normally used until Complexity and uncertainty elements can have a
the problem (and/or the model) is structured and only negative impact on the problem definition in some
when these conditions are satisfied does it become a decision situations, above all when different, and
powerful method to transparently compare solutions, in sometimes conflicting, points of view require the
relation to all the different criteria, and to rigorously involvement of some specific competences, from the
synthesize evaluations that are associated to the client’s organization, as a not easy, but almost obligatory
consequences of each decision. course of action.
Therefore, our proposal was: the AHP would be used A structured procedure can support the acquisition of
in the problem definition step, when pertinent the different points of view and their translation into
information has to be identified together with the client, mathematical models and then into product requirements,
by means analysis and selection of conceptual solutions, and can prevent, or at least control, ambiguous
while the ELECTRE III would be used at the end, in specifications by an activity that has the aim of verifying
the overall consistency of the models.
The opportunity to produce conceptual solutions in a
3
www.decision-deck.org
short time (a solution requires only few seconds of
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CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011
calculation time), with the guarantee of technical Norese, M.F, & Liguigli, E. (2009). The conceptual
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