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Implementation of value-driven optimisation for the design of aircraft fuselage panels
ARTICLE IN PRESS Int. J. Production Economics 117 (2009) 381–388
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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe
Implementation of value-driven optimisation for the design of aircraft fuselage panels Sylvie Castagne a,, Richard Curran a,1, Paul Collopy b a
Centre of Excellence for Integrated Aircraft Technology, School of Mechanical and Aerospace Engineering, Queen’s University Belfast, Ashby Building, Belfast BT9 5AG, UK DFM Consulting, PO Box 247, Urbana, IL 61803, USA
b
a r t i c l e in fo
abstract
Article history: Received 3 January 2008 Accepted 2 December 2008 Available online 10 December 2008
The work presented investigates a methodology for the implementation of value-driven design (VDD) with application to the optimisation of aircraft fuselage panels. The VDD approach integrates manufacturing and operating costs as optimisation drivers at the design stage. In particular, manufacturer’s profit, airlines expenses and revenue, and surplus value relating to competitor products are taken into account in the objective function proposed for the design optimisation. The study shows that using VDD concepts, the manufacturer has the possibility to develop more efficient designs with an increase of both his own profit and the operator’s gains. & 2008 Elsevier B.V. All rights reserved.
Keywords: Value-driven design Optimisation Aircraft structure Cost modelling
1. Introduction The total cost of bringing a new plane to market generally reaches several billions of dollars; Morimoto and Hope (2005) reported a development cost of $9–10 billion for the A380 (Morimoto and Hope, 2005). This type of investment, which comprises design, certification and tooling costs, has to be made responsibly. In particular, to succeed in the market place, the design engineers must be focused on creating a product that will provide a good value for prospective customers. Although lots of efforts have been made to develop cost models to support preliminary designs incorporating emerging technologies (Gieger and Dilts, 1996; Westphal and Scholz, 1997; Mavris et al., 1999; Scanlan et al., 2002; Curran et al.,
Corresponding author. Current address: Nanyang Technological University, School of Mechanical and Aerospace Engineering, 50 Nanyang Avenue, Singapore 639798, Singapore. Tel.: +65 6790 4331; fax: +65 6792 4062. E-mail addresses: [email protected] (S. Castagne), [email protected] (R. Curran), [email protected] (P. Collopy). 1 Current address: Delft University of Technology, Faculty of Aerospace Engineering, PO Box 5058, 2600 GB Delft, The Netherlands.
0925-5273/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2008.12.005
2004; Park and Simpson, 2005; Roy et al., 2005; Peoples and Willcox, 2006; Ibusuki and Kaminski, 2007), today’s design teams lack the economic tools to translate among engineering parameters, market needs, and costs. Design requirements based on goals that neglect airline revenue and manufacturing costs, for example ‘‘to reduce the operating costs by 10%’’, do not always lead to optimal design as they do not incorporate a complete representation of market operation. Cost is an important attribute of any product and highly relevant to the engineering design process as it determines customer affordability (Wierda, 1990; Hoult et al., 1996). Along with product quality and market timeliness, cost drives competitive advantage (Sheldon et al., 1991). In this context, the manufacturer is the stakeholder who balances unit cost relative to market forces and operational requirements. As the impact of the manufacturer decisions is the most influential at the design stage, this paper addresses the issue of linking cost, profit, and structural considerations at the initial development stage with a view of defining a methodology for the implementation of valuedriven design (VDD). The American Institute of Aeronautics and Astronautics (AIAA) VDD programme committee
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proposes the following definition for VDD: ‘‘VDD is an improved design process that uses requirements flexibility, formal optimisation and a mathematical value model to balance performance, cost, schedule, and other measures important to the stakeholders to produce the best outcome possible’’ (http://www.vddi.org/vdd-home.htm). In this work, VDD optimisation is addressed by utilising an objective function which relates manufacturing cost and the manufacturer’s profit; the direct operating cost (DOC) to be borne by the airlines and their revenue (including the discount rate); and also includes the surplus value (SV) calculation relating to competitor products (Collopy, 2001; Younghans et al., 1998; Collopy, 2006). After this introduction, the paper describes the general optimisation model that is proposed to drive the design process. The specific application presented is the design of fuselage stringer–skin panels (see Fig. 1), typically being driven by a minimal weight goal seek when using a traditional design approach. Then a full description of the new objective function proposed, i.e. the profit, is presented followed by a case study relative to the design of a regional passenger jet. 2. General optimisation model Rather than only looking at manufacturing cost, a preliminary study showed that DOC, which is the cost of transporting a given weight of aircraft structure during the aircraft’s life span, could also be considered in terms of the impact of weight on fuel burn, in addition to the acquisition cost to be borne by the operator (Curran et al., 2006; Castagne et al., 2008). Ultimately, there was a tradeoff between driving design according to minimal weight and driving it according to reduced manufacturing cost. The analysis of cost was facilitated with a genetic-causal
stringer area = 2hts
b
ts
h
t Fig. 2. Modelling of the panel for structural analysis.
cost modelling methodology (Curran et al., 2004) and the structural analysis was driven by numerical expressions of appropriate failure modes that utilise Engineering Sciences Data Unit (ESDU) reference data. However, this preliminary study did not considered SV and manufacturer’s profit, which are focused on in this paper. The generic part families appearing in a typical stringer–skin panel are the panel itself, which forms the skin of the aircraft, the stringers and the frames that support it in the longitudinal and lateral directions, and the shear cleats that are present at the stringer–frame junctions. To be integrated in an optimisation model, the structural and cost analyses have to share the same design variables. Therefore, the panel is modelled as shown in Fig. 2, where b is the stringer pitch, h the stringer height, t the skin thickness, ts the stringer thickness and rp the rivet pitch. Failure modes considered are long and short wave panel buckling (flexural and local buckling), interrivet buckling (since riveting is a major cost factor) and material stress limits. Explicit formulae were derived for each of these, to facilitate their use in combination with cost formulae in a cost–weight optimisation, making use in part of data in the ESDU structures series (ESDU International, 1970). A detailed description of the structural analysis approach is given in the authors’ previous paper (Curran et al., 2006), which used the same panel design, whereas the developments of the cost equations are presented in Refs. (Curran et al., 2006; Castagne et al., 2008). Regarding manufacturing cost, the equations are divided in three categories for each component family included in the design (skin, stringers, frames, cleats and rivets). These categories of costs are distinguished by the exponent used: cost exponent m refers to material, f to fabrication and a to assembly. A summary of the equations used for manufacturing cost and structural analysis is given in Table 1.
3. Profit as an objective function 3.1. Definition of profit
Fig. 1. Illustration of the panel.
Profit appears to be an obvious objective function, perhaps superior to DOC, which has been used in earlier studies. In a competitive market, manufacturer’s profit can be related to DOC, manufacturing cost and airline
Table 1 Manufacturing cost and structural analysis equations for T-stringer panels.
Material cost ($)
Fabrication cost ($)
Assembly cost ($)
4 Ask Cm sk ¼ 3:051 10
C fsk ¼ r fsk ½ufsk1 ð1:524 104 Ask þ 3:261 103 p þ 56:4Þ þ ufsk2 ðn 2:452 105 Ask þ 9:464 106 tr Ask þ 1:087 104 Ask Þ
Stringer
5 Ast þ 7:934 104 Þ Lst 1:15 Cm st ¼ ð7:252 10
C fst ¼ rfst ufst ð2:283 102 Lst 1:15 þ 151:73Þ
5:059 þ nauto 1Þ C ast ¼ rast uast ðnman st st
Frame
Cm fr
C afr ¼ rafr uafr ðnman 5:059 þ nauto 1Þ fr fr
Cleat
Cm cl Cm pr
C ffr C fcl
Rivets
5
t fr Afr 1:15
5
t cl Acl 1:15
¼ 2:798 10 ¼ 2:798 10
2
¼ 1:215 10
;
Cm cs
2
¼ 1:580 10
¼
rffr r fcl
uffr ufcl
1
7:731 10
Lfr
¼ 30 Included in material cost
5:918 C acl ¼ r acl uacl nman cl –
where Ask is the total skin material surface area, Ask the final skin surface area, p the perimeter of the pockets, n the number of passes for chemi-milling, tr the thickness to be removed, Lst the stringer length, Ast m the stringer cross-section area, t fr=cl the frame/cleat sheet material thickness, Afr=cl the frame/cleat sheet material surface area, Lfr the frame length, C m pr the cost of 1 protruding head rivet, C cs the cost of 1 man=auto
countersunk rivet and nst=fr=cl
the number of manual/automatic rivets for stringer/frame/cleat assembly
Utility factors: ufsk1 ¼ ufsk2 ¼ 1:30, ufst ¼ uffr ¼ ufcl ¼ 1:45 and uast ¼ uafr ¼ uacl ¼ 1:20. Rates: r fsk ¼ 3:103 101 , r fst ¼ r ffr ¼ r fcl ¼ 3:116 101 and rast ¼ r afr ¼ r acl ¼ 2:850 101 .
Structural analysis equations Local buckling
Flexural buckling
Inter-rivet buckling
2 2 2 2 t t s t t b sL ¼ K L E ; tB ¼ K S E ; þ sR ¼ K R E ¼1 sF ¼ K F E sL tB b b rp LF where sL is the local buckling stress, tB the buckling stress in pure shear, s the applied compressive stress, t the applied shear stress, E the Young’s modulus, t the panel thickness, b the stringer pitch, LF the frame pitch and rp the rivet pitch. Buckling factors: KL and KF from Ref. ESDU International (1970), KS ¼ 4.83 and KR ¼ 2.46 for protruding heads rivets and 1.23 for countersunk rivets. All dimensions in mm, all costs in $.
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Manufacturing cost equations
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revenue using the following equation:
p¼
aircraft X life
½ðR DOCÞ ð1 þ rÞi MC SV 2
(1)
i
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} RP |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} SV
where p is the manufacturer’s profit, R the airline’s revenue, DOC the direct operating cost (excluding manufacturing cost or investment, since this is addressed explicitly), MC the manufacturing cost, SV2 the second largest SV among the competing aircrafts and r the airline’s discount rate, i.e. a measure of the relative value that the airline places on money over time (Collopy, 1997). The SV for an aircraft is the difference between the reservation price (RP), i.e. the present value of the profits from the aircraft operation, which corresponds to the upper limit on the price that the airline will pay in the absence of competition, and the total manufacturing cost. An analysis of the competition model shows that optimising SV will automatically optimise unit profit. Therefore, a design that optimises SV can be assured of producing the most profitable product within the capabilities of the manufacturer (Collopy, 1997). 3.2. Methodology for optimisation The model, which comprises the manufacturing cost equations (Curran et al., 2006; Castagne et al., 2008), structural equations (Curran et al., 2006) and objective functions, has been implemented in Microsoft Excels where it is used in junction with the Premium Solver PlatformTM. This solver is suitable for global optimisation and is designed for use with integer variables. The optimisation method chosen is a generalised reduced gradient method with multi-start options for global optimisation. The active design variables are chosen to be: number of stringers ns, stringer height h, skin thickness t, stringer thickness ts and rivet pitch rp. The number of stringer is an integer value linked to the panel width Hp and stringer pitch b as described by Eq. (2) in which one unit is subtracted to account for the fact that there is no stringer on the sides of the panel in the cost model when a single panel is analysed. As ns is an integer and as Hp is a constant for the problem, only discrete values of b are permitted. ns ¼
Hp 1 b
(2)
The rivet pitch is included as it makes a major contribution to the cost of manufacture while the other four are, of course, primary variables in the design of stringer–skin panels, as well as having significant influence on the manufacturing cost. The frame pitch LF is not varied during optimisation and the panel is loaded in pure compression, at a structural index value p/LF ¼ 0.5 N/mm2, where p is the compression loading intensity. This is a relatively small value, resulting in a low stress level in the panel, but is appropriate to the design of panel from which the actual cost data was extracted. The optimisation for weight or for manufacturing cost is pretty straightforward as the weight and manufacturing
cost of a square metre of fuselage panel can be directly calculated using the spreadsheet model. The optimisation for profit is less obvious as it requires the combination of several terms as shown in Eq. (1), each of which having to be reported to the same unit, i.e. 1 m2 of fuselage panel. The aim being to analyse the variations in the structural configurations between the panels optimised for different objectives, one solution is to relate the terms of Eq. (1) to the variations in weight and manufacturing cost that will results from the different configurations. Then, it is possible to analyse the impact of the structural configuration on profit and optimise for maximum profit. To achieve this goal it is not necessary to calculate an absolute value for the profit that will relate to the whole aircraft but it is sufficient to use variations of the profit based on the impact of weight and manufacturing on the cost and revenue. 3.3. Impact of the configuration on the cost elements In order to calculate the total impact of configuration changes on profit, this section introduces first the equations required to calculate the impact of weight on DOC and on revenue. The impact of a change of configuration on the manufacturing cost is directly introduced in Eq. (1) by using the results given by the manufacturing cost model (Castagne et al., 2008). 3.3.1. Impact of weight on DOC The impact of weight on the DOC is linked to the increase in fuel consumption. Considering that the amount of fuel consumed per year per available seat is represented by the variable fc, the number of available seats by the variable nseat and the operating weight by the variable Wop, the impact of a weight increase on annual fuel consumption (IDOC) is calculated as follows: IDOC ¼
f c nseat W op
(3)
If the fuel consumed and operating weight are given in kg, IDOC is measured in kg of fuel consumed per kg of aircraft weight per year. Considering that the weight of 1 l of fuel is given by Wf and the cost of 1 l of fuel by Cf, it is possible to translate Eq. (3) in terms of cost as follows:
DDOC ¼
IDOC C f Wf
(4)
where DDOC is the variation of DOC due to the increase of weight. If Cf is in $ and Wf in kg, DDOC is measured in $/year/kg of aircraft weight and it represents the fuel cost that will have to be incurred per year for each additional kg of aircraft weight. It is possible to calculate the variation of DOC due to weight increase for the total life of the aircraft, DDOC life , by introducing the discount rate r as shown in Eq. (5).
DDOC life ¼
aircraft X life
½DDOC ð1 þ rÞi
i¼1
(5)
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3.3.2. Impact of weight on revenue The impact of weight on revenue is of two contributions: (1) cargo related and (2) passengers related. With regards to cargo, considering that the cargo hold is full, aircraft weight displaces cargo weight and cargo revenue is lost. In other words, for a constant total weight, if the aircraft weight is increased, less weight allocation will be available for cargo. With regards to passengers, the same analysis can be made: for flights that exceed the design range of the aircraft in terms of total weight, passengers can be displaced, leading to less passenger revenue. As regional jets almost never fly routes that use their full range, all the impact of weight on revenue is considered to be of the first type only in this study. The cost of one lost kg of cargo, Icar can be calculated as follows: Icar ¼ dist nflight Rcar
(6)
where dist is the average distance flown per flight (in Nmi), nflight the number of flights per year and Rcar the cargo revenue/kg/Nmi. Earlier studies have shown that for regional jets, the cargo hold was only full a certain percentage of the time. Therefore, the impact of weight on cargo revenue (Drev) is
Drev ¼ Icar a
(7)
where a is the percentage of time for which the cargo hold is full. Drev is the loss of revenue per additional kg of aircraft weight per year. The impact of weight on revenue for the total life of the aircraft ðDrevlife Þ is calculated as follows:
Drevlife ¼
aircraft X life
½Drev ð1 þ rÞi
(8)
i¼1
where r is the discount rate. Drevlife is the loss of revenue per additional kg of aircraft weight. 3.3.3. Total impact of configuration change on profit The total cost impact of weight increase on SV over the entire aircraft life (IW) is given by the sum of the impact on DOC and on revenue calculated using Eqs. (5) and (8), respectively: IW ¼ DDOC life þ Drevlife
(9)
IW is then the cost attached to each additional kg of aircraft weight over the entire life span of the aircraft. Finally, the total impact of a change of configuration on profit can be found by replacing Eq. (1) as follows:
Dp ¼ DM IW DMC
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} DRP |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
(10)
DSV
where Dp is the variation of profit in $/m2 of aircraft fuselage panel; and DM and DMC are, respectively, the mass variation and the manufacturing cost variation of 1 m2 of aircraft fuselage panel due to a configuration change. By maximising Dp, the model assures that the maximum profit is realised; the second surplus SV2 remaining constant as the change of configuration of the
385
analysed aircraft does not influence directly the other competitor products available on the market. 4. Case study: application to the design of a regional passenger jet The results presented in this section concern the optimisation of a regional jet. The data used for the analysis are summarised in Table 2 and are typical for a 50 passenger seats aircraft. Two types of analyses have been done using the optimisation model. First, the impact of the choice of the objective function has been assessed by comparing the structural configuration obtained in each of the cases. The second application analyses the sensitivity of the results of the optimisation for profit to the fuel cost and discount rate. The results of the first set of optimisations are shown in Table 3 in term of structural design variables for the initial case where the fuel cost is 2$/gal (1 gal ¼ 4.546 l) and the discount rate 17%. Considering the infinite life of the aircraft, Eqs. (5) and (8) can be simplified as follows:
DDOClife ¼ revlife
1 DDOC X ½DDOC ð1 þ rÞi ¼ rev rev r i¼1
(11)
The cost impacts obtained with the set of data of Table 2 are DDOC life ¼ 375$/kg and Drevlife ¼ 21$=kg, i.e. IW ¼ 396$/kg, over the life of the aircraft. Three objective functions have been tested: minimum weight, minimum manufacturing cost and maximum profit. Compared to the minimum weight configuration, the panel optimised for minimum manufacturing cost contains less stringers of bigger size riveted on a skin which is 75% thicker, i.e. that the panel comprises a smaller number of bigger parts. Due to the increase in the stiffness of the individual parts, the rivet spacing can also be increased, which together with a smaller number of parts reduces the assembly cost. The maximum profit configuration lies in between the minimum weight and minimum manufacturing cost configurations in term of stringers number (also linked to the assembly cost), stringers and panel sizes and weight. It is a compromise that suits both the manufacturer and airline operator. It is to be noted that the ratio of the stringer thickness to the skin thickness is equal to 1 for each of the configurations obtained; this is due to the constraints arising from the Table 2 Data used for the analysis. Variable
Value
Units
fc nseat Wop Wf Dist nflight Rcar
67 130 50 34 020 0.68 428 2288 0.18 103 0.02 2209.8 406.4
kg/year – kg kg/l Nmi /year $/kg/Nmi – mm mm
a Hp Lf
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Table 3 Design variables after optimization. Panel optimised for
b
ns
h
t
ts
rp
Minimum weight Minimum manufacturing cost Maximum profit
81.8 167.0 116.3
26 12 18
22.54 34.00 23.38
1.72 3.04 2.27
1.72 3.04 2.27
46.5 96.6 65.3
All dimensions in mm, fuel cost ¼ 2$/gal and discount rate ¼ 17%.
Table 4 Variation of the possible objectives after optimisation. Panel optimised for
DM (kg/m2)
DMC ($/m2)
Dp ($/m2)
Minimum weight Minimum manufacturing cost Maximum profit
Reference configuration 2.24 0.49
896 527
51 344
Fuel cost ¼ 2$/gal and discount rate ¼ 17%.
limits of validity of the local buckling data which have been reached for the particular cases tested. Table 4 indicates the impact of the choice of the objective on weight, manufacturing cost and profit. The minimum weight configuration is chosen as a reference so that the values in the table are the differences between the studied case (either minimum manufacturing cost or maximum profit) and the minimum weight case. Analysing the table globally, it can be seen that the maximum profit solution is achieved by increasing slightly the manufacturing cost compared to the minimum manufacturing cost solution but without having a huge impact on the weight. By optimising the structural configuration, it is possible to realise savings in manufacturing cost that compensate the loss of revenue and the increase of DOC so that the profit or SV as defined by Eq. (1) is increased. The previous analyses have been realised using a fixed fuel cost and discount rate. It is interesting to check the sensitivity of the model to these two parameters. The calculation of the impact of weight on SV as presented previously can be updated automatically in the spreadsheet when the fuel cost and discount rate vary. Fig. 3 presents the results after optimisation in terms of number of stringers for a discount rate varying from 10% to 25% and for two fuel costs. The reference fuel cost corresponds to an average fuel cost of 2$/gal for the analysed year whereas the second value (3$/gal) simulates an increase of 50% of the fuel cost. Due to the nature of the model, the structural configuration is marked by step changes in the number of stringers. The number of stringers generally drives the optimisation and the other structural variables naturally follow to meet the structural requirements. The tendency shown on Fig. 3 is that the optimal number of stringers is reduced when the discount rate is increased. This can be explained by the fact that when the discount rate increases, the discounted fuel cost becomes lower which implies that the weight can be slightly increased without impacting so much on the profit. A lower number of stringers corresponds to a lower manufacturing cost and is usually also associated to a higher weight. Therefore,
the combined effect will lead to an increased profit. Likewise, a lower initial fuel cost leads to an optimised number of stringers which is lower. Figs. 4 and 5 show the increase in profit compared to the minimum weight configuration as a function of the discount rate for different geometric configurations represented by the number of stringers they comprise. Fig. 4 corresponds to a fuel cost of 2$/gal while Fig. 5 relates to the case where the fuel cost increases to 3$/gal. On the two figures, the optimal number of stringers that leads to the maximum profit can be defined following the external envelope of all the curves. Although the optimisation routine is designed to converge automatically to the maximum profit solution, there is no mathematical proof that the global optimum value will be reached every time due to the high nonlinearity of the problem and to the presence of integer variables. In particular, it has been observed through practical examples that the exact location of the step change for the number of stringers (as represented in Fig. 3) is not always correctly defined when using an automated optimisation solver. In the present application, the use of a multi-start technique generally gave better results than the evolutionary method based on genetic algorithms for global optimisation. Nevertheless, looking at the results in terms of the value of the objective, it can be seen that around the step change, the differences between the profit increases for the two configurations involved are very small. For example, for a fuel cost of 2$/gal, the step change from 19 to 18 stingers arises at a discount rate of 13% but keeping a configuration with 19 stringers at a discount rate of 13% would only have a limited impact on the profit as shown in Fig. 4 where the two corresponding data points are almost superimposed. Similar observations can be made at every step change in Figs. 4 and 5. This explains why an automated optimisation process can converge to one or the other solution but also indicates that there is flexibility in the design and that the need to go from one configuration to the other can be discussed in relation to the sensitivity to the objective.
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Optimum number of stringers
22 21 fuel cost = 2$/gal fuel cost = 3$/gal
20 19 18 17 16 15 10%
12%
14%
16% 18% Discount rate
20%
22%
24%
450
450
400
400
350 300 ns=16 ns=17 ns=18 ns=19 Optimised solution
250 200 150 10%
12%
14%
16%
18%
20%
22%
24%
Increase in profit [$/m2]
Increase in profit [$/m2]
Fig. 3. Optimisation for profit: optimal number of stringers.
350 300 250 fuel cost = 2$/gal fuel cost = 3$/gal
200 150 10%
12%
Discount rate
Increase in profit [$/m2]
400 350 300 250 ns=18 ns=19 ns=20 ns=21 Optimised solution
200 150
12%
14%
16%
18%
16%
18%
20%
22%
24%
Discount rate
Fig. 4. Profit increase relative to the number of stringers for a fuel cost ¼ 2$/gal.
100 10%
14%
20%
22%
24%
Discount rate Fig. 5. Profit increase relative to the number of stringers for a fuel cost ¼ 3$/gal.
The maximal values of the profit variation, i.e. the external envelope of the profit increase curves of Figs. 4 and 5, are summarised in Fig. 6 as a function the discount rate for the two fuel costs. The first comment about Fig. 6 is that the profit increase is reduced if the fuel cost is higher. In case of fuel cost increase, the airline DOC is higher and this is reflected directly on the SV and profit.
Fig. 6. Profit increase for the optimal configuration.
Analysing Figs. 3 and 6 in parallel, it is also worth highlighting that when the discount rate increases the variation in profit increases as well but this tendency is only maintained by introducing step changes in the configuration. For each discount rate, the variation in profit is calculated with reference to the profit that would be realised, with the same discount rate, for the minimum weight configuration. The profit relative to the minimum weight configuration is a quantity that is fixed for each discount rate and that decreases when the discount rate increases as the manufacturing cost is fixed for this configuration and the RP is discounted. Therefore, the trend shown in Fig. 6 does not imply that the total profit also increases with the discount rate when the optimal configuration is chosen but it only means that when the discount rate increases, the lower value of discounted fuel cost obtained allows reducing the number of stringers, to keep the manufacturing cost low and to maintain a maximum increase in profit compared to the minimum weight configuration although the weight is slightly increased at the same time. 5. Conclusions The main objective of this research is to develop a methodology and tools to estimate the cost implications
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of design decisions by integrating cost as a design parameter at the conceptual design stage. This has been achieved by investigating a methodology for the implementation of value-driven design (VDD). This included a VDD optimisation that utilised an objective function which related manufacturing cost and manufacturer’s profit; the DOC borne by the airlines and their revenue (including the discount rate). The main contribution of the paper is the analysis of the manufacturer’s profit and the influence of its maximisation on the structural configuration of an aircraft fuselage panel. Results of optimisations carried out for minimum weight, minimum cost and maximum profit are also presented and major changes in the optimal structural configuration are observed depending on the chosen objective. It is concluded that it is crucial to consider what actually needs to be optimised in the design process and for whom. It is shown that manufacturer’s profit, as the principle owner of the design process, can be increased while also improving the operator’s gains over current less efficient designs. Ultimately, the methodology calls for a value judgement to be made and converted into an objective function that tests the quality of any given design. This can be made to drive a VDD optimisation process if the performance and manufacturing analyses can be linked.
Acknowledgements The work has been carried out through the Centre of Excellence for Integrated Aircraft Technology (CEIAT), funded by Invest Northern Ireland and Bombardier Aerospace Belfast (BAB). The authors would like to acknowledge the strong collaboration with BAB, involving the gathering of industrial data and the ultimate relevance of the work. References Castagne, S., Curran, R., Rothwell, A., Price, M., Benard, E., Raghunathan, S., 2008. A generic tool for cost estimating in aircraft design. Research in Engineering Design 18 (4), 149–162.
Collopy, P, 1997. Surplus value in propulsion system design optimization. In: 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Seattle, WA. Collopy, P.D., 2001. Economic-based distributed optimal design. AIAA Paper 2001-4675, American Institute of Aeronautics and Astronautics, Reston, VA. Collopy, P.D, 2006. Value-driven design and the global positioning system. AIAA Paper 2006-7213, American Institute of Aeronautics and Astronautics, Reston, VA. Curran, R., Raghunathan, S., Price, M., 2004. Review of aerospace engineering cost modeling: the genetic causal approach. Progress in Aerospace Sciences 40 (8), 487–534. Curran, R., Rothwell, A., Castagne, S., 2006. A numerical method for cost–weight optimization of stringer–skin panels. Journal of Aircraft 43 (1), 264–274. ESDU International, 1970. Local buckling of compression panels with unflanged integral stiffeners. Engineering Sciences Data Item 70003, structures series. Gieger, T.S., Dilts, D.M., 1996. Automated design-to-cost: integrating costing into the design decision. Computer Aided Design 28 (6–7), 423–438. Hoult, D. P., Meador, C. L., Deyst, J., Dennis, M., 1996. Cost awareness in design: the role of data commonality. SAE Technical Paper 60008. /http://www.vddi.org/vdd-home.htmS (accessed on 06.01.09). Ibusuki, U., Kaminski, P.C., 2007. Product development process with focus on value engineering and target costing: a case study in an automotive company. International Journal of Production Economics 105 (2), 459–474. Mavris, D.N., Bandte, O., DeLaurentis, D.A., 1999. Robust design simulation: a probabilistic approach to multidisciplinary design. Journal of Aircraft 36 (1), 298–307. Morimoto, R., Hope, C., 2005. Making the case for developing a silent aircraft. Transport Policy 12 (2), 165–174. Park, J., Simpson, T.W., 2005. Development of a production cost estimation framework to support product family design. International Journal of Production Research 43 (4), 731–772. Peoples, R., Willcox, K., 2006. Value-based multidisciplinary optimization for commercial aircraft design and business risk assessment. Journal of Aircraft 43 (4), 913–921. Roy, R., Colmer, S., Griggs, T., 2005. Estimating the cost of a new technology intensive automotive product: a case study approach. International Journal of Production Economics 97 (2), 210–226. Scanlan, J., Hill, T., Marsh, R., Bru, C., Dunkley, M., Cleevely, P., 2002. Cost modelling for aircraft design optimization. Journal of Engineering Design 13 (3), 261–269. Sheldon, D.F., Huang, G.Q., Perks, K., 1991. Design for cost: past experience and recent development. Journal of Engineering Design 2 (2), 127–139. Westphal, R., Scholz, D.A., 1997. Method for predicting direct operating costs during aircraft system design. Cost Engineering 39 (6), 35–39. Wierda, L., 1990. Design-oriented cost information: the need and the possibilities. Journal of Engineering Design 1 (2), 147–167. Younghans, J.L, Donaldson, R.M., Wallace, D.R., Long, L.L., Stewart, R.B., 1998. Preliminary design of low cost propulsion systems using next generation cost modeling techniques. GE Aircraft Engines, Cincinnati, OH.
Contents lists available at ScienceDirect
Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe
Implementation of value-driven optimisation for the design of aircraft fuselage panels Sylvie Castagne a,, Richard Curran a,1, Paul Collopy b a
Centre of Excellence for Integrated Aircraft Technology, School of Mechanical and Aerospace Engineering, Queen’s University Belfast, Ashby Building, Belfast BT9 5AG, UK DFM Consulting, PO Box 247, Urbana, IL 61803, USA
b
a r t i c l e in fo
abstract
Article history: Received 3 January 2008 Accepted 2 December 2008 Available online 10 December 2008
The work presented investigates a methodology for the implementation of value-driven design (VDD) with application to the optimisation of aircraft fuselage panels. The VDD approach integrates manufacturing and operating costs as optimisation drivers at the design stage. In particular, manufacturer’s profit, airlines expenses and revenue, and surplus value relating to competitor products are taken into account in the objective function proposed for the design optimisation. The study shows that using VDD concepts, the manufacturer has the possibility to develop more efficient designs with an increase of both his own profit and the operator’s gains. & 2008 Elsevier B.V. All rights reserved.
Keywords: Value-driven design Optimisation Aircraft structure Cost modelling
1. Introduction The total cost of bringing a new plane to market generally reaches several billions of dollars; Morimoto and Hope (2005) reported a development cost of $9–10 billion for the A380 (Morimoto and Hope, 2005). This type of investment, which comprises design, certification and tooling costs, has to be made responsibly. In particular, to succeed in the market place, the design engineers must be focused on creating a product that will provide a good value for prospective customers. Although lots of efforts have been made to develop cost models to support preliminary designs incorporating emerging technologies (Gieger and Dilts, 1996; Westphal and Scholz, 1997; Mavris et al., 1999; Scanlan et al., 2002; Curran et al.,
Corresponding author. Current address: Nanyang Technological University, School of Mechanical and Aerospace Engineering, 50 Nanyang Avenue, Singapore 639798, Singapore. Tel.: +65 6790 4331; fax: +65 6792 4062. E-mail addresses: [email protected] (S. Castagne), [email protected] (R. Curran), [email protected] (P. Collopy). 1 Current address: Delft University of Technology, Faculty of Aerospace Engineering, PO Box 5058, 2600 GB Delft, The Netherlands.
0925-5273/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2008.12.005
2004; Park and Simpson, 2005; Roy et al., 2005; Peoples and Willcox, 2006; Ibusuki and Kaminski, 2007), today’s design teams lack the economic tools to translate among engineering parameters, market needs, and costs. Design requirements based on goals that neglect airline revenue and manufacturing costs, for example ‘‘to reduce the operating costs by 10%’’, do not always lead to optimal design as they do not incorporate a complete representation of market operation. Cost is an important attribute of any product and highly relevant to the engineering design process as it determines customer affordability (Wierda, 1990; Hoult et al., 1996). Along with product quality and market timeliness, cost drives competitive advantage (Sheldon et al., 1991). In this context, the manufacturer is the stakeholder who balances unit cost relative to market forces and operational requirements. As the impact of the manufacturer decisions is the most influential at the design stage, this paper addresses the issue of linking cost, profit, and structural considerations at the initial development stage with a view of defining a methodology for the implementation of valuedriven design (VDD). The American Institute of Aeronautics and Astronautics (AIAA) VDD programme committee
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proposes the following definition for VDD: ‘‘VDD is an improved design process that uses requirements flexibility, formal optimisation and a mathematical value model to balance performance, cost, schedule, and other measures important to the stakeholders to produce the best outcome possible’’ (http://www.vddi.org/vdd-home.htm). In this work, VDD optimisation is addressed by utilising an objective function which relates manufacturing cost and the manufacturer’s profit; the direct operating cost (DOC) to be borne by the airlines and their revenue (including the discount rate); and also includes the surplus value (SV) calculation relating to competitor products (Collopy, 2001; Younghans et al., 1998; Collopy, 2006). After this introduction, the paper describes the general optimisation model that is proposed to drive the design process. The specific application presented is the design of fuselage stringer–skin panels (see Fig. 1), typically being driven by a minimal weight goal seek when using a traditional design approach. Then a full description of the new objective function proposed, i.e. the profit, is presented followed by a case study relative to the design of a regional passenger jet. 2. General optimisation model Rather than only looking at manufacturing cost, a preliminary study showed that DOC, which is the cost of transporting a given weight of aircraft structure during the aircraft’s life span, could also be considered in terms of the impact of weight on fuel burn, in addition to the acquisition cost to be borne by the operator (Curran et al., 2006; Castagne et al., 2008). Ultimately, there was a tradeoff between driving design according to minimal weight and driving it according to reduced manufacturing cost. The analysis of cost was facilitated with a genetic-causal
stringer area = 2hts
b
ts
h
t Fig. 2. Modelling of the panel for structural analysis.
cost modelling methodology (Curran et al., 2004) and the structural analysis was driven by numerical expressions of appropriate failure modes that utilise Engineering Sciences Data Unit (ESDU) reference data. However, this preliminary study did not considered SV and manufacturer’s profit, which are focused on in this paper. The generic part families appearing in a typical stringer–skin panel are the panel itself, which forms the skin of the aircraft, the stringers and the frames that support it in the longitudinal and lateral directions, and the shear cleats that are present at the stringer–frame junctions. To be integrated in an optimisation model, the structural and cost analyses have to share the same design variables. Therefore, the panel is modelled as shown in Fig. 2, where b is the stringer pitch, h the stringer height, t the skin thickness, ts the stringer thickness and rp the rivet pitch. Failure modes considered are long and short wave panel buckling (flexural and local buckling), interrivet buckling (since riveting is a major cost factor) and material stress limits. Explicit formulae were derived for each of these, to facilitate their use in combination with cost formulae in a cost–weight optimisation, making use in part of data in the ESDU structures series (ESDU International, 1970). A detailed description of the structural analysis approach is given in the authors’ previous paper (Curran et al., 2006), which used the same panel design, whereas the developments of the cost equations are presented in Refs. (Curran et al., 2006; Castagne et al., 2008). Regarding manufacturing cost, the equations are divided in three categories for each component family included in the design (skin, stringers, frames, cleats and rivets). These categories of costs are distinguished by the exponent used: cost exponent m refers to material, f to fabrication and a to assembly. A summary of the equations used for manufacturing cost and structural analysis is given in Table 1.
3. Profit as an objective function 3.1. Definition of profit
Fig. 1. Illustration of the panel.
Profit appears to be an obvious objective function, perhaps superior to DOC, which has been used in earlier studies. In a competitive market, manufacturer’s profit can be related to DOC, manufacturing cost and airline
Table 1 Manufacturing cost and structural analysis equations for T-stringer panels.
Material cost ($)
Fabrication cost ($)
Assembly cost ($)
4 Ask Cm sk ¼ 3:051 10
C fsk ¼ r fsk ½ufsk1 ð1:524 104 Ask þ 3:261 103 p þ 56:4Þ þ ufsk2 ðn 2:452 105 Ask þ 9:464 106 tr Ask þ 1:087 104 Ask Þ
Stringer
5 Ast þ 7:934 104 Þ Lst 1:15 Cm st ¼ ð7:252 10
C fst ¼ rfst ufst ð2:283 102 Lst 1:15 þ 151:73Þ
5:059 þ nauto 1Þ C ast ¼ rast uast ðnman st st
Frame
Cm fr
C afr ¼ rafr uafr ðnman 5:059 þ nauto 1Þ fr fr
Cleat
Cm cl Cm pr
C ffr C fcl
Rivets
5
t fr Afr 1:15
5
t cl Acl 1:15
¼ 2:798 10 ¼ 2:798 10
2
¼ 1:215 10
;
Cm cs
2
¼ 1:580 10
¼
rffr r fcl
uffr ufcl
1
7:731 10
Lfr
¼ 30 Included in material cost
5:918 C acl ¼ r acl uacl nman cl –
where Ask is the total skin material surface area, Ask the final skin surface area, p the perimeter of the pockets, n the number of passes for chemi-milling, tr the thickness to be removed, Lst the stringer length, Ast m the stringer cross-section area, t fr=cl the frame/cleat sheet material thickness, Afr=cl the frame/cleat sheet material surface area, Lfr the frame length, C m pr the cost of 1 protruding head rivet, C cs the cost of 1 man=auto
countersunk rivet and nst=fr=cl
the number of manual/automatic rivets for stringer/frame/cleat assembly
Utility factors: ufsk1 ¼ ufsk2 ¼ 1:30, ufst ¼ uffr ¼ ufcl ¼ 1:45 and uast ¼ uafr ¼ uacl ¼ 1:20. Rates: r fsk ¼ 3:103 101 , r fst ¼ r ffr ¼ r fcl ¼ 3:116 101 and rast ¼ r afr ¼ r acl ¼ 2:850 101 .
Structural analysis equations Local buckling
Flexural buckling
Inter-rivet buckling
2 2 2 2 t t s t t b sL ¼ K L E ; tB ¼ K S E ; þ sR ¼ K R E ¼1 sF ¼ K F E sL tB b b rp LF where sL is the local buckling stress, tB the buckling stress in pure shear, s the applied compressive stress, t the applied shear stress, E the Young’s modulus, t the panel thickness, b the stringer pitch, LF the frame pitch and rp the rivet pitch. Buckling factors: KL and KF from Ref. ESDU International (1970), KS ¼ 4.83 and KR ¼ 2.46 for protruding heads rivets and 1.23 for countersunk rivets. All dimensions in mm, all costs in $.
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Manufacturing cost equations
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revenue using the following equation:
p¼
aircraft X life
½ðR DOCÞ ð1 þ rÞi MC SV 2
(1)
i
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} RP |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} SV
where p is the manufacturer’s profit, R the airline’s revenue, DOC the direct operating cost (excluding manufacturing cost or investment, since this is addressed explicitly), MC the manufacturing cost, SV2 the second largest SV among the competing aircrafts and r the airline’s discount rate, i.e. a measure of the relative value that the airline places on money over time (Collopy, 1997). The SV for an aircraft is the difference between the reservation price (RP), i.e. the present value of the profits from the aircraft operation, which corresponds to the upper limit on the price that the airline will pay in the absence of competition, and the total manufacturing cost. An analysis of the competition model shows that optimising SV will automatically optimise unit profit. Therefore, a design that optimises SV can be assured of producing the most profitable product within the capabilities of the manufacturer (Collopy, 1997). 3.2. Methodology for optimisation The model, which comprises the manufacturing cost equations (Curran et al., 2006; Castagne et al., 2008), structural equations (Curran et al., 2006) and objective functions, has been implemented in Microsoft Excels where it is used in junction with the Premium Solver PlatformTM. This solver is suitable for global optimisation and is designed for use with integer variables. The optimisation method chosen is a generalised reduced gradient method with multi-start options for global optimisation. The active design variables are chosen to be: number of stringers ns, stringer height h, skin thickness t, stringer thickness ts and rivet pitch rp. The number of stringer is an integer value linked to the panel width Hp and stringer pitch b as described by Eq. (2) in which one unit is subtracted to account for the fact that there is no stringer on the sides of the panel in the cost model when a single panel is analysed. As ns is an integer and as Hp is a constant for the problem, only discrete values of b are permitted. ns ¼
Hp 1 b
(2)
The rivet pitch is included as it makes a major contribution to the cost of manufacture while the other four are, of course, primary variables in the design of stringer–skin panels, as well as having significant influence on the manufacturing cost. The frame pitch LF is not varied during optimisation and the panel is loaded in pure compression, at a structural index value p/LF ¼ 0.5 N/mm2, where p is the compression loading intensity. This is a relatively small value, resulting in a low stress level in the panel, but is appropriate to the design of panel from which the actual cost data was extracted. The optimisation for weight or for manufacturing cost is pretty straightforward as the weight and manufacturing
cost of a square metre of fuselage panel can be directly calculated using the spreadsheet model. The optimisation for profit is less obvious as it requires the combination of several terms as shown in Eq. (1), each of which having to be reported to the same unit, i.e. 1 m2 of fuselage panel. The aim being to analyse the variations in the structural configurations between the panels optimised for different objectives, one solution is to relate the terms of Eq. (1) to the variations in weight and manufacturing cost that will results from the different configurations. Then, it is possible to analyse the impact of the structural configuration on profit and optimise for maximum profit. To achieve this goal it is not necessary to calculate an absolute value for the profit that will relate to the whole aircraft but it is sufficient to use variations of the profit based on the impact of weight and manufacturing on the cost and revenue. 3.3. Impact of the configuration on the cost elements In order to calculate the total impact of configuration changes on profit, this section introduces first the equations required to calculate the impact of weight on DOC and on revenue. The impact of a change of configuration on the manufacturing cost is directly introduced in Eq. (1) by using the results given by the manufacturing cost model (Castagne et al., 2008). 3.3.1. Impact of weight on DOC The impact of weight on the DOC is linked to the increase in fuel consumption. Considering that the amount of fuel consumed per year per available seat is represented by the variable fc, the number of available seats by the variable nseat and the operating weight by the variable Wop, the impact of a weight increase on annual fuel consumption (IDOC) is calculated as follows: IDOC ¼
f c nseat W op
(3)
If the fuel consumed and operating weight are given in kg, IDOC is measured in kg of fuel consumed per kg of aircraft weight per year. Considering that the weight of 1 l of fuel is given by Wf and the cost of 1 l of fuel by Cf, it is possible to translate Eq. (3) in terms of cost as follows:
DDOC ¼
IDOC C f Wf
(4)
where DDOC is the variation of DOC due to the increase of weight. If Cf is in $ and Wf in kg, DDOC is measured in $/year/kg of aircraft weight and it represents the fuel cost that will have to be incurred per year for each additional kg of aircraft weight. It is possible to calculate the variation of DOC due to weight increase for the total life of the aircraft, DDOC life , by introducing the discount rate r as shown in Eq. (5).
DDOC life ¼
aircraft X life
½DDOC ð1 þ rÞi
i¼1
(5)
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3.3.2. Impact of weight on revenue The impact of weight on revenue is of two contributions: (1) cargo related and (2) passengers related. With regards to cargo, considering that the cargo hold is full, aircraft weight displaces cargo weight and cargo revenue is lost. In other words, for a constant total weight, if the aircraft weight is increased, less weight allocation will be available for cargo. With regards to passengers, the same analysis can be made: for flights that exceed the design range of the aircraft in terms of total weight, passengers can be displaced, leading to less passenger revenue. As regional jets almost never fly routes that use their full range, all the impact of weight on revenue is considered to be of the first type only in this study. The cost of one lost kg of cargo, Icar can be calculated as follows: Icar ¼ dist nflight Rcar
(6)
where dist is the average distance flown per flight (in Nmi), nflight the number of flights per year and Rcar the cargo revenue/kg/Nmi. Earlier studies have shown that for regional jets, the cargo hold was only full a certain percentage of the time. Therefore, the impact of weight on cargo revenue (Drev) is
Drev ¼ Icar a
(7)
where a is the percentage of time for which the cargo hold is full. Drev is the loss of revenue per additional kg of aircraft weight per year. The impact of weight on revenue for the total life of the aircraft ðDrevlife Þ is calculated as follows:
Drevlife ¼
aircraft X life
½Drev ð1 þ rÞi
(8)
i¼1
where r is the discount rate. Drevlife is the loss of revenue per additional kg of aircraft weight. 3.3.3. Total impact of configuration change on profit The total cost impact of weight increase on SV over the entire aircraft life (IW) is given by the sum of the impact on DOC and on revenue calculated using Eqs. (5) and (8), respectively: IW ¼ DDOC life þ Drevlife
(9)
IW is then the cost attached to each additional kg of aircraft weight over the entire life span of the aircraft. Finally, the total impact of a change of configuration on profit can be found by replacing Eq. (1) as follows:
Dp ¼ DM IW DMC
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} DRP |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
(10)
DSV
where Dp is the variation of profit in $/m2 of aircraft fuselage panel; and DM and DMC are, respectively, the mass variation and the manufacturing cost variation of 1 m2 of aircraft fuselage panel due to a configuration change. By maximising Dp, the model assures that the maximum profit is realised; the second surplus SV2 remaining constant as the change of configuration of the
385
analysed aircraft does not influence directly the other competitor products available on the market. 4. Case study: application to the design of a regional passenger jet The results presented in this section concern the optimisation of a regional jet. The data used for the analysis are summarised in Table 2 and are typical for a 50 passenger seats aircraft. Two types of analyses have been done using the optimisation model. First, the impact of the choice of the objective function has been assessed by comparing the structural configuration obtained in each of the cases. The second application analyses the sensitivity of the results of the optimisation for profit to the fuel cost and discount rate. The results of the first set of optimisations are shown in Table 3 in term of structural design variables for the initial case where the fuel cost is 2$/gal (1 gal ¼ 4.546 l) and the discount rate 17%. Considering the infinite life of the aircraft, Eqs. (5) and (8) can be simplified as follows:
DDOClife ¼ revlife
1 DDOC X ½DDOC ð1 þ rÞi ¼ rev rev r i¼1
(11)
The cost impacts obtained with the set of data of Table 2 are DDOC life ¼ 375$/kg and Drevlife ¼ 21$=kg, i.e. IW ¼ 396$/kg, over the life of the aircraft. Three objective functions have been tested: minimum weight, minimum manufacturing cost and maximum profit. Compared to the minimum weight configuration, the panel optimised for minimum manufacturing cost contains less stringers of bigger size riveted on a skin which is 75% thicker, i.e. that the panel comprises a smaller number of bigger parts. Due to the increase in the stiffness of the individual parts, the rivet spacing can also be increased, which together with a smaller number of parts reduces the assembly cost. The maximum profit configuration lies in between the minimum weight and minimum manufacturing cost configurations in term of stringers number (also linked to the assembly cost), stringers and panel sizes and weight. It is a compromise that suits both the manufacturer and airline operator. It is to be noted that the ratio of the stringer thickness to the skin thickness is equal to 1 for each of the configurations obtained; this is due to the constraints arising from the Table 2 Data used for the analysis. Variable
Value
Units
fc nseat Wop Wf Dist nflight Rcar
67 130 50 34 020 0.68 428 2288 0.18 103 0.02 2209.8 406.4
kg/year – kg kg/l Nmi /year $/kg/Nmi – mm mm
a Hp Lf
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Table 3 Design variables after optimization. Panel optimised for
b
ns
h
t
ts
rp
Minimum weight Minimum manufacturing cost Maximum profit
81.8 167.0 116.3
26 12 18
22.54 34.00 23.38
1.72 3.04 2.27
1.72 3.04 2.27
46.5 96.6 65.3
All dimensions in mm, fuel cost ¼ 2$/gal and discount rate ¼ 17%.
Table 4 Variation of the possible objectives after optimisation. Panel optimised for
DM (kg/m2)
DMC ($/m2)
Dp ($/m2)
Minimum weight Minimum manufacturing cost Maximum profit
Reference configuration 2.24 0.49
896 527
51 344
Fuel cost ¼ 2$/gal and discount rate ¼ 17%.
limits of validity of the local buckling data which have been reached for the particular cases tested. Table 4 indicates the impact of the choice of the objective on weight, manufacturing cost and profit. The minimum weight configuration is chosen as a reference so that the values in the table are the differences between the studied case (either minimum manufacturing cost or maximum profit) and the minimum weight case. Analysing the table globally, it can be seen that the maximum profit solution is achieved by increasing slightly the manufacturing cost compared to the minimum manufacturing cost solution but without having a huge impact on the weight. By optimising the structural configuration, it is possible to realise savings in manufacturing cost that compensate the loss of revenue and the increase of DOC so that the profit or SV as defined by Eq. (1) is increased. The previous analyses have been realised using a fixed fuel cost and discount rate. It is interesting to check the sensitivity of the model to these two parameters. The calculation of the impact of weight on SV as presented previously can be updated automatically in the spreadsheet when the fuel cost and discount rate vary. Fig. 3 presents the results after optimisation in terms of number of stringers for a discount rate varying from 10% to 25% and for two fuel costs. The reference fuel cost corresponds to an average fuel cost of 2$/gal for the analysed year whereas the second value (3$/gal) simulates an increase of 50% of the fuel cost. Due to the nature of the model, the structural configuration is marked by step changes in the number of stringers. The number of stringers generally drives the optimisation and the other structural variables naturally follow to meet the structural requirements. The tendency shown on Fig. 3 is that the optimal number of stringers is reduced when the discount rate is increased. This can be explained by the fact that when the discount rate increases, the discounted fuel cost becomes lower which implies that the weight can be slightly increased without impacting so much on the profit. A lower number of stringers corresponds to a lower manufacturing cost and is usually also associated to a higher weight. Therefore,
the combined effect will lead to an increased profit. Likewise, a lower initial fuel cost leads to an optimised number of stringers which is lower. Figs. 4 and 5 show the increase in profit compared to the minimum weight configuration as a function of the discount rate for different geometric configurations represented by the number of stringers they comprise. Fig. 4 corresponds to a fuel cost of 2$/gal while Fig. 5 relates to the case where the fuel cost increases to 3$/gal. On the two figures, the optimal number of stringers that leads to the maximum profit can be defined following the external envelope of all the curves. Although the optimisation routine is designed to converge automatically to the maximum profit solution, there is no mathematical proof that the global optimum value will be reached every time due to the high nonlinearity of the problem and to the presence of integer variables. In particular, it has been observed through practical examples that the exact location of the step change for the number of stringers (as represented in Fig. 3) is not always correctly defined when using an automated optimisation solver. In the present application, the use of a multi-start technique generally gave better results than the evolutionary method based on genetic algorithms for global optimisation. Nevertheless, looking at the results in terms of the value of the objective, it can be seen that around the step change, the differences between the profit increases for the two configurations involved are very small. For example, for a fuel cost of 2$/gal, the step change from 19 to 18 stingers arises at a discount rate of 13% but keeping a configuration with 19 stringers at a discount rate of 13% would only have a limited impact on the profit as shown in Fig. 4 where the two corresponding data points are almost superimposed. Similar observations can be made at every step change in Figs. 4 and 5. This explains why an automated optimisation process can converge to one or the other solution but also indicates that there is flexibility in the design and that the need to go from one configuration to the other can be discussed in relation to the sensitivity to the objective.
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387
Optimum number of stringers
22 21 fuel cost = 2$/gal fuel cost = 3$/gal
20 19 18 17 16 15 10%
12%
14%
16% 18% Discount rate
20%
22%
24%
450
450
400
400
350 300 ns=16 ns=17 ns=18 ns=19 Optimised solution
250 200 150 10%
12%
14%
16%
18%
20%
22%
24%
Increase in profit [$/m2]
Increase in profit [$/m2]
Fig. 3. Optimisation for profit: optimal number of stringers.
350 300 250 fuel cost = 2$/gal fuel cost = 3$/gal
200 150 10%
12%
Discount rate
Increase in profit [$/m2]
400 350 300 250 ns=18 ns=19 ns=20 ns=21 Optimised solution
200 150
12%
14%
16%
18%
16%
18%
20%
22%
24%
Discount rate
Fig. 4. Profit increase relative to the number of stringers for a fuel cost ¼ 2$/gal.
100 10%
14%
20%
22%
24%
Discount rate Fig. 5. Profit increase relative to the number of stringers for a fuel cost ¼ 3$/gal.
The maximal values of the profit variation, i.e. the external envelope of the profit increase curves of Figs. 4 and 5, are summarised in Fig. 6 as a function the discount rate for the two fuel costs. The first comment about Fig. 6 is that the profit increase is reduced if the fuel cost is higher. In case of fuel cost increase, the airline DOC is higher and this is reflected directly on the SV and profit.
Fig. 6. Profit increase for the optimal configuration.
Analysing Figs. 3 and 6 in parallel, it is also worth highlighting that when the discount rate increases the variation in profit increases as well but this tendency is only maintained by introducing step changes in the configuration. For each discount rate, the variation in profit is calculated with reference to the profit that would be realised, with the same discount rate, for the minimum weight configuration. The profit relative to the minimum weight configuration is a quantity that is fixed for each discount rate and that decreases when the discount rate increases as the manufacturing cost is fixed for this configuration and the RP is discounted. Therefore, the trend shown in Fig. 6 does not imply that the total profit also increases with the discount rate when the optimal configuration is chosen but it only means that when the discount rate increases, the lower value of discounted fuel cost obtained allows reducing the number of stringers, to keep the manufacturing cost low and to maintain a maximum increase in profit compared to the minimum weight configuration although the weight is slightly increased at the same time. 5. Conclusions The main objective of this research is to develop a methodology and tools to estimate the cost implications
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of design decisions by integrating cost as a design parameter at the conceptual design stage. This has been achieved by investigating a methodology for the implementation of value-driven design (VDD). This included a VDD optimisation that utilised an objective function which related manufacturing cost and manufacturer’s profit; the DOC borne by the airlines and their revenue (including the discount rate). The main contribution of the paper is the analysis of the manufacturer’s profit and the influence of its maximisation on the structural configuration of an aircraft fuselage panel. Results of optimisations carried out for minimum weight, minimum cost and maximum profit are also presented and major changes in the optimal structural configuration are observed depending on the chosen objective. It is concluded that it is crucial to consider what actually needs to be optimised in the design process and for whom. It is shown that manufacturer’s profit, as the principle owner of the design process, can be increased while also improving the operator’s gains over current less efficient designs. Ultimately, the methodology calls for a value judgement to be made and converted into an objective function that tests the quality of any given design. This can be made to drive a VDD optimisation process if the performance and manufacturing analyses can be linked.
Acknowledgements The work has been carried out through the Centre of Excellence for Integrated Aircraft Technology (CEIAT), funded by Invest Northern Ireland and Bombardier Aerospace Belfast (BAB). The authors would like to acknowledge the strong collaboration with BAB, involving the gathering of industrial data and the ultimate relevance of the work. References Castagne, S., Curran, R., Rothwell, A., Price, M., Benard, E., Raghunathan, S., 2008. A generic tool for cost estimating in aircraft design. Research in Engineering Design 18 (4), 149–162.
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