The determination of function costs to achieve success-oriented

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1 Beriht Nr. / Januar The determination o untion osts to ahieve suess-oriented design o engineering produts theory and appliion Haio Shlin Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswissenshaten Beuth Hohshule ür Tehni Berlin (uvor: Tehnishe Fahhohshule Berlin) ISSN (Print) ISSN 86-8 (Internet)

2 ii Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Berihte aus dem Fahbereih I, Wirtshats- und Gesellshatswissenshaten, Beuth Hohshule ür Tehni Berlin Beriht Nr. / Shlin, Haio: The determination o untion osts to ahieve suess-oriented design o engineering produts theory and appliion About the author: Pro. Dr. rer. pol. Haio Shlin is Proessor or Business Administration / Engineering Design at Beuth University o Applied Sienes in Berlin/Germany. He has six years woring experiene in the medial devie industry with Dräger Medial AG & Co. KG in Lübe/Germany. His proessional baground is in business administration and engineering and he ompleted his dotorate with the prodution and operations management group at Ilmenau Tehnial University in. His speii researh interests are in innovation management and produt development. Impressum Herausgeber: Fahbereih I der Beuth Hohshule Berlin Beuth Hohshule ür Tehni Berlin (uvor: Tehnishe Fahhohshule Berlin) Luxemburger Str. 5 Berlin Redation: Pro. Dr. Ing. Werner Ullmann Tel.: Fax: bi@beuth-hohshule.de Internet: Verantwortlih ür den Inhalt ist/sind die Autor/en der Berihte. ISSN (Print) ISSN 86-8 (Internet) Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

3 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts iii Content Introdution. The Elements o suess-oriented engineering design. The m:n-relationship between untions and omponents Method or the determination and breadown o untion osts 4. Explanation o the relationship between untions and omponents 4. Estimation o the osts o Category One. Calulation and brea down o untion osts.4 Importane o the dierent egories o untion osts Funtions osts or a ar par management system 5. Analysing the untions and omponents o the ar par system 5. Estimation o the osts o Category One 8. Calulation and brea down o untion osts.4 Importane o the dierent egories o untion osts 4 Conlusion 5 Reerenes 4 Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

4 iv Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Figures Fig. : Funtions and their importane as igures o osts and beneits in suess-oriented engineering design... Fig. : Priniples o ost alloion over a produt, its untions and its omponents... Fig. : The general proess o ost-oriented engineering design... Fig. 4: P relations between untions () and omponents () o engineering produts... 4 Fig. 5: Arrow diagram to show the Category One osts (or a partiular omponent j) whih are diretly attributable to the untions and require estimation... Fig. 6: Struture o the estimation tas in respet o Category One osts or a partiular omponent j... Fig. 7: Signiiane o the Category Two and Four untion osts or ost-oriented design o engineered produts... 4 Fig. 8: Format o the ar par management system, onsisting o a entral oie with a personal omputer, plus 5 pay-and-display mahines on the paring area... 5 Tables Table : Presentation o the m:n-relationship (rom Fig. 4) as a table o ombinations... 5 Table : Important equations or the determination and breadown o untions osts. The index T in the equations 9 and indies the transposed matrix... 7 Table : Table o ombinations or the itive :-relationship rom igure Table 4: Table o ombinations or the itive :n-relationship rom igure Table 5: Table o ombinations or the itive m:-relationship rom igure 4... Table 6: Funtions o the ar paring system, expressed as noun and verb... 6 Table 7: Results o the ABC-analysis or the omponents o the ar paring system... 6 Table 8: Table o ombinations, indiing the relations between the untions and omponents o the ar paring system... 7 Table 9: Struture o the estimation tas or the oin proessing unit as a representative omponent... 9 Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

5 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Introdution. The Elements o suess-oriented engineering design Engineering design an be deined as a proess o transorming the ustomer s statement o requirements into a ull desription o the proposed engineering produt (re. Huba 987, p. and Pahl/Beit 996). It is obviously the goal o all engineering design to produe a suessul produt. Suess an be measured in omparing the turnover (prie multiplied by quantity sold) with the osts generated or the ompany by this turnover (see Fig. ). To analyse and predit produt suess, representative igures will be required or the inputs and outputs o the prodution proess i.e., not only or the generation o the goods (outputs) but also or the onsumption o resoures (inputs). In the engineering design ontext, it is then a question o how best to inluene eah o the igures (that or the turnover and that or the ost o the turnover, whih are both suess ators) so as to improve the produt s eventual suess. It is possible to hange the turnover or the produt, i.e. item prie and quantity sold, by modiying the produt beneit and/or the osts (the latter by modiying the onsumption o resoures). Produt suess Turnover o = - produt Costs o turnover Fators or suess => Beneit to ustomer Consumption o resoures Demonstrated suess => Costs and beneits o produt untions Fig. : Funtions and their importane as igures o osts and beneits in suess-oriented engineering design The goal o suess-oriented design o a produt an thus be desribed as improvement o produt beneit and redution o resoure onsumption. To bring this down to operational level in engineering design, it is neessary to brea down the goals into targets or individual elements o the produt the omponents or the untions, or instane (re. Ansari/Bell 997, p. 46). I one taes the omponents, it is easy to get a representative igure or the osts but not or the beneits. That leaves the untions as the only ators suseptible to demonstration o both osts and beneits. The untions are thus o entral importane in oniguring a produt or maximum suess (see Fig. ). The beneit whih a produt owes to its untions will relate to the maret segment the produt is designed or, and Conjoint Analysis is one way o estimating it (re. Green/Srinivasan 978, These ators o suess are also used when Value Engineering is applied. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

6 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Green/Srinivasan 99). Funtion osts, on the other hand, have to be obtained rom the ompany where the produt is produed. The osts are usually generated by the omponents the produt onsists o. Produt onsumption o resoures beneit to ustomer Produt untions onsumption o resoures onsumption o resoures Produt omponents Fig. : Priniples o ost alloion over a produt, its untions and its omponents Cost-oriented engineering design, whih is to be seen as part o suess-oriented design, is at heart a ost-oriented seletion o alternatives. The produt with the minimum osts is the one liely to ost least by virtue o the hoies made or it out o a given array o design options. There are ive steps in the proedure or ost-oriented design (see Fig. ). Step Three is the really vital part. This is when the hoie is made o the design alternative thought liely to be the most eonomial whih is a diret deision about whih onsumables are in uture liely to be most in shortage. Step Two is a prognosis o the osts liely to be generated by the various alternative designs assembled. Step One is to assemble the inormation both available and relevant to the deision-maing proess. This inormation will inlude not only standard manuaturing osts but also details o lie-yle onsiderations already neessary to tae into aount. One the hoie has allen on one alternative, the produt an be turned rom an idea into reality and then sold (Step Four). With hindsight (Step Five), the osts atually generated are reorded and an then serve as a oundation or urther deision-maing (re. Horngren et al. 5). As ost management an be basially interpreted as deisions about goods in short supply, the pratial impliion is that options have to be hosen whih best meet the relevant targets. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

7 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Step : Step : Assemble o relevant inormation Prognostie ost onsequenes o alternative designs Feedba Step : Choose alternative liely to be most eonomi Step 4: Exeute alternatives and sell produt(s) Calulate atual osts Step 5: with hindsight Fig. : The general proess o ost-oriented engineering design In the ontext o the proess o ost-oriented design here introdued, ost is assumed throughout the design proess to be an ative (ausative) ator rather than a passive (aused) ator (re. Blanhard 978, p. ).. The m:n-relationship between untions and omponents For the determination o untion osts it is neessary to assign the osts rom the elements o the struture o omponents to the elements o the struture o untions. Between both o these strutures there is a very omplex m:n-relationship. Looing at this relationship the question arises o whether it is possible in priniple to determine untion osts on the basis o omponent osts. The problem beomes even more omplex i one loos at the at that or every relation between a single untion and a single omponent weightings are neessary, whih are usually estimations. The two undamental questions whih require an answer when untion osts are being determined are - What untion osts are relevant to the purpose underlying the alulation? - How an the assignment o osts between untions and omponents be exeuted in a situation with a omplex m:n-relationship? Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

8 4 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Method or the determination and breadown o untion osts. Explanation o the relationship between untions and omponents Target Costing involves breaing down the Target Costs or the whole produt to relet the individual produt untions or operational purposes (re. Yoshiawa et al. 99, pp. 5 and Monden 995, pp. 7). The next stage is to distribute the target osts or the untions over the various omponents. However, there is usually an m:n relationship between the untions and the omponents o an engineered produt, ditated by the design. What this means is that it is not only possible or one untion to be realised by a number o omponents, but also or a single omponent to be involved in the realising o a number o untions. Looed at rom the mathematial standpoint, what there is here is a relation. A relation is the desription given to the lin between the elements o a set (in this ase, two sets, the set o untions and the set o omponents). This situation, symbolially exempliied in Fig. 4, is the starting point or this paper and its urther observations. : : n m : 4 4 m : n 4 4 Fig. 4: P relations between untions () and omponents () o engineering produts The relationships between untions and omponents in engineering design is a binary one, as there are only two possibilities, i there is a relation between a partiular untion and a partiular omponent, and i there is none. The set o untions an be shown in relation to the set o omponents using a ombinatory table whih presribes the lin in eah ase (see Table ). I it is neessary to wor on the relations or the untions (as is the ase when untion osts are being alulated bottom-up, on the basis o omponent osts), Table will be read downwards rom the top. I the omponents osts are being alulated top-down on the basis o the untion osts, the relations will be read o rom let to right. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

9 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts 5 Table : Presentation o the m:n-relationship (rom Fig. 4) as a table o ombinations Comp. j Funtions i As the ase may arise o untions or omponents appearing twie, a ase exempliied by omponent no. in Fig. 4, these elements should really be entered twie into the matrix. To avoid having to do this, a ator ij is introdued or the bottom-up ase whih will show how many idential omponents j are in a relationship with a ertain untion i. The alloion presription between the olumn vetor o the produt untions F (I,) and the olumn vetor o the produt omponents K (J,) is equivalent to the multipliion o C ( I, J ) by K (J,) and is given in Equation. Equation desribes the elements o the matries and Equation ontains the igures or the quadrati matrix C ( I, J ) or the relations shown in Figure 4. () F( I,) C( I, J ) K( J,) () I I I J J IJ J () I it is a question o alulating the osts o the untions in the reverse diretion (i.e., a topdown alulation), the situation is omparable. The alloion presription between the olumn vetor o the omponents and the olumn vetor o the untions is produed, as shown in Equations 4 and 5, by multiplying H ( I, J ) by F (I,). Here the ator h ij reveals how many idential untions i are in relation to a ertain omponent demonstrates the situation in the example shown in Fig. 4. (4) K( J,) H( I, J ) F( I,) j. Equation 6 (5) J h h h J h h h J h h I I h IJ I Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

10 6 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts (6) To alulate osts o Category Three (bottom-up or top-down) it is now neessary to ind a share-o-osts ator a / b, whih will indie what proportion o the osts o the relevant ij ij omponents related to untions, or untions related to omponents, is appropriate to be alloed. The share-o-osts ators are assigned to the relevant relations. The olumn vetor o the untion osts CA ( I, J ) is the produt o the matrix Z K ( J,), and the olumn vetor o the omponent osts CA ( I, J ) (see Equations and 4 in Table ), whereby the matrix ij onsists o the ators a ij and the share-o-ost ators Z F ( I,), alloed. For the reverse ase, the alulation o omponent osts on the basis o the untion osts, Equation 5 or 6 an be applied. The olumn vetor o the omponent osts HB ( I, J ) is omposed o the produt o the Z F ( I,), matrix and the olumn vetor o the untion osts, Z K ( J,),. The h ij matrix ontains the ator HB ( I, J ) b ij and the share-o-osts ator. This share-o-osts ator indies what proportion o the osts o a untion is to be attributed to the relevant omponent. See also table on the subjet o egorising untion and omponent osts. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

11 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts 7 Table : Important equations or the determination and breadown o untions osts. The index T in the equations 9 and indies the transposed matrix Categories Funtions Components Category One U U (7) = oij = o i, ijuo (8) = oij = o j iju u= u=, o Category Two Category Three (9) T = KO J C i (, ), (, J ) () = [ oi oi oij] i i, i () Z F = CA ( I,), ( I, J ) Z K( J,), (4) = I a a a I I a a a I J J a a a Ji I J IJ J J IJ T () = KO( I,) C(,) j, I () = [ o o o ] j j, j j ji j (5) Z K = HB ( J,), ( I, J ) ZF ( I,), (6) h = h h J b b b J h h h J b b b J I I b b b Ij J I h h h IJ I I IJ Category Four J (7) = ( ) i, 4 j, ij + j, i, j= - a-weightings b-weightings Cost weightings (8) a ij o ij ij j, ij = (9) b ij = aij j, i, The m:n relationship onsidered so ar represents the general ase, in whih one untion an be related to a variety o omponents and one omponent to a variety o untions. Now ollows a onsideration o the three speial ases, a : relationship, a :n relationship and an m: relationship. These are depited in Figure 4 in the orm in whih they an appear in priniple. 4 The : relationship is rom the point o view o ost alulation the simplest ase o a relation between the untions to be perormed by a tehnial produt and the omponents required or their perormane. Reading o the ombination table rom the top down, it is lear that eah untion stands in relation to a single or to several idential omponents. 4 The literature desribes the our potential types o relationship, m:n, :n, m: und : (Yoshiawa et al. 99, p. 5). Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

12 8 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts The same is true or this type o relation i Table is read rom let to right. Eah omponent is related to only a single or to several idential omponents. Table : Table o ombinations or the itive :-relationship rom igure 4 Comp. j Funtion i I the ombination table is expressed as a matrix, the : relation is lear rom the at that in eah row and eah olumn o C ( I, J ) and H ( I, J ) only one ield is not equal to ero, i.e. represents an atual relationship. An example o this an be ound in equations and or the situation shown in Fig. 4. () () The nature o the : relationship means that the osts o omponents do not have to be split over two or more dierent untions and the osts o untions do not have to be distributed aross two or more omponents. The share-o-osts ators b ij and a an thus only have one o the two values, (no relation present) and (relation exists) as shown in Equations and. () (),,,, = =,,,, I the relationship is :n, one untion an be related to move than dierent omponents. This situation is shown in Table 4, i it is read rom the top down, i.e. rom the point o view o the untions. In the reverse diretion eah omponent is related to a single or to several idential omponents. ij Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

13 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht / 9 The :n relationship is reognisable in the matrix rom the at that, in ), ( J I C eah row and in ), ( J I H eah olumn, ontains at least two ields whih are not equal to ero. The situation o a :n relationship is demonstrated or the example depited in Fig.4 by Equations 4 and 5. (4) 4 (5) 4 Another harateristi o this type o relation is that the ij a share-o-osts ators an only have the value or, exatly as in the ase o a : relationship (see Equation 6), as eah omponent is only related to one untion (or several idential ones).in ontrast, the ij b share-o-osts ator an assume any value between and and is represented as a ormulai symbol in Equation 7. (6) = 4,,,,,, (7) =,, 4,,,, 4 b b b b Table 4: Table o ombinations or the itive :n-relationship rom igure 4 Funtion i Comp. j 4 4

14 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht / I the relations is an m: type, one omponent an stand in a relationship with a number o dierent untions. On the other hand, one untion relates only to a single omponent (or to several idential ones - see Table Table Table Table 5). From Equations 8 and 9 it an be seen that a m: relationship is present in that in eah olumn o ), ( J I C and eah row o ), ( J I H, at least two ields are not equal to ero. (8) 4 (9) 4 In this ase, that o the m:l relationship, the ij b share-o-osts ators an only assume the values or (see equation ), but the ij a share-o-osts ij b will be any value rom to (shown in Equation ). () =,, 4,,,, 4 a a a a () = 4,,,,,, Table 5: Table o ombinations or the itive m:-relationship rom igure 4 Funtion i Comp. j 4 4

15 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts. Estimation o the osts o Category One Fig. 5 shows an exerpt rom an m:n relationship in whih the osts o egory whih require estimation are entered. I o j o j o Ij The ollowing three questions, whih express the internal logi o the estimation proess, must be answered in onnetion with this estimation: Question : What resoures are onsumed or the prodution o omponents j? - Answer: Resoures U or V (see also the struture in Fig. 6). Question : For what purpose are these omponents j required i.e., indiretly, what are the resoures required or? - Answer: To ulil the untions I. Question : By how muh will the onsumption o the resoures v, be redued i untion i ails to be ulilled? - Answer: By q (see also the struture in Fig. 6). j Fig. 5: Arrow diagram to show the Category One osts (or a partiular omponent j) whih are diretly attributable to the untions and require estimation Level Level Level o j o j o Ij o o jo jo o juo o o jo jo o juo o o o Ijo Ijo IjUo o o = p q j j = p q j j jv = p V q j V o Fig. 6: Struture o the estimation tas in respet o Category One osts or a partiular omponent j Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

16 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts The struture o the estimation tas has three levels and is divided into three struturally idential branhes. Eah branh shows the struture o the resoures that are used to produe the omponents j, and is onerned with a untion i, whih relates to the omponent. Level one ontains the osts o Category One o ij or all untions o ij standing in relation to the omponents. On level Two the types o osts aused by the predition o the omponents are ontained, grouped into egories. Suh ost egories are, or example, materials osts or manuaturing osts (re. Monden 995, pp. 9). As this osts struture is liely to be too omplex or many uses, osts egories should be urther dierentiated on Level Three. There, the ost egories suh as materials osts are broen down urther, e.g. ost o opper. The estimated igures will be ombined or eah egory. On Level Three the type o ost will also be split up into its quantity and prie per item elements. In this manner, Level Three o the ost estimation onstitutes a mehanism whereby a hange q in the quantity o a resoure (opper, or example), is estimated i a untion is deleted whih had a relationship with a partiular omponent.. Calulation and brea down o untion osts As an be seen rom the struture o the estimation tas (see Figure 6), hanges in quality are estimated on the lowest level (see Level Three). These redutions inreases are multiplied by the prie or the relevant resoure, whih results in the ost modiiion designated by the ormulai symbol o. I these hanges in ost are added together or ijuv eah resoure u (see Equation ) used in produing the omponent j (see Level Two), the result is the omponent osts in egory or the omponent; in relation to untion i; and this result an be expressed either as o ij or as j, (see Equation 8 in Table ). V () o iju o = o ijuv v= Using the C ( I, J ) matrix produed on analysis o the m:n relationship, the untions osts o Category Two an be alulated on the basis o Equations 9 or. To determine the untion osts or Category Three, it is irst neessary to alulate the share-o-osts a ators whih an be done using Equation 8. The a share-o-osts ators or a partiular omponent must add up to (one) see Equation. This is neessary, as % o the osts o any omponent should be used or the alulation o untion osts. I () a ij = i= ij Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

17 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts To alulate the share-o-osts ators, the Category One omponent osts j,, obtained rom the estimations, are required, as are the Category Two omponent osts. Then with the aid o the share-o-osts a ators, the Category Three untion osts j, are determined by applying Equations or 4. i, Category Four untion osts i, 4 an ensue aording to Equation 7. Category Three osts o the omponents j, ij with a relation to the untion are entered in this Equation, together with the Category Two omponent osts j, and the Category Two untion osts. The Category Two omponent osts will have had to be alulated beore having using Equations or. For the target osts split, the untion osts have to be broen down and assigned to the individual omponents o the produt (re. Ansari/Bell 997, p. 56). This splitting o the untion osts is ahieved in essene with the assistane o the share-o-osts b ator, whih an be determined on the basis o the Category Three untions and omponents osts ( i, and j, ) together with the share-o-osts a ators (see Equation 9). As % o the osts o a untion are to be assigned to the omponents standing in relationship with that untion, all b ij- values or the omponents added up must always be equal to (one), see Equation 4. J (4) b ij = j= Using the share-o-osts b ators, the target untion osts an be alulated rom either Equation or Equation 6..4 Importane o the dierent egories o untion osts I there is a deision to eliminate a untion rom a produt as urrently onigured, the Category Two untion osts are relevant to that deision, as they are the osts whih are deleted i the relevant untion no longer has to be ulilled (see Fig. 7). This egory o untion ost is thus partiularly important i produts are being reengineered, to instane in the ontext o a Value Analysis (re. Miles 96 and Saurai 996, pp. 55) or i the design is being adapted. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

18 4 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Eliminate this untion? (egory ) Only this untion? (egory 4) Fig. 7: Signiiane o the Category Two and Four untion osts or ost-oriented design o engineered produts The Category Three untions osts are signiiant in the early stages o engineering design, when the produt oniguration is settled on. It is they whih show the part played by untion osts i in the produt osts Z, and they an be ompared with the target untion osts. The latter omprise the Category Two untion osts plus a undamental element that is not generated by an individual untion but does arise or the produt as a whole. Together these are the osts aused by the untion within the ontext o the partiular oniguration o untions. Target Costing usually wors with Category Three untion osts, as the design and the osts are required to meet the maret setors speiiions in the medium term. Category Four untion osts an be interpreted as marginal osts in relation to the ero situation, i.e. the position where no untion o the produt has yet been ulilled. I a maret setor or a partiular potential ustomer only requests one untion, the osts or that untion will be in the amount o Category Four (see Figure 7). I the produt is to ulil more than one untion, but yet not all those originally proposed, urther egories o untion osts must be deined as a basis or that type o deision. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

19 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts 5 Funtions osts or a ar par management system. Analysing the untions and omponents o the ar par system A ar par management system basially onsists o two areas geographially separate rom one another: the entral management oie and the paring spae itsel. In the latter, the pay-and-display mahines are ereted or the ustomers to use. The user puts money into the mahine and reeives a tiet, whih is usually to be let on show in the ar. Small systems will have up to 5 mahines, major ones may well onsist o hundreds. The entral oie monitors and regulates the ar par harging system. Essential inormation must be stored in the mahines and transmitted to the oie. There are various omputer programs whih an be used to perorm or improve the monitoring and regulation. In the ase studied, the system was relatively small, in that it onsisted o 5 pay-anddisplay mahines. This sie o system an be managed rom a personal omputer and its peripherals (monitor, printer, DFÜ-PC point, tape drive) - see Fig. 8. Tape reorder Monitor Personel omputer Printer Long-distane data transmission Central oie Paring area Tiet mashine Tiet mashine Tiet mashine 5 Fig. 8: Format o the ar par management system, onsisting o a entral oie with a personal omputer, plus 5 pay-and-display mahines on the paring area The mahine provides the tiets or the paring spae being managed. The user an insert oins as the means o seleting a period (up to a programmed maximum time). The amount o time paid or, when it ends, and how muh has been paid as paring ee will be shown on the display ater eah oin is inserted. As the mahine has a modular onstrution, its untions an be varied to suit the operator. It an be set up, or instane, with the option o ard payment instead o or in addition to ash. Liewise, alternative display modules and other options are available. The number o possible variations is wide, but not every omponent is required or eah version o the mahine. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

20 6 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts As the share-o-osts or the dierent possible omponents o the ar par management system varies greatly as a proportion o the ost o the whole system, it maes ommerial sense to dierentiate between the omponents that have a signiiant eet on osts and those that do not. ABC analysis is o assistane here. To selet the omponents with high relevane to ost, there must irst be a ready-onigured version o the management system or whih omponents osts an be determined. As soon as the struture o entire system has thus been laid down, ost analysis an start. No. Table 6: Results o the ABC-analysis or the omponents o the ar paring system Desription Purhased parts in $ Manuatur ing in $ omplete mahine in $ 5 mahines in $ Costs (umulated) Fration in % Basi ormat ,85, Coin proessing , 8,95 5. trans- Data mission ,86 6, Hardware ,88 4, Energy supply ,5 47, Printer 4 6, 5, Sotware - - -,8 5, For reasons o eonomy, it is valuable only to inlude the signiiantly ostly omponents in the determination o untion osts. In the study, an ABC analysis was arried out, with the outome shown in Table 6. The seven most expensive omponents were then inluded in the investigation, ranging rom (basi ormat) to 7 (management sotware). As these seven overed 9.9% o the osts o the ar par management system, they were deemed suiient or the study. Table 7: Funtions o the ar paring system, expressed as noun and verb No. Verb Funtions Noun inorm user reeive paring ee ix paring ee 4 onirm payment 5 label ar 6 supervise untionality 7 supervise money transer 8 protet system Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

21 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts 7 Analysing the untion struture (as a untion tree) starts with an analysis o the purpose o the system in question. Expressed in omplex, abstrat terms this is the ommerial management o the paring spae. The overall untion an be subdivided into subordinate untions whih relet the strutural omponents o the system. Further subdivision is aompanied by redution in omplexity: i.e., the omplex overall untion is broen down into less omplex subdivisions (re. Huba/Eder 984, pp. 7 and Aiyama 99, p. 5). As alulating the osts or absolutely all the sub-untions would be uneonomi, a degree o detail has to be seleted whih is adequate to ost-oriented produt design, by exluding untions with low omplexity. In Table 7 there is a summary o the untions whih require their ost to be analysed. They are stated in the onventional (re. Aiyama 99, p. 4) orm o noun and verb. There is an m:n relationship between the untions and the omponents in this produt, and it an be depited in a ombination table whih desribes the relation between the elements o two sets, in this ase the set o untions and that o omponents (see Table 8). Table 8: Table o ombinations, indiing the relations between the untions and omponents o the ar paring system Funtions i Components No. j There are eight elements ontained in the untion set and 78 in the omponents set; o this set, omponents nos.,,, 5 and 6 are ontained 5 times in the ar par management system in idential orm. The igures entered in Table 8 indie a relation between the relevant omponent and untion. I there is no entry in the table, the elements do not have a relation to one another. It is learer to show the relation as a matrix i the situation is one where ertain omponents or untions reur in idential rom, as in the present example. I a omponent or a untion only appears singly, the matrix will depit the ombination table presented as Table 8 with either a (relation exists) or an (no relation exists). Reading the ombination table rom the top down, the matrix is obtained or the bottom-up situation - untion osts determined on the basis o omponent osts, as shown in Equation 5. For the ar par system and the bottom-up situation, the proportion o the ost o a omponent (e.g. omponent no. ) assignable to a untion (e.g. untion no. ) is multiplied on the number i Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

22 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht / 8 idential omponents that are related to that untion (5 in the example). What is meant is that the 5 omponents o type are all involved in the ulilment o the untion no.. (5) On the other hand, i the ombination table is read o rom let to right, the situation is topdown and is desribed by Equation 6: the untion osts are broen down and assigned. In this ase, the proportion o the ost o a untion (e.g. untion no. ), whih alls on to the omponents standing relation to the untion (e.g. omponent no. ) must be divided by the number o idential omponents whih have that relation (5 in the example). This means that only /5 o the osts o untion an be attributed to a single no. type omponent. (6) Estimation o the osts o Category One The struture o the estimation test as it an be onstruted or the ar par system is shown intable Table Table Table 9. The omponent oin proessing (no. in the system) is in a relationship to untions,, 7 and 8 (see olumn A). Costs arise in onnetion with the installation o oin proessing in the system: osts or purhased parts and their assembly (see olumn B). The amount o these osts in the event is entered in olumn C and their estimated value in Column D. The estimator gives the value at whih the omponent osts alter.

23 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts 9 Table 9: Struture o the estimation tas or the oin proessing unit as a representative omponent A B C D Cost egory Funtion Formula Desription Initial base in $ Estimated value in $ o purhase o manuaturing 9 7 o purhase o manuaturing o 7 purhase o 7 manuaturing 9 8 o 8 purhase o 8 manuaturing 9 It is a vital preondition o proper estimations that the estimator is amiliar with the onstrution o the omponents and the ontent o the untions o the ar par management system. Only with suh omprehensive nowledge (onerning or example, oin proessing) an a ertain judgment be made as to the inluene o the untions on the partiular omponent. Not only is this nowledge o the onstrution o the omponents and the resultant osts o purhased parts neessary, but also experiene o manuature and assembly in the partiular ield, to aid understanding o the manuaturing osts. Estimation on a seure basis also requires other nowledge besides that o the onstrution and manuaturing proess. Knowledge o the ontent o the individual untions is indispensable, and suh is only to be obtained with good insight into that ontent (e.g., what is meant under untion no., reeive paring ee ). It is helpul to the estimator i the overall struture o the untions is laid out beore him or her, with relevant notes and possible highlighting. Then the untion in question an be viewed rom the standpoint o how it interats with other untions. The estimator, must, urthermore, be able to imagine a virtual omponent design 5 in whih these is no ulilment o the untions whatsoever. He or she must not only be apable o imagining the onstrution o the omponents to arrive at estimated osts or purhased parts, but also to arrive at the estimated manuaturing and assembly osts whih would arise rom the virtual omponent design as manuaturing proesses and times. The qualiiions neessary or the estimator an be laid down on the basis o the speiiions deined or the system. Suh qualiiions would generally inlude the overall personal sills, abilities and nowledge whih they possess to enable them to perorm a speii tas. In this ase the tas is the estimation tas, and the estimator must be equal to it. 5 A virtual omponent design here means the estimator s mental onstrut o ideal omponents. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

24 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts. Calulation and brea down o untion osts The data or omponent no. were obtained in the study rom a questionnaire ompleted by the way o example (see Table 9). This omponent osts (Category One) to be alulated aording to equation 8. Taing omponent no. as an example diret omponent osts or the untions (Category One) are the sum o the dierenes between the starting point and the estimated igures or the two types o ost: purhased parts and manuature. The osts ome to o = 5 $ or untion no., and to o = $ or untion no.. In ase o untion 7 and 8 they ome to o 7 = 7 $ and o 8 = 7 $. Equation 7 taes omponent no. as an example and shows how the Category Two omponent osts an be alulated with the aid o Equations or. The Category One, or diretly attributable, osts or omponent no. are added together as they are alulated or all untions to whih the omponent is related. (7), = [ ] =,785 $ Now untion may be taen as an example o how Category Two untion osts are alulated: the equation is Equations 8 and it proeeds using Equations 9 or. The Category One osts o omponent no. in relation to untion no. were determined as o = $. Given that omponent no. is ontained 5 times in the paring system, and that untion no. is related not only to omponent no. but also to nos. and 5, the Category Two the untion osts ome to =,77 $. (8), =, 65 [ ] =,77 $ Category Three untion osts an only be alulated i the share-o-osts ators have irst been produed. The a-share-o-osts ators are determined using Equation 8: below, the alulation o the a ator is demonstrated in Equation 9. The share-o-osts ators are Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

25 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts then entered into the matrix or the alulation o the Category Three untion osts (see Equation 4). o $ 5 (9) a = = =.,785 $ (4), ,95 5.7,7 5.8, =, , ,6 5.74, ,8 54 5, ,8. By multiplying the olumn vetor or the omponents osts by the matrix or the share-oosts ators, the neessary vetor or the untion osts an be ound. The sum o the osts or all the ators omes to 5.98 $ and is the atual ost o the entire ar par management system. This sum is also that obtained (but or small variations rom rounding up or down) when the osts o all 78 omponents are added together. To alulate the Category Four untions osts or untion no. aording to Equation 5 ( = 9 $, =,8 $, = 4 $ ) must irst be multiplied by the,, 5, number o these omponents (, 5 ) whih have a relation to untion no.., 5 = The untions osts are the sum o the dierenes (,6 $ ), =, plus the Category Two untion osts (,5 $, =, ), i.e. (,95 $ 5, 5 = 5,, =,77 $ )., To split the untion osts, the b share-o-osts ators are required. Equation 4 shows how this is done, using the b as an example.,,8 $ 5 (4) b = a =.=. 7,,7 $ The b ij -share-o-osts ators and the untion osts rom equation 4 an now be entered in the matrix used to alulate the omponents osts (see Equation 4). Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

26 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts (4) 9,8 54 5,88= 4, ,95.7 5,7. 5,96.9, ,9 4,6.7,8 The omponents osts alulated in Equation 4 must agree with those rom Table 6. The sum o 78 omponents omes to 5,98 $ and thus again relets the overall osts o the system..4 Importane o the dierent egories o untion osts The Category One osts are the osts applying to a single untion and a single omponent. It ollows that a single omponent no. (oin proessing) though it must be remembered that there are 5 o this omponent in the system an be alulated as being responsible or = o = $ o untion no. (ix paring ees). Conversely, and this is o, importane or untion osts splitting, = o = $ an also be broen down to untion no. or a single omponent no.., It is, however, interesting rom the point o new engineering design to as how high the osts o untion (ix paring ees) are i the Category One osts o all 5 omponent no. `s assoiated with this untion (whih are basi ormat and energy supply) are added together. A deision an be made, in the ontext o a Value Analysis (or example), on the basis o these osts, =,77 $, as to whether untion no. (ix paring ees), should atually be deleted rom the ar paring management system. I it is being deided in the early design engineering stages whether to inlude untion no. (ix paring ees) in how the system is onigured, the Category Three untion osts o =,7 $ are relevant. During Target Costing they an be ompared with the, untion osts derived rom maret researh and related to the ustomer beneit. The question an, indeed, be ased how high the ar par management osts are i solely the untion no. (ix paring ees) is to be ulilled; that is, i all the other seven untions are to be eliminated. The Category Four osts or untion no. would ome out at = 7,9 $., 4 Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

27 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts 4 Conlusion The question here addressed is how the alulated ost o onsumption o all prodution ators relevant to the entire lie yle o a produt an be alloed to individual produt untions. A method with general validity has been developed to alulate suh untion osts. Signiiant among the results obtained are the proposed solutions to the hitherto intransigent problems o untion ost determination, whih inlude thorough analysis o the m:n relationship between untions and omponents, a mathematial onept to desribe the untion osts in Categories One to Four, and presentation o the tas involved in estimating diretly attributable omponent osts (Category One). Funtion ost splitting onstitutes a urther issue whih is losely assoiated with untions osts determination and arises in assoiation with Target Costing. As the only question addressed in alulating and assigning osts between omponent and untions is whether they atually ause the ost, untion ost splitting is at heart untion ost determination. This being reognised, the question arises whether there is any target ost splitting going on at all when untion osts are split. As the splitting o target osts, at least those derived rom maret researh, is only logial i it ulils the ost/beneit priniple, the answer must be no. The aim o a untion osts determination method has been ormulated thus: it must be generally valid, truly represent ause and eet, and be ross-heable internally and usable in pratie. To assign omponent osts to untions, it is neessary to have a ormula whih does relet what auses what. To at as a basis or the ormula, an atual igure is required, the diretly attributable omponent osts (here alled Category One omponent osts) produed by the diret inluene the untion has on the omponent. I this is the ase, a high degree o reliability or the ause-and-eet lin is ensured. Cross-heability is ahieved when dierent people an produe the same or similar results. This is an issue, i or no other reason, beause there are subjetive elements ontained not only in untion ost analysis, but already in the untion models (partiularly the derivation o produt untions). By desribing in detail the proess o untion osts analysis, the amount o ree play allowed the investigating sta an be ixed rom the beginning, and the eets o subjetivity limited. By thorough pursuit o the analysis o the m:n relation and the detailed desription o the estimation tas, the wor desribed in this paper has made a signiiant step in the neessary diretion. To date, the subjet o untion ost analysis has been dealt with only with the tools o ostoriented engineering design, suh as Value Analysis, Target Costing or Quotation Calulations. Although the present wor oers its approah to untion osts analysis hiely as a servie to ost-oriented design in general and only seondarily to its urrentlyapplied instruments, it may well also serve a useul purpose in the resolution o the overall issues urrently onronting those instruments. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

28 4 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts 5 Reerenes Aiyama, K. Funtion Analysis: Systemati Improvement o Quality and Perormane. Cambridge, Massahusetts: Produtivity Press, 99. Ansari, S. L. and Bell, J. E. Target Costing: The next rontier in strategi ost management. Chiago: Irwin, 997. Blanhard, B. S. Design and Manage to Lie Cyle Cost. Portland: M/A Press, 978. Cooper, R. (): Target Costing or New-Produt Development. Journal o Cost Management 6(May/June): 5- (). Cooper, R. and Slagmulder, R. Target Costing or New-Produt Development: Component- Level Target Costing. Journal o Cost Management 6(September/Otober): 6-4 (). Ehrlenspiel K. Integrierte Produtentwilung. Münhen, Wien: Hanser, 9. Ehrlenspiel, K.; Kiewert, A. and Lindemann, U. Kostengünstig Entwieln und Konstruieren: Kostenmanagement bei der integrierten Produtentwilung. Berlin: Springer,. Green, P. E. and Srinivasan, V. Conjoint Analysis in Consumer Researh: Issues and Outloo. Journal o Consumer Researh 5(September): - (978). Green, P. E. and Srinivasan, V. Conjoint Analysis in Mareting: New Developments with Impliions or Researh and Pratie. Journal o Mareting 54(Otober): -9 (99). Horngren, C. T.; Rajan, M; Forster, G. and Datar, S. M.: Cost Aounting A Managerial Emphasis. London: Prentie Hall, 8. Huba, V. Priniples o Engineering Design. Berlin: Springer 987. Huba, V. and Eder, W. E. Theory o Tehnial Systems: A Total Conept Theory or Engineering Design. Berlin: Springer, 988. Miles, L. D. Tehnique o Value Analysis and Engineering. New Yor: MGraw-Hill, 96. Monden, Y.: Cost redution systems: Target Costing and Kaien Costing. Portland: Produtivity Press, 995. Monden, Y. and Hamada, K. Target Costing and Kaien Costing in Japanese Automobile Companies. Journal o Management Aounting Researh (Fall): 6-4 (99). [6] Pahl, G. and Beit, W. Engineering Design: A Systemati Approah. London: Springer 996. Saurai, M. Target Costing and How to Use It. Journal o Cost Management (Summer): 9-5 (989). Saurai, M. Integrated Cost Management: A Companywide Presription or Higher Proits and Lower Costs. Portland: Produtivity Press, 996. Shlin, H. Bestimmung von Funtionsosten tehnisher Produte: Grundlagen einer ostenorientierten Produtentwilung. Wiesbaden: Gabler, 4. Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

29 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts 5 Shlin H., Shneider H. and Höhne G. The Determination o Funtion Costs in Engineering Produts. International Conerene o Engineering Design, Vol., 9-6, Glasgow:,. Shneider, H. Zielostenmanagement in rühen Phasen der Produtentwilung. In: Das Rehnungswesen im Spannungseld wishen strategishem und operativen Management, H.-U. Küpper and E. Trossmann (eds.) Berlin:, 997. Tanaa, M. Cost Planning and Control Systems in the Design Phase o a New Produt. In: Japanese Management Aounting, Y. Monden and M. Saurai (eds.). Cambridge, Massahusetts: Produtivity Press, 989, pp Tanaa, M. Cost and Proit Engineering System in the Produt Design Stage in Japanese Companies. International Federation o Sholarly Assoiation o Management (IFSAM) Conerene Proeedings, 99, pp Wübbenhorst, K. L. Lie Cyle Costing or Constrution Projets. Long Range Planning 9: (986). Yoshiawa, T.; Innes, J.; Mithell, F. and Tanaa, M. Contemporary Cost Management. London: Chapman & Hall, 99. Yoshiawa, T.; Innes, J. and Mithell, F. Applying Funtional Cost Analysis in a Manuaturing Environment. International Journal o Prodution Eonomis 6: 5-64 (994). Yu-Lee, R. T. Target Costing: What you see is not what you get. Journal o Cost Management (July/August): -8 (). Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /

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31 Shlin: The determination o untion osts to ahieve suess-oriented design o engineering produts Bisher veröentlihte Berihte in dieser Reihe: Jahrgang 6 Beriht / 6: Beriht / 6: Beriht / 6 Beriht 4 / 6: Beriht 5 / 6 Jahrgang 7 Beriht / 7: Beriht / 7: Beriht / 7 Beriht 4 / 7: Jahrgang 8 Beriht / 8 Beriht / 8 Jahrgang 9 Beriht / 9 Beriht / 9 Beriht / 9 Ullmann, W.; Jordans, I.: Untersuhungen ur Standortrage von Logisti- Standorten unter dem Einluss der EU-Osterweiterung. Teil : Daten & Faten Ullmann, W.; Jordans, I.: Untersuhungen ur Standortrage von Logisti- Standorten unter dem Einluss der EU-Osterweiterung. Teil : Umrage- Ergebnisse Kleinert, H.: Studierende an Tehnishen Fahhohshulen: Lebensentwüre, Zuuntsbilder, Erwartungen. Bromann, H.; Greaney, P.K.: Gründungen aus Hohshulen: Ergebnisse und Impliationen einer Beragung von Drittsemestern der TFH Berlin Rohbo, U.: Entwilung eines Koneptrahmens ür den ommuniativen Autritt des Fahbereihs I der Tehnishen Fahhohshule Berlin Walter, H.-C.: Systementwilung - Planung, Realisierung und Einührung von EDV-Anwendungssystemen. Teil I: Systemoneption Doese, A.; Stallmann, M.: Worlie-Balane-Erwartungen von Ingenieurstudentinnen: ein Forshungsprojet. Kleinert, H..: Produtentwilung in tehnologie-orientierten Gründungsunternehmen: ein Erahrungsberiht Ullmann, W.; Axmann, R.; Doberstein, D.: Einsat von RFID in der Baulogisti: Ergebnisse einer Unternehmensberagung Bromann, H.; Greaney, P.K.: Gründungen aus Hohshulen: Ergebnisse und Impliationen einer Beragung von Drittsemestern der TFH Berlin (Spätphase) Pattloh, A.; Sholt, G.: Der Einsat von Blogs in der internen Unternehmensommuniation. Doese, A.: Der Einluss neuerer Gesetgebung au Einstellungs- und Karrierehanen qualiiierter Frauen, unter besonderer Berüsihtigung der Ingenieurinnen König, A.: Anerennung beruliher Vorerahrungen am Beispiel von Studierenden der Dru- und Medientehni - Doumentation einer Analyse Blo, J.H.; Bromann,H.; Klandt, H.; Kohn, K.: Gründungshemmnisse in Martmehanismen und umeld Faetten empirisher Eviden Berihte aus dem Fahbereih I Wirtshats- und Gesellshatswiss. Beuth Hohshule Beriht /