Clément Chatras
email: clement.chatras@renault.com

Vincent Giard
email: vincent.giard@dauphine.fr

Standardization, Commonality, Modularity: a Global Economic Perspective

Keywords: Standardization, management of diversity, optimization, product design, BOM definition

This paper deals with the problem of simultaneous standardization of a set of modules and of multiple sets of components that may be combined in these modules. The aim is to minimize future costs. The components and modules, whether already existing or yet to be created are not related to predetermined BOMs. The problem takes into account coupling constraints between components because not all components included in a module may be coupled (coupling restriction), although some of the restrictions can be lifted through "junction components". Our approach is readily implemented and significantly improves decisional consistency when compared to the standardization approaches that deal with the problem in isolation as opposed to globally. It also matches the level of detail used in large organizations for forecasting purposes. This approach is illustrated with a real case study of great dimension.

Introduction

Standardization is a process aiming to rationalize the definition of a set of components with different functional features that are used to satisfy a number of needs of similar nature (Rutenberg 1969[START_REF] Fisher | Component Sharing in the Management of Product Variety: A Study of Automotive Braking Systems[END_REF][START_REF] Dupont | Standardisation D'une Famille Ordonnée de Composants Dont Le Coût D'obtention Est Concave[END_REF][START_REF] Perera | Component Part Standardization: A Way to Reduce the Life-Cycle Costs of Products[END_REF], Baud-Lavigne et al. 2012…). We call these components 'alternative components (ACs)' and related sets 'set of alternative components (SAC)'. In general, when this process is in place, a SAC already exists and can be completed by a set of components that are still in the pre-development, study phase. The functional features of the related ACs are of the same nature as that which currently define the needs to which demand is associated. The proposed rationalization exercise generally results in reducing the number of components as well as the expenses committed to satisfy the needs. Standardization, therefore, is key to improving competitive advantage, particularly in the context of mass production. In practice, the combination of different SACs is limited by technical restrictions that affect the efficiency of models that standardize each SAC separately. We propose a solution to lift some of these restrictions and the related interfacing issues between two ACs through what we call "junction components". Modules are particular components that combine elementary ACs belonging to multiple SACs. Modules may exist physically and be delivered to an assembly plant, or virtual and be set up at the production line. Standardization, therefore, can occur at module level, with "alternative modules (AMs)" being selected from a set of AMs (SAM). The modules match needs that we call "services" while the different kinds of needs are called "alternative services (ASs)". These represent the diversity of combinations of functions delivered to customers via such devices as web configurators. The set of ASs must be covered by the relevant SAM. By introducing modules one is able to use the sales forecasts usually prepared at AS, aggregated level. This level of aggregation moreover is adequate to make reliable forecasts down to AC level, where most of the cost saving opportunities are.

A particular AC can be mounted on several AMs, thus creating a commonality, from which valuable economies of scale may be derived. In this context, standardization must be handled jointly at AM and AC level, it being understood that AC demand stems from demand for the relevant AMs. This aspect is all the more valuable as demand forecasts may be limited to an aggregate level and as, in the approach we use, the BOMs for the AMs remain to be defined. The simultaneous optimization of SAM and component SACs standardization is the first contribution of our paper. Its other contribution relates to the cost savings opportunity. We shall show that the cost-benefit analysis enabled by the model covers both the time horizon and spatial dimensions.

Our paper opens with a review of literature on standardization as circumscribed to the relevant scope (Section2). This shall highlight a number of gaps that our model proposes to close. The next section shall present our model which builds on the work described in the literature we reviewed and enables a simultaneous standardization of AMs and their component ACs to be performed (Section 3). We end the paper with a a quantified case study and a conclusion.

2

Literature review

Our article is geared to standardization models and we therefore reviewed papers proposing prescriptive methods to reduce diversity. Accordingly, our analysis excludes both papers dealing with diversity management methods as well as descriptive papers [START_REF] Martin | Design for Management and Control of Production and Logistic Variety: Developing Standardized and Modularized Product Platform Architectures[END_REF][START_REF] Fonte | A de-Proliferation Methodology for the Automotive Industry[END_REF]Sered and Reich, 2006;[START_REF] Perera | Component Part Standardization: A Way to Reduce the Life-Cycle Costs of Products[END_REF]. We reviewed research into ways of standardizing components, modules or both. Our definition of modules is compatible with that expounded in the body of reference literature [START_REF] Ulrich | The Role of Product Architecture in the Manufacturing Firm[END_REF][START_REF] Sanchez | Modularity, Flexibility, and Knowledge Management in Product and Organization Design[END_REF][START_REF] Baldwin | Managing in an Age of Modularity[END_REF][START_REF] Dahmus | Modular Product Architecture[END_REF]. We are not seeking to define an optimal modular architecture, a matter we consider settled, but rather to define AM diversity in a way that is relevant for any particular SAM. We found two distinct approaches in the prescriptive research surveyed.

 That of the school of research focusing on postponed differentiation. Here, the set of SACs and their ACs is known and the question is to find the optimal level of AM diversity (where AMs are seen as groups of components) to be managed ). These papers address quality and assembly time rather than cost reduction issues. In this case, the make-up of SACs used to build the modules is predetermined and not open to amendment through introduction of new ACs. This approach therefore appears to be quite remote from the multi-level standardization approach we chose.  In the second school of research, that founded by Renard (1877), the starting point is a set of needs and of a set of components suitable to meet them. Here, the onus is on determining the corresponding diversity at the lowest cost for this set to be used and therefore produced [START_REF] Rutenberg | Design Commonality to Reduce Multi-Item Inventory: Optimal Depth of a Product Line[END_REF][START_REF] Dupont | Standardisation D'une Famille Ordonnée de Composants Dont Le Coût D'obtention Est Concave[END_REF][START_REF] Fisher | Component Sharing in the Management of Product Variety: A Study of Automotive Braking Systems[END_REF][START_REF] Lamothe | An Optimization Model for Selecting a Product Family and Designing Its Supply Chain[END_REF][START_REF] Giard | Analyse Économique de La Standardisation Des Produits[END_REF][START_REF] Giard | Economical analysis of product standardization[END_REF][START_REF] Chatras | Economic variety control and modularity[END_REF]. This question can be posed at any phase of the life cycle of a product or set of products. Here, the aim is to find the best compromise between the cost of excessively diverse solutions tuned to a wide variety of needs and the cost of a single, overperforming solution, capable of meeting all needs. The definition of a SAC is sometimes implicit in the literature [START_REF] Rutenberg | Design Commonality to Reduce Multi-Item Inventory: Optimal Depth of a Product Line[END_REF][START_REF] Dupont | Standardisation D'une Famille Ordonnée de Composants Dont Le Coût D'obtention Est Concave[END_REF][START_REF] Lamothe | An Optimization Model for Selecting a Product Family and Designing Its Supply Chain[END_REF] as it is not linked to the definition of any function used to define needs and components. Where the SAC is explicit, it is defined either through a single function (Renard, 1877;[START_REF] Fisher | Component Sharing in the Management of Product Variety: A Study of Automotive Braking Systems[END_REF] or through several fuctions [START_REF] Giard | Analyse Économique de La Standardisation Des Produits[END_REF][START_REF] Giard | Economical analysis of product standardization[END_REF]. From an operational standpoint it is clear that defining components through multiple functions is both more efficient for analytical purposes and for the purposes of defining the input data for the optimization model. Some authors on standardization as it is defined in our introduction have attempted to standardize several interdependent SACs simultaneously [START_REF] Rutenberg | Design Commonality to Reduce Multi-Item Inventory: Optimal Depth of a Product Line[END_REF][START_REF] Dupont | Standardisation D'une Famille Ordonnée de Composants Dont Le Coût D'obtention Est Concave[END_REF][START_REF] Lamothe | An Optimization Model for Selecting a Product Family and Designing Its Supply Chain[END_REF]. But they did not propose to introduce "junction components" to lift some of the coupling restrictions and so further streamline costs. Moreover, none of these articles include a simultaneous analysis of standardization at two levels of the BOM to deal with the overall diversity of a SAM and of its component SACs as the first step of an approach that can have several levels.

The approach that we develop aims to fill the gap through a model readily useable by business actors to directly and easily integrate all of the technical constraints and junction components capable of lifting some of them. The determination of demand through ACs is a major stake for the model as it is crucial to the solution [START_REF] Fisher | Component Sharing in the Management of Product Variety: A Study of Automotive Braking Systems[END_REF][START_REF] Baud-Lavigne | Mutual Impacts of Product Standardization and Supply Chain Design[END_REF]. Approaches that fail to take demand into account in the target function thus appear not to be entirely relevant from an economic standpoint (Renard, 1877;Agard and Tollenaere, 2002;Agard and Penz, 2009). All of the other approaches rely on volume or percentage by type of need. Our model improves the definition of demand used for economic analysis in three important respects: first by lending consistency to the demand to be satisfied by the AMs and the ACs without reference to any predetermined BOM. Here the BOM actually stems from the optimization exercise. Second, recourse to modules uses an aggregate level of forecasting similar to that produced by sales departments. Third but not least, not only does it take into account demand but also demand change and life cycle dynamics as well as the emergence of new future needs.

Additionally, the fact that the model is capable of integrating the time horizon, an essential feature of strategic choices, enables it to account for both existing and future needs [START_REF] Fisher | Component Sharing in the Management of Product Variety: A Study of Automotive Braking Systems[END_REF]. Our recommendation diverges slightly from that by [START_REF] Lamothe | An Optimization Model for Selecting a Product Family and Designing Its Supply Chain[END_REF] (only paper to have explicitly taken time into account in the target function). To conclude this literature review, we note that our approach is in line with part of the body of research and introduces a number of substantial improvements.

Formulation of the standardization problem

Our description of the problem is a two-stage process. We begin by a quick analysis (Section2.1) of the models our approach actually extends. This will enable us to discuss a few important concepts as well as introduce our analytical approach. We go on (Section2.2) to fully develop our model against a general context. One can find a table of notations by using the link in section 4.

The Single SAC Standardization Model

Renard (1877) appears to be the first author to have streamlined the number of ACs required to meet multiple demands. A single functional characteristic f is used to specify the need to be satisfied by an AC and a single technical characteristic q of the AC is taken into account; in the case studied by Renard, q is the diameter of cable and f is the maximum traction the cable can sustain before breaking. Through an experimental study, f is described by a monotonous increasing function of q. Renard proposes to define the variety arbitrarily, by breaking up the possible values for f into a fixed number of ranges whose upper limits are subject to geometrical growth. One may criticize this approach in three respects, all of which are actual shortcomings of a number of current ISO standards: it uses a single functional characteristic of continuous nature; one has no reason to determine a priori the optimal number of ACs; the definition of the number of ranges and their boundaries is not based on any economic criteria since demand and costs are not part of the reasoning.

An explicit reference to several functional features and economic criteria is proposed by [START_REF] Giard | Analyse Économique de La Standardisation Des Produits[END_REF]Giard ( , 2002)). The selected features may be quantitative (weight, torque…) or qualitative (reference to a standard…). of these ACs, either existing or under study can be drawn up, with item R fc corresponding either to a numeric value or to a qualitative attribute (see tables below). The inclusion of ACs in the study phase refers to a perception of future needs, useful in substantiating the conclusions of the selection process. In order to harmonize the terminology used, we consider in this paragraph that an AS is directly satisfied by an AC, since we consider a single BOM level. To each AS s ( 1..S) s  is associated demand p d , these ASs actually corresponding to the breakdown of demand. An AS is satisfied by a single AC, which is justified in the absence of production constraints, by the fact that we should use the most cost-efficient AC to satisfy an AS, with any mix leading to a cost increase. On the other hand, an AC can satisfy several ASs. The analysis of these ASs is based on the same functional AC features with quantitative features corresponding to value ranges and qualitative features to the list of acceptable attributes. The cost function developed by [START_REF] Giard | Analyse Économique de La Standardisation Des Produits[END_REF]Giard ( , 2002) ) in this formulation of the problem is more complex: it is a monotonous increasing function, which is partly linear. This enables the inclusion of new AC study and investment fixed costs stemming from development of new CAs while in their pre-launch, study phase. It also enables the inclusion of any positive or negative synergy effects induced by production of several ACs at a particular site.

Table 1. example of functional definition of 10 ACs, 14 ASs and the Boolean matrix resulting from the cross-referencing of these definitions This approach, however, present three important limitations that we address under Section 3.2: first the SACs are supposed to be independent but this is not realistic (Chatras & Giard, 2014); moreover, defining needs and, therefore, demand at component level is very difficult in practice; finally, these approaches largely ignore the spatial (logistical chain) and temporal aspects (demand change and possible launch of new components) in the cost function.

Formulation of joint standardization of a SAM and its component SACs

The originality of our extended model lies in the simultaneous selection of AMs and their component ACs to satisfy the requirements of a set of ASs. In our proposed model, Boolean variables are linked to these decisions (Section3.2.1). The way in which both the time horizon and spatial dimensions are factored into the coefficients of the target function is described under Section3.2.2. below.

The basic model

Our formulation uses four kinds of sets: ASs, ACs and SACs complemented by another set, discussed below, so as to include the junction components required to couple two ACs from two different sets in the absence of any suitable interface.

 The set of alternative services includes S ASs, subscripted by s. s d is the Demand for service s.  The set of alternative modules includes M AMs, subscripted by m. Some AMs may not meet the needs of some ASs. The Boolean parameter asm takes a value of 1 where AM m is suitable to meet demand for AS s, and the value 0, if it does not. An AM may satisfy several ASs. Since the needs for an AS are met by a single AM, the number of AMs selected in the solution cannot exceed S. The fixed cost fm corresponding to the development and investment expenditure for the selected AM m is then added to the formula as well as its direct variable production cost, gm .  One distinguishes K sets of alternative components (SACs), subscripted by k ( 4). The constraint [START_REF] Baud-Lavigne | Mutual Impacts of Product Standardization and Supply Chain Design[END_REF] enforces that the AM m uses only one AC from each SAC. , 1..M, 1.. , 1.

.

kk kk mc mc kk u v m k K c C         (4) 1 , 1..M, 1.
.

cC kkk m c mc kk v y m k K         (5)
One must introduce a second auxiliary variable k ck s =1 if AC k c from SAC k is chosen for one or several modules. This binary variable is related to the decision variables k mck u by constraint ( 6). This constraint is sufficient because the cost function to be minimized integrates variable

k ck s , weighted by fixed cost w k ck . M 1 , 1..K, 1..C m kk kk m mc c kk u s k c          (6)
The above formulation rests on the implicit assumption that there is no constraint on possible combinations of ACs assembled in a module. It is, however, possible that ACs 1 k c and 2 k c belonging to SACs 1 k and 2 k cannot be assembled in the same module, in particular for reasons of interfacing. In this case, the Boolean parameter 12 12 1 kk cc kk    is used to represent this coupling restriction; alterna- tively it will be = 0. This leads to creation of the Boolean matrix 12 kk 



for each couple of SACs whose ACs can be interfaced. This restriction results in the introduction of constraint [START_REF] Dahmus | Modular Product Architecture[END_REF] to deal with cases of incompatibility.

12 1 12 12 1 2 2 1 1 1 2 2 12 1..M, 1..K, 1..K / 1, 1.. , 1.
.

sS kk sm mc mc s kk kk k k k k cc kk u u x m k k k k c C c C                    (7)
In some cases, impossibility of coupling ACs



. And constraints [START_REF] Dahmus | Modular Product Architecture[END_REF] is to be replaced by constraint [START_REF] Fisher | Component Sharing in the Management of Product Variety: A Study of Automotive Braking Systems[END_REF].

1 2 1 2 1 1 2 1 2 12 1 2 2 1 1 1 2 2 12 1..M, 1..K, 1..K, 1.. , 1.. / 1 sS k k k k sm mc mc s mc c k k k k kk k k k k cc kk u u x m k k c C c C k k                        (8) 12 1 12 1 2 1 2 1 2 2 1 1 1 2 2 1 2 1 2 1..M, 1..K, 1..K, 1.. , 1.. / 1 sS kk sm mc mc s kk k k k k k k k k c c c c k k k k u u x m k k c C c C k k                     (9)
One must introduce a second auxiliary variable

θ kk cc kk  . 1 2 1 2 1 1 2 1 2 12 1 2 2 1 1 1 2 2 12 1..K, 1..K, 1.. , 1.. / 1 mM k k k k m mc c c c k k k k kk k k k k cc kk k k c C c C k k                      (10)
The objective function to be minimized is the weighted sum of binary variables corresponding to the sum of fixed costs and variable costs, proportional to the quantities to be produced. The three fixed costs are those induced by the selected AMs,

M 1 f m mm m y     , the selected ACs, KC 11 w kc kk kk k c c c k k k s    
and by the junction components

K K C C 1 1 2 2 1 1 2 2 1 2 1 2 1 1, 1 1 1 2 1 2 1 2 1 2 1 2 θ k k c c k k k k k k k k k k k k c c c c c c k k k k k k                
. Three variable costs, proportional to the quantities to be produced, have to be distinguished.

 Total demand for AM m,



, is to be weighted by its direct variable cost v k ck , inducing partial cost

K C M 1 1 1 v k c m kkkk k c c m mc k k k u           .  Finally,
    
, is to be weighted by its direct variable cost 12 12 η kk cc kk  , inducing partial cost

K K C C M 1 1 2 2 1 1 2 2 1 2 1 2 1 1, 1 1 1 1 2 1 2 1 2 1 2 1 2 η k k c c m k k k k k k k k k k k k c c c c m mc c k k k k k k                    .
This cost function is an affine function that combines, for every selected item (AC or AM), an expenditure that depends on production volume equal to demand to be met, plus a fixed cost independent of volume. It is possible, as in [START_REF] Giard | Analyse Économique de La Standardisation Des Produits[END_REF]Giard ( , 2002)), to formulate the problem in a more complex cost function, being "monotonically non-decreasing and piecewise linear" and to integrate the cost synergy (positive or negative) resulting from simultaneous production of several ACs at the same plant. This transformation of the problem, easy to operate but not selected here, substantially increases the number of variables.

Temporal and spatial dimensions included in the objective function

Though seemingly static, this model is flexible enough to efficiently integrate change in demand, which only impacts direct variable costs. It can also easily be customized to take new AC launch dates into account. AS demand induces AM demand and, consequently, AC demand. Taking into account the change of demand over time involves replacing u , for periods t belonging to a common economic horizon, and to discount production costs using an appropriate periodic discount rate  . In the absence of change in direct variable costs, assuming their real value is constant, the discounted partial cost of AC k c , chosen for illustration, is

TM 11 v ( 1
)
tm kk t c t m mc t kk u         . Function T 1 (1 ) t k k t mc t mc t kk uu        
restores the initial formulation which is to apply instantly to all the direct variable costs of the target function. Three additional remarks may be made.

 By factoring in demand change over time through discounted demand one can address demand beyond the first year simply by changing the lower limit of summation. This device is valuable where new services are coming up or where certain services are slated to replace current services.

 Where some ACs (or AMs) are in the pre-development study phase, the fixed costs associated with the selection of such products is a discounted value of their development cost and, if necessary, investment. Certain constraints must then be included in the formulation of the problem since an AC which is in the study phase cannot be mounted on an AM selected to satisfy immediate demand for one or more ASs. This can result in dividing certain services into two: demand for existing products being defined prior to launch of new ACs while demand for forthcoming products will be defined subsequently. The related data consistency issue is to be dealt with upstream of optimization process.  Defining the relevant economic horizon (H) presents methodological difficulties common to all economic analyses in connection with product launches; it will therefore not be addressed here.

Coefficients for the target function implicitly include a spatial dimension: the location of AC and AM production plants determines manufacturing costs. If one supposes the location of final assembly lines to be predetermined along with their assigned production, the shipping costs to final delivery are hardly impacted by any decisions. The choice of AM produced in a given plant only impacts assembly cost, which is integrated in direct variable cost. If an AM is produced at multiple plants, this reasoning is valid only if the economic impact is similar. The choice of location of a production plant for new ACs impacts direct variable cost, which includes manufacturing costs as well as delivery costs of the ACs to the AM plants. The choice is relatively straightforward in the absence of impact from decisions concerning other ACs which ought to be manufactured at the same site to achieve synergies. To take such synergies into account, one should adjust the formulation of the problem by integrating supply chain design considerations. This aspect is left aside here.

Numerical Example

We have implemented this model on a real case of an automotive company. We take as an example the engine cooling system of cars. Our example that rests on functional definition for linking parts to services, takes into account 178 AMs that need 3 SACs: radiator (RAD), charged air cooler (CAC) and fan. Those three SACs have respectively 71, 40 and 61 ACs. Some CAs from two different SACs cannot be combined freely. The AMs aim at meeting a list of 390 ASs. Matrices sm a and k mck b are around 96% null. With this set of data the number of variables created is 11989 and the number of constraints is 10499. Xpress-IVE solved it with an optimal solution in 3.5s as it is linear. For more information (table of notations, data and results) see Example.

The solution permits to reduce drastically the diversity of the two BOM levels. The number of AMs goes from 178 to 82, the number of RAD goes from 71 to 24, the number of CAC goes from 40 to 15 and the number of FAN goes from 61 to 23. The optimal solution found uses junction components for 8 (RAD, FAN) 2 (RAD, CAC) and 12 (CAC,FAN).

Conclusion

The multi-level standardization approach we propose delivers several advantages compared to previous approaches. It relies on a multi-functional standpoint readily implemented by business players and engineers to define the needs (ASs), the AMs and the ACs. It supports simultaneous standardization of AMs and of all the SACs they comprise while taking into account any interfacing incompatibilities and allowing for introduction of junction components. The BOM then stems from this optimization process. The sets may integrate existing components (or modules) as well as others that are still in the design stage. The definition of ASs can be made at a sufficient level of aggregation, which is that used by many configurators, such that demand forecasts are relevant. Finally, the economic model factors the temporal and spatial dimensions both of which are crucial for business.

  cs x = 1 if AC c is used to satisfy service s; and of course, this variable is only relevant where 1 cs A  . The constraint 1 cs c x   guarantees that each AS shall be satisfied by a single AC. Total AC c demand is written s cs s dx   . The function of cost to be kept down refers to AC production costs. If one only uses direct variable costs

1 k c and 2 kck and 2 k 1 k c and 2 kc

 12212 belonging to SACs 1 k and 2 k may be lifted through a junction component whose impact in the target function is fixed cost components lifting the coupling prohibition. One then introduces decision variable12 12 kk mc c kk   standing for the demand for junction component to lift the coupling prohibition of ACs 1 for the purposes of module m. This variable is used only where   to be equal to the demand for module m if ACs are selected, we introduce constraint[START_REF] Dupont | Standardisation D'une Famille Ordonnée de Composants Dont Le Coût D'obtention Est Concave[END_REF], dedicated to coupling incompatibilities. The total demand of this junction component is

Table R

 R

	cross-referencing ACs ( 1..C) c 	and functional features (	f 	1..F)

  Table S describes ( S ) To optimize the selection of the ACs to be used, we introduce binary variable

				sf	the conditions for AC eligibility. The combina-
	tion of tables R and S information serves to draw up the table of Booleans A indicating whether the
	AC c meets (	1) A  or not ( cs	0)

cs

A  the specifications of AS s.

  This variable is only utilized if AS s can be provided through module m ( a 1) is composed of one AC from each SAC and that demand for each AC from AM m is equal to the total demand for m.

	One must create auxiliary variable k mck v =1 if AC k c from SAC k is chosen for module m. This binary
	variable is related to the decision variables k mck u by constraint (
								1.. ) kK 	. SAC k
	includes Ck alternative components (				1..C
								sm  .
	Service s is met by an AM, as enforced by constraint (1).
			M 1  m m 	sm x	, d s s   	1.. S	(1)
	The demand for module m, possibly null, is		1 sS s  	sm x	. It is then useful to create auxiliary variable
	1 y  if AM m is chosen. This binary variable is related to the decision variables sm m x by constraint
	(2) in which constant  is a big value (for example		1 sS s d s  	). Constraint (2) is sufficient because
	the cost function to be minimized integrates variable m y , weighted by fixed cost gm .
		1 sS s  	sm x	, y m m    	1..M	(2)
	Let k mck u be a decision variable that corresponds to the demand for AC k c from SAC k used to pro-
	duce the AM m. This variable is only utilized if AC k c can be assembled in module m (  k mck b	1)
	. The total demand for AC k c from SAC k, possibly null, is noted		1 mM k m mck u  	. The relation (3) en-
	forces that module m 11 c C s S kk k c mc s kk u    	sm x	,	m  	1..M,   k	1.. K	(3)

kk c  ). The choice of AC k c from SAC k is associated to a fixed cost w k ck , corresponding to development and investment expenditure, plus direct variable production cost v k ck . Where one has to factor in two SACs simultaneously, subscripts 1 k and 2 k are used. An AM always includes an AC drawn from each SAC. The same AC can be mounted in multiple AMs and some ACs cannot be mounted on certain AMs. The Boolean parameter b k mck takes a value of 1 where AM m can comprise AC k c from the SAC, and 0, if it does not.

Let sm x be a decision variable that corresponds to the demand for the AM m selected for the purpose of the AS s.

  total demand for the junction component linking ACs 1

	and 2 k ,	m m	M 1	12 kk 12 mc c kk	k c and 2 k c belonging to SACs 1 k


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email: david.mitton@ifsttar.fr

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Non-destructive assessment of human ribs mechanical properties using quantitative ultrasound

Keywords: Modulus of elasticity, Maximal strength, Cortical bone, Quantitative ultrasound, Ultrasound velocity Word count: 2144

Advanced finite element models of the thorax have been developed to study, for example, the effects of car crashes. While there is a need for material properties to parameterize such models, specific properties are largely missing. Non-destructive techniques applicable in vivo would, therefore, be of interest to support further development of thorax models. The only non-destructive technique available today to derive rib bone properties would be based on quantitative computed tomography that measures bone mineral density. However, this approach is limited by the radiation dose. Bidirectional ultrasound axial transmission was developed on long bones ex vivo and used to assess in vivo health status of the radius. However, it is currently unknown if the ribs are good candidates for such a measurement. Therefore, the goal of this study is to evaluate the relationship between ex vivo ultrasonic measurements (axial transmission) and the mechanical properties of human ribs to determine if the mechanical properties of the ribs can be quantified non-destructively. The results show statistically significant relationships between the ultrasonic measurements and mechanical properties of the ribs.

These results are promising with respect to a non-destructive and non-ionizing assessment of rib mechanical properties.

This ex vivo study is a first step toward in vivo studies to derive subject-specific rib properties.

2

1.

Introduction

Thoracic injuries are frequently observed in automotive collisions and have been reported to be a major cause of automotive related fatalities [START_REF] Van Don | Biofidelity impact response requirements for an advanced mid-sized male crash test dummy[END_REF]Kent et al. 2005;[START_REF] Brumbelow | Impact and injury patterns in frontal crashes of vehicles with good ratings for frontal crash protection[END_REF]). The thorax accounts for approximately 30% of injuries to belted drivers over age 34 who are fatally injured in frontal collisions (Kent et al. 2005). To improve users' safety, enhanced knowledge of the ribcage biomechanics is needed [START_REF] Stitzel | Defining regional variation in the material properties of human rib cortical bone and its effect on fracture prediction[END_REF][START_REF] Kemper | Material properties of human rib cortical bone from dynamic tension coupon testing[END_REF][START_REF] Vezin | Structural characterization of human rib cage behavior under dynamic loading[END_REF]. Based on biomechanical knowledge, numerical models have mainly focused on standard individuals (e.g. 50 th percentile male) [START_REF] Ruan | Prediction and analysis of human thoracic impact responses and injuries in cadaver impacts using a full human body finite element model[END_REF][START_REF] Song | Evaluation of thoracic deflection as an injury criterion for side impact using a finite elements thorax model[END_REF]). However, there is a need to improve protection for the entire population of transport users. Thus, specific thorax models have been developed for children [START_REF] Mizuno | Development of a three-year-old child FE model[END_REF][START_REF] Jiang | Development of a 10-year-old paediatric thorax finite element model validated against cardiopulmonary resuscitation data[END_REF], the small female [START_REF] Kimpara | Development of a Three-Dimensional Finite Element Chest Model for the 5(th) Percentile Female[END_REF], and for adults taking into account the aging effect (Kent et al. 2005;[START_REF] El-Jawahri | Development and validation of age-dependent FE human models of a mid-sized male thorax[END_REF][START_REF] Forman | Predicting rib fracture risk with whole-body finite element models: development and preliminary evaluation of a probabilistic analytical framework[END_REF].

The global geometry of the ribcage can be obtained from medical imaging, and in particular using biplanar Xrays [START_REF] Dansereau | Measurements of the three-dimensional shape of the rib cage[END_REF][START_REF] Benameur | Three-dimensional biplanar reconstruction of scoliotic rib cage using the estimation of a mixture of probabilistic prior models[END_REF][START_REF] Mitton | 3D reconstruction of the ribs from lateral and frontal X-rays in comparison to 3D CT-scan reconstruction[END_REF][START_REF] Jolivet | Fast 3D reconstruction of the rib cage from biplanar radiographs[END_REF], to build these specific models. Detailed geometry (e.g. cortical thickness) can be obtained from high-resolution computed tomography.

In addition to these geometrical features, the mechanical properties of the bone must be considered to build specific models, as Kemper et al. concluded (Kemper et al. 2007).

Variations of the trabecular bone properties produce a negligible influence on rib response [START_REF] Li | Influence of mesh density, cortical thickness and material properties on human rib fracture prediction[END_REF]. Thus, our study focuses on the cortical bone. The age effect on cortical bone mechanical properties has been assessed at the femoral, humeral, and tibial locations. The failure properties (strength, strain, energy) of these cortical bones were found to decrease with age [START_REF] Lindahl | Cortical bone in man. II. Variation in tensile strength with age and sex[END_REF][START_REF] Mccalden | Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure[END_REF][START_REF] Zioupos | Changes in the stiffness, strength, and toughness of human cortical bone with age[END_REF], whereas no variation [START_REF] Lindahl | Cortical bone in man. II. Variation in tensile strength with age and sex[END_REF][START_REF] Mccalden | Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure[END_REF] or decrease with age [START_REF] Zioupos | Changes in the stiffness, strength, and toughness of human cortical bone with age[END_REF]) was reported for the modulus of elasticity. For the ribs, maximal strength was also found to decrease with age [START_REF] Stein | Rib structure and bending strength: an autopsy study[END_REF]). However, studies which have quantified other material properties of human ribs were either performed on groups of subjects too small (3 to 6 subjects) to draw reliable conclusions regarding the effect of age [START_REF] Granik | Human ribs: static testing as a promising medical application[END_REF][START_REF] Kemper | Material properties of human rib cortical bone from dynamic tension coupon testing[END_REF][START_REF] Kemper | The biomechanics of human ribs: material and structural properties from dynamic tension and bending tests[END_REF] or the age effect was not assessed [START_REF] Yoganandan | Biomechanics of human thoracic ribs[END_REF][START_REF] Subit | Tensile material properties of human rib cortical bone under quasi-static and dynamic failure loading and influence of the bone microstucture on failure characteristics[END_REF]). In addition, the effect of age has not been well documented for children due to the limited availability of paediatric tissue [START_REF] Agnew | The response of pediatric ribs to quasi-static loading: mechanical properties and microstructure[END_REF][START_REF] Crandall | Pediatric Injury Biomechanics: Archive and Textbook[END_REF]. Thus, a non-invasive technique applicable in vivo is of interest for the assessment of age effect on the mechanical properties of the rib cortical bone during both growth and aging.

How can the apparent mechanical properties of the ribs be measured non-invasively? Today, quantitative computed tomography is the only clinical modality that could provide a non-invasive estimation of rib mechanical properties based on rib density measurements. This approach relies on the hypothesis that the relationship between bone mineral density (assessed using quantitative computed tomography) and modulus of elasticity, which has been determined for vertebral cancellous bone [START_REF] Kopperdahl | Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone[END_REF] and femoral cortical bone [START_REF] Duchemin | Prediction of mechanical properties of cortical bone by quantitative computed tomography[END_REF])) can be determined for the ribs [START_REF] Zhu | Relationship between human rib mechanical properties and cortical bone density measured by high-resolution quantitative computed tomography[END_REF]. One drawback of this approach is the radiation dose of this imaging modality. To overcome this limit, ultrasound techniques offer an interesting alternative. An ultrasound method (ex vivo in a water tank) has been applied on rib specimens collected during surgery [START_REF] Berteau | Computed tomography, histological and ultrasonic measurements of adolescent scoliotic rib hump geometrical and material properties[END_REF].. In the current paper, bidirectional axial transmission was used as it allows bone examination through the skin [START_REF] Talmant | In vivo performance evaluation of bi-directional ultrasonic axial transmission for cortical bone assessment[END_REF][START_REF] Kilappa | Low-frequency axial ultrasound velocity correlates with bone mineral density and cortical thickness in the radius and tibia in pre-and postmenopausal women[END_REF]. We assume that this technique, initially developed for peripheral long cortical bones (radius, tibia, phalanges) (Bossy et al. 2004), can be extended to the ribs. The goal of this study is to assess the relationship between ex vivo ultrasonic measurements (axial transmission) and the mechanical properties of human ribs obtained from three-point bending experiments.

2.

Materials and methods

Specimens

Seventeen human rib specimens (6 and 8 levels), from 9 subjects (67 to 80 years old) were provided by the Departement Universitaire d'Anatomie Rockefeller (Lyon, France) through the French program on voluntary corpse donation to science. Rib segments (120 mm long) were cut from the midsection of each rib (Figure 1) to perform three complementary measurements. Specimens were kept frozen (-20°C) until the experiments. They were thawed at 4°C for 12h and at 20°C for 2 hours before the experiments.

Experiments

First, all segments were scanned using a High Resolution peripheral Quantitative Computed Tomography (HR-pQCT) device (XtremeCT, Scanco Medical AG, Brüttisellen, Switzerland) that provides parallel slices with an isotropic voxel size of 82 μm (Figure 2). The orientation of the rib in the CT scanner was maintained in a foam in a similar position to the one of the 3-point bending experiment. Grey level images were segmented semiautomatically using a Gaussian filter and a threshold-based algorithm incorporated within the manufacturer's analysis software (μCT Evaluation, Scanco Medical AG, Brüttisellen, Switzerland). The separation of the cortical and trabecular bone compartment was based on a double contouring method of the periosteal and endosteal margins [START_REF] Burghardt | Reproducibility of direct quantitative measures of cortical bone microarchitecture of the distal radius and tibia by HR-pQCT[END_REF].

The Cortical thickness (Ct.Th) and cross-sectional area moment of inertia needed for the calculation of mechanical properties were computed within the scanner manufacturer's Image Processing Language (IPL V5.16, Scanco Medical AG, Brüttisellen, Switzerland). The Ct.Th was calculated using a direct method [START_REF] Hildebrand | Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus[END_REF].

Then, ultrasound measurements were performed along the bone surface, using the bidirectional axial transmission extensively described in Bossy et al. (Bossy et al. 2004). The ultrasound parameter is the velocity of the first arriving signal (VFAS). Measurements were performed on the central area of the samples, with the probe positioned on the external side of the rib, using a standard ultrasound gel. The average value of triplicate VFAS measurements performed on each specimen with intermediate repositioning was kept for the final analysis.

Finally, three-point bending experiments (Figure 3) were performed until failure. A servo-hydraulic testing machine (INSTRON 8802, High Wycombe, England) with a sampling rate of 1000 Hz and no filter was used.

Tests were performed at room temperature. Load and displacement were recorded using a 1 kN load cell (accuracy 0.5%) and the testing machine displacement transducer (accuracy 1%), respectively. The loading speed was 0.5 m.s -1 [START_REF] Cormier | Regional variation in the structural response and geometrical properties of human ribs[END_REF]. The modulus of elasticity and the maximal bending strength were computed in two ways:

1/ analytically assuming that the rib is a beam with a constant cross-section, using the following equations:

(1)

(2)

with E a : the modulus of elasticity from the analytical approach, K: the stiffness, L: the span length, I: the cross-sectional area moment of inertia, σ max a : the maximal strength computed from the analytical approach, F max : the maximum load and c: the maximum distance to the neutral axis.

2/ using a numerical model and an inverse approach [START_REF] Bosisio | Apparent Young's modulus of human radius using inverse finite-element method[END_REF]. In this case, the modulus of elasticity (E n ) and the maximal strength (σ max n ) were identified using an inverse approach combining the finite element model of the rib and its corresponding experiment (load-displacement curve).

For each rib, custom software was used to build a rough mesh from masks representing the volume of interest of the cortical compartment exported as DICOM files Then the software Hypermesh (HyperWorks, Altair, USA) was used to refine the mesh with hexahedral elements. The external part of the model was defined as a shell with a thickness corresponding to the mean value of the cortical bone thickness derived from the HR-pQCT. The internal part was composed of solid elements to represent the cancellous bone. Constitutive laws for both cortical and cancellous components of the model were elasto-plastic. Lower parts of the three-point bending device and the upper part were considered rigid cylinders. Simulations were then performed using LS-DYNA (LSTC, USA). A vertical loading was applied at 0.5 m.s -1 in a manner similar to the experiments. Then the modulus of elasticity and the maximal strength of the cortical bone were adapted manually to fit the numerical load-displacement curve from the simulation with the curve from the corresponding experiment. A difference below 5% for stiffness and load was considered as obtaining the identified values (E n and σ max n ) from this inverse approach. The cancellous bone properties were kept constant for all specimens because they do not influence the rib response [START_REF] Li | Influence of mesh density, cortical thickness and material properties on human rib fracture prediction[END_REF]).

Statistical analysis

The descriptive statistics (mean and standard deviation) were calculated for each parameter. The Student test was used for paired comparisons and the Pearson coefficient was used to report the correlations between variables. The statistical analysis was performed using Statgraphics (version 16.2.03).

3.

Results

No statistical difference was found between rib levels 6 and 8 for either the ultrasonic or the mechanical properties from the numerical approach (p>0.10).

The nominal values for the velocity of the first arriving signal and the mechanical properties are presented for all the specimens in Table 1. The mechanical properties using both calculation methods are correlated, as seen in Table 2.

Statistically significant correlations were found between VFAS and both mechanical parameters (modulus of elasticity and maximal strength) (Table 2). The highest correlation coefficient was 0.78 (p<0.001) for the correlation between VFAS and the modulus of elasticity obtained from the inverse method (Figure 4).

Discussion

This study was designed to assess the relationship between quantitative ultrasound measurements (axial transmission) and mechanical properties of human ribs. No statistical difference was observed for the different parameters (ultrasonic and mechanical properties (numerical approach) on the 6 th and 8 th rib levels. Kemper et al. [START_REF] Kemper | The biomechanics of human ribs: material and structural properties from dynamic tension and bending tests[END_REF]) reported a similar observation for mechanical properties. To the best of our knowledge, ultrasonic velocities of human ribs measured using axial transmission have never been reported. Rib velocity (VFAS) values are typical of those found in long bones, such as the radius [START_REF] Muller | Prediction of bone mechanical properties using QUS and pQCT: study of the human distal radius[END_REF]). Nevertheless, lower velocities (3591±116 m.s -1 ) were measured on ribs in the current study compared to the velocity values reported for human radius specimens (3946±93 m.s -1 ), which may be explained by the lower modulus of elasticity of the rib versus the radius [START_REF] Bosisio | Apparent Young's modulus of human radius using inverse finite-element method[END_REF]. Mechanical properties are consistent with those Stitzel et al. [START_REF] Stitzel | Defining regional variation in the material properties of human rib cortical bone and its effect on fracture prediction[END_REF] obtained when comparing anterior sample locations. Three-point bending overestimates the modulus of elasticity in comparison to coupon tension tests [START_REF] Kemper | The biomechanics of human ribs: material and structural properties from dynamic tension and bending tests[END_REF]). However, the modulus of elasticity is in the lower range of the previously reported data (Table 3). This result may be explained by the age of the subjects considered in the current work. As expected, the maximal strength was higher using the analytical approach than the numerical approach. The analytical approach is based on elastic beam theory and is known to overestimate the maximal strength [START_REF] Burstein | The ultimate properties of bone tissue : the effects of yielding[END_REF].

No relationship between ultrasound measurement and the mechanical properties of the ribs has been reported

previously. However, this type of relationship has been proposed on the radius [START_REF] Muller | Prediction of bone mechanical properties using QUS and pQCT: study of the human distal radius[END_REF]. The modulus of elasticity was nicely predicted by the ultrasonic velocity of human ribs measured using axial transmission.

The standard estimate of error (1.32 GPa) of the current study was determined in addition to the correlation coefficient, thereby validating the quality of the prediction.

Such results open the way for non-invasive assessment of input data for numerical models of the thorax for various ages in the population.

There are some limitations in the present study. First, the modulus of elasticity in the inverse approach is defined by a manual adjustment; an optimization routine would be more robust. The orientation of the rib in the High Resolution peripheral Quantitative Computed Tomography scanner was not strictly controlled. This may have affected the calculation of the cross-sectional area moment of inertia. The use of a tension coupon test instead of a three-point bending experiment would provide a more accurate measurement of the rib cortical bone material properties [START_REF] Kemper | The biomechanics of human ribs: material and structural properties from dynamic tension and bending tests[END_REF]). However, apparent properties (from 3-point bending) are related to ultrasound measurements, as shown in the current study. Finally, it would be worthwhile to assess the relationship between ultrasound measurements and failure strain given that the failure strain of cortical bone has been shown to decrease significantly with increased age [START_REF] Lindahl | Cortical bone in man. II. Variation in tensile strength with age and sex[END_REF][START_REF] Mccalden | Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure[END_REF].

Conclusions

This study shows that for human ribs there is a significant relationship between the velocity of the first arriving signal (VFAS) assessed using ultrasound axial transmission and the mechanical properties obtained from bending experiments. This ex vivo study opens the way to the development of a methodology to non-invasively assess the material properties of ribs. This is a first step toward in vivo studies to obtain subject-specific rib properties. Table 1: Data on rib specimens (Ct.Th: Cortical Thickness, VFAS: Velocity of the First Arriving Signal, E a , σ max a , E n and σ max n : modulus of elasticity and maximal strength computed respectively from the analytical approach (subscript a) and from the numerical approach (subscript n)).

6.

Figures and table legends

Table 2 : Correlation matrix between ultrasound velocity and mechanical properties (VFAS: Velocity of the First Arriving Signal, E a , σ max a , E n and σ max n : modulus of elasticity and maximal strength computed respectively from the analytical approach (subscript a) and from the numerical approach (subscript n)).

Table 3: Comparison of the mechanical properties of the cortical bone from human ribs using tension coupon and three-point bending tests. Young's modulus (inverse method), GPa Velocity of the first arriving signal, m/s

Figure 1 :

 1 Figure 1: The rectangle represents the location of the specimen (120 mm) cut from the rib.

Figure 2 :

 2 Figure 2: Grey level image of a cross-section of a rib specimen performed by the HR-pQCT device (voxel size

Figure 3 :

 3 Figure 3: Three-point bending experiments. The rib specimens were placed on the lower supports (free to rotate)

Figure 4 :

 4 Figure 4: Relationship between modulus of elasticity (inverse method) of the ribs and the velocity of the first

  Figure 1

Table 3

 3

	Table 2
	N=17	VFAS	E a	σ max a	E n	σ max n
	VFAS		0,70*	0,72*	0,77**	0,64*
	E a	0,70*		0,85**	0,89**	0,81**
	σ max a	0,72*	0,85**		0,81**	0,88**
	E n	0,78**	0,89**	0,81**		0,85**
	σ max n	0,64*	0,81**	0,88**	0,85**
	* p<0.01, ** p<0.001

Acknowledgments

The authors wish to acknowledge Georges Boivin and Hélène Follet for their important contribution in bones collection, Charlène Delimoge and Yuan Fang for their technical contributions to this study, and Nicolas

Conflict of interest statement

There is no conflict of interest for any of the authors.

7.

E n (GPa)


Manuel Rippel
email: mrippel@ethz.ch

Johannes Schmiester

Paul Schönsleben

Why do plant managers struggle to synchronize production capacity and costs with demand in face of volatility and uncertainty? -Obstacles within strategizing volume-oriented changeability in practice

Keywords: Uncertainty, Volatility, Resilience, Changeability, Strategizing

Production plants are currently facing an increase in volatility and uncertainty of demand volumes. This environmental condition comes with highly fixed costs and capacity structures, which are mostly planned on the basis of forecasts and demand projections. Thereby, changing demand causes variances in manufacturing unit costs, endangering production plants' profitability, competitiveness and liquidity. Hence, synchronizing capacities and costs with demand volumes becomes an essential target for plant managers in the face of demand volatility and uncertainty. Approaching this target in practice entails various obstacles due to dynamic and interdependent target conflicts as well as a lack of a dedicated and applicable strategizing approach. In this paper, these obstacles are disclosed and evaluated based on action research cases.

Introduction

Production plants are currently facing an increasingly volatile and uncertain environment. Demand volatility materializes in fluctuations with shorter cycles and higher amplitudes. Spillovers from a company's market environment (e.g. financial markets, political conflicts, trade embargos) enhance the dynamics behind demand volume fluctuations. Disruptions as a distinct form of volatility due to extreme events are likely to happen more frequently and severely affect companies [START_REF] Tainton | The Behavioural Effects of Extreme Events in Global Supply Chains[END_REF]. These extreme events are highly distinctive in their characteristics making each a one-of-a-kind event [START_REF] Tainton | The Behavioural Effects of Extreme Events in Global Supply Chains[END_REF]. A variety of scientific approaches and concepts have been developed regarding the responsiveness towards changing business environments of organizations and organizational units in the manufacturing sector [START_REF] Kampker | Analysis of socio-technical structures in order to increase the changeability of producing companies[END_REF]. There is still no uniform understanding and terminology in academia, neither in one discipline nor cross different disciplines. Instead, several terms (e.g., flexibility, changeability, agility, resilience) are used with partly different, partly overlapping focuses [START_REF] Wiendahl | Changeable Manufacturing -Classification, Design and Operation[END_REF][START_REF]Wandlungsfähige Produktionssysteme -Heute die Industrie von morgen gestalten[END_REF][START_REF] Petit | Ensuring Supply Chain Resilience: Development of a conceptual Framework[END_REF]. In addition, technical issues are given priority, and an integration of disciplinary perspectives is mostly left unregarded [START_REF] Kampker | Analysis of socio-technical structures in order to increase the changeability of producing companies[END_REF].

Recently conducted action research cases (in eight production plants in six countries over two years) addressed in depth strategizing and implementing abilities in production plants to handle demand volatility and uncertainty. These cases mainly provide the data for this paper and constitute the basis of the presented findings. The objective of this paper is to identify and evaluate the obstacles for economically and competitively handling demand volatility and uncertainty in production plants. The purpose is to provide the explicitly revealed problem context for further research on an academically sound and practically relevant approach for strategizing the required abilities of production plants. Therefore, the following reflection questions will be answered by presenting and evaluating the observed and experienced problem context and circumstances in managerial practice: (a) Which implications have demand volatility and uncertainty on production plants? (b) Which obstacles arise and hamper managers when dealing with the implications?

2

Implications of demand volatility and uncertainty

The first step examines the fundamental issues that arise from the external environmental factors demand volatility and uncertainty and the effect they have on the "production plant." Based on this, a dedicated target is derived and defined.

Volatility is exacerbated by a high degree of uncertainty, making it almost impossible for manufacturing companies to predict future demands and interfering fluctuations and disruptions. In addition, progressing globalization sets requirements for manufacturing companies (e.g. in regard to competitiveness, sourcing and supply chain management) [START_REF] Koch | Methodik zur Steigerung der Wandlungsfähigkeit von Fabriken im Maschinenund Anlagenbau[END_REF]. Production plants face increasing pressure by corporate entities regarding their competitiveness to external peers (e.g. within Make-or-Buy decisions, performance benchmarks). Furthermore, production plants are also exposed to increasing competition in their own manufacturing networks (e.g. within relocation decisions from high-wage to low-wage countries). Demand forecasts and scenarios are often the main basis for planning and decision-making in industrial practice. These forecasts are based either on mathematical extrapolation of historical data or on individual experiences of experts. As the frequency and extent of extreme events increases and are hardly possible to forecast in an uncertain world, their assumptions and recommendations often turn out to be wrong, and plans and decisions regarding capacity structure of production plants fail to materialize.

The above mentioned environmental factors affect capacity structures of manufacturing plants, which are typically characterized by a high level of fixed costs. These structures refer to the main production factors, people, assets and resulting cost positions. Due to their rigid and specific nature, investments into fixed assets can often be regarded as sunk costs, and the related depreciation and financing costs make up a significant share of manufacturing plants' fixed costs [START_REF] Rippel | Building Blocks for Volume-Oriented Changeability of Assets in Production Plants[END_REF]. When volatile and uncertain demand markets clash with high levels of rigid fixed costs at the manufacturing plant, high variances of unit costs evolve, which significantly impact the plant's operational performance, i.e. its profitability. Variances of unit costs occur when the antecedent projected unit costs cannot be realized since deviations emerge between forecasted and factual production volume. In particular, the fixed cost cannot be absorbed as intended in the forecast. It is not about managing volatility and uncertainty because their occurrence cannot be influenced as external factors. What can be managed is the ability of the system to handle these economic and competitive factors. Taking these problems into account, a synchronization of capacities and costs with demand volumes becomes an essential target for the production plant management (see Fig. 1). As an idealized target state: Manufacturing costs always emerge simultaneously with the production output as well as with the demanded and appropriately provided capacity. In growth phases, delivery reliability can be ensured while manufacturing costs increase less than production output in order to reduce unit costs and enhance profit margin. In decline phases, manufacturing costs can be adapted downwards according to the descending production output. This kind of synchronization is defined as volume-oriented changeability (VoC), which should ensure robust and sustainable profitability and competitiveness of a production plant [START_REF] Rippel | Building Blocks for Volume-Oriented Changeability of Assets in Production Plants[END_REF]. VoC was introduced as concept in order to specifically focus on and address the challenges, obstacles, requirements and solutions of handling the implications of volume fluctuations in industrial practice [START_REF] Rippel | Building Blocks for Volume-Oriented Changeability of Assets in Production Plants[END_REF][START_REF] Rippel | Profiling as a means of implementing volume-oriented changeability in the context of strategic production management[END_REF]. VoC can be regarded as a specific subset of the broad concept of changeability [START_REF] Wiendahl | Changeable Manufacturing -Classification, Design and Operation[END_REF] and should contribute to a company's demand-responsive supply chain [START_REF] Sheffi | The Resilient Enterprise: Overcoming Vulnerability for Competitive Advantage[END_REF].

Obstacles when dealing with implications

Dealing with the above mentioned implications involves preventively changing and influencing the system's configuration and characteristics as well as to taking measures when necessary. Plant managers should take action and prepare the plant by strategizing and implementing VoC with the goal of synchronizing capacities and costs with demand fluctuations. Arising obstacles are identified and evaluated in the following.

Business cycle-continuous profitability (O1)

The intended synchronization of costs and capacities with demand volume is mostly guiding plant managers towards reducing fixed costs and increasing the share of variable costs. Thereby, conflicts evolve in a multi-period perspective (see Fig. 2). While during decline phases (recession and crisis) variable costs contribute to stabilizing the unit cost level, fixed costs degression effects cannot be realized during growth phases (recovery and expansion). Nevertheless, these effects are requested as an inbuilt contribution to achieve productivity targets. Accordingly, plant managers face the dilemma of choosing diametric-advantageous alternatives for configuring their system: On the one hand, the preventively built-in adjustment abilities would be very advantageous for potential declines since negative impact on the product margin can be mitigated. This strategic orientation requires configuring the production plant with a high percentage of variable costs. On the other hand, the (almost) effortless contribution to productivity targets (and possibly associated personal incentives related to high productivity achievements) is appreciated for potential growth. This approach involves a configuration of the plant's structure with a high percentage of fixed costs.

Multi-period competitiveness (O2)

Several approaches for handling volatility and uncertainty propose a transfer of the inevitable entrepreneurial risks to third parties (e.g. via outsourcing to suppliers, via buyorder-transfer models to service providers or via temporal work to employees). Eventually, this transfer of risks mostly is not for free.

In a socio-technical dimension, transferring the entrepreneurial risk to those third parties might adversely affect among others the innovativeness of the company (e.g. if own know-how gets lost after outsourcing to suppliers), the satisfaction and state of health of employees, or the attractiveness of the production plant as employer. Frequently, these risk premiums cannot be explicitly revealed. The effect is very indirect and elusive since the implications will appear in the long term. Therefore, the extent is often not transparent to the management at the time the decision must be made. In a financial dimension, this external third party might charge this "risk premium" in comparison to proprietary, in-house production. Apparently, it keeps the unit costs (i.e.

Example:

With 80% fixed and 20% variable costs, an decrease of -13.3% could theoretically be achieved in case of a +20% growth scenario.

Advantageous strategy:

A high share of fixed costs enables to decrease unit costs and to achieve productivity targets.

Advantageous strategy:

A high share of variable costs reduces the impact of a volume decline.

Remark: Theoretical, mathematical calculation price as allocated costs) constant despite lower quantity of purchased units in comparison to captive production (in particular in the case of cost centers). In the short-term and (probably) in the middle-term, this is possible if the mixed calculation along several periods works and the third party can benefit from an implicit price surcharge ("risk premium") in periods with stable or even higher demand than projected. As a consequence, the plant integrating such external third parties as variable cost might provide a more stable unit cost level due to lower fixed costs but possibly on a higher general level (see Fig. 3). The higher the uncertainty and incalculability, the higher the implicit or explicit risk premium, which continuously arise every period.

Fig. 3. Unit costs dependent on demand fluctuation and implementation approach (schematic).

Besides, one-time costs within the implementation increase the costs for the ability to synchronize capacity and costs with demand. These (financial and social) costs will depend on the approach to build up the ability. In order to achieve the target sooner than later and to a higher extent ("ambitious" approach), more offensive and proactive measures and significant initial structural adaptations will be required (e.g. to preventively replace employees by temporary workers). In contrast, to achieve the target stepby-step and to a lesser extent ("evolutionary" approach), a combination of proactive and reactive measures are preferred. Initial structural adaptations are restrictively conducted, but every upcoming opportunity to build up VoC is utilized (e.g. if an employee retires, his position is refilled by a temporary worker). The faster and more comprehensive the target is achieved, the more expensive the approach will be.

The financial risk premium can also be non-transparent at times and might be priced unknowingly. Thus, the reverse case can be considered as well. The revealing of implicit price surcharges as well as actively and explicitly discussing risk sharing could be utilized to reduce the price. Nevertheless, the accruing additional costs for the risk premiums for VoC give rise to the core issue and an inevitable debate on principles between plant and corporate management. How valuable is the adjustment potentials for our company? How much do we want and can we afford to invest in these potentials? The main downside is, when thinking and acting with a focus on isolated single periods, these costs endanger the competiveness of the company (in comparison to competitors) or of the plant (in comparison to external suppliers or other plants, which are less prepared for these scenarios). The benefits might emerge if the accumulated costs over a multitude of periods are compared between both options. Using demand scenarios could even so cause biases due to the inevitable uncertainty.

3.3

Multi-dimensional performance (O3)

The synchronization of costs and capacities with demand volumes implies a variety of target conflicts when applied by practitioners in strategic management of manufacturing plants. At first, the synchronization has implications for other target dimensions and can stand in conflict to these. Other target dimensions affected by the synchronization are technical targets (e.g. capacity and capability targets such as speed, productivity, quality or innovativeness, etc.), financial targets (e.g. cash-flow and profit targets, such as manufacturing costs and liquidity, etc.) and social targets (e.g. employee satisfaction and employer attractiveness consisting of employee motivation, market power on the labor market, etc.) (see Fig. 5) [START_REF] Rippel | Building Blocks for Volume-Oriented Changeability of Assets in Production Plants[END_REF][START_REF] Rippel | Building blocks for volume-oriented changeability in personnel cost structure of manufacturing companies[END_REF]. In these target dimensions, the synchronization can have impacts that can be beneficial or contradicting with existing strategies. For example, buy-order-transfer models can lower the cash outflow but also decrease the ability of the plant to be innovative since the asset is owned and operated by an external party. In addition, these multi-dimensional target conflicts become dynamic since the weighting of the target dimensions varies with the individual above mentioned phases of the business cycles. While during growth delivery reliability might be prioritized, liquidity becomes the main focus during declines. Accordingly, strong dependencies of multi-dimensional performance with the business cycle-continuous profitability (O1) and multi-period competitiveness (O2) exist since the target prioritization is subject to temporal aspects. These dynamics of the target conflicts are to be considered when building up structures, during planning processes, and have to be included in performance measurement and assessment tools.

Vigorous effectiveness (O4)

The obstacle of vigorous effectiveness explicitly describes the degree to which the idealized target state of synchronizing (see chapter 2) can be achieved. The factor "extent" details how far capacities and respective costs can be adjusted to demand fluctuations and accordingly the extent to which the targeted underlying issue can be solved. The achievable extent strongly depends on the potential to influence the costs by means of appropriate and available levers. The management of fixed costs is an essential element in order to adapt costs to demand fluctuations. Cost remanence as a characteristic of the plant is a main issue which needs to be addressed [START_REF] Zell | Kosten-und Performance Management -Grundlagen -Instrumente -Fallstudien[END_REF]. The extent of fixed costs is often underestimated since the effective influenceability and particularly the reducibility of the plant's cost structure is over-optimistically estimated. Besides, production plants struggle to adapt their costs in supportive and administrative functions. However, these cost positions should not be neglected since 50% are bound in support processes, and their cost structure mainly consists of fixed costs [START_REF] Remer | Einführen der Prozesskostenrechnung: Grundlagen, Methodik, Einführung und Anwendung der verursachungsgerechten Gemeinkostenzurechnung[END_REF]. The factor speed characterizes how fast capacities can be adjusted to demand fluctuations. Many companies take action if the market demand and associated production volumes will not evidently recover. Only then do they evaluate, select, and implement measures to adapt capacity. Capacity costs continuously accumulate in doing so, and this cannot be compensated for later on. Interdependencies to O1, O2 and O3 are apparent.

3.5

Practice-oriented Applicability (O5)

Practitioners have difficulties implementing existing approaches and tools since important requirements might not be given (e.g. data availability, data consistency, data quality) or too laborious to apply so that effort and benefits (e.g. gained knowledge by an analysis) bear no proportion. In addition, some tools are too complex to allow explanation to occasional users or the results to senior management. If many assumptions are necessary and a lot of time and effort required to explain the underlying hypotheses and background fundamentals, various decision makers tend to insufficiently understand and trust the results and consequently reject it as basis for decision making. However, the opposite trend can also be observed: increasingly gathering and analyzing huge amounts of data, building more complex mathematical models and simulations for decision making. These might help to understand the implications of external factors on the considered system. However, it should be questioned whether quantifying and projecting future risks and their probability of occurrence based on data of the past will lead to reliable results for practitioners in face of uncertainty. In particular, extreme events like black or grey swans [START_REF] Taleb | The Black Swan: The Impact of the Highly Improbable[END_REF] can hardly be quantified. Gigerenzer argues that incorrectly assuming to know risks in an uncertain world and using complex calculations and mathematical models for future predictions might result in an illusion of accuracy and certainty within decision making and erroneous beliefs [START_REF] Gigerenzer | Risk Savvy: How to Make Good Decisions[END_REF].

Conclusion and Outlook

Based on observations and experiences within action research cases in industrial practice, the implications of demand volatility and uncertainty on production plants are analyzed. Variances of unit costs occur when the antecedent projected unit costs cannot be realized since deviations emerge between forecasted and factual production volume. They significantly impact the plant's operational performance, i.e. its profitability. Therefore, volume-oriented changeability (VoC) sets the target to synchronize production capacity and costs with demand fluctuations. Arising obstacles are identified and evaluated when developing strategies to build up structures in order to synchronize costs and capacity with demand volumes in practice. The obstacles can be distinguished in approach-immanent and target-immanent and are summarized in Fig. 4. Based on these obstacles, requirements can be derived for further research on an academically sound and practically relevant approach for strategizing volume-oriented changeability (VoC) as the ability to economically and competitively handle demand volatility and uncertainty in production plants.

Fig. 1 .

 1 Fig. 1. Volume-oriented changeability -Synchronizing capacity and costs with demand.

Fig. 2 .

 2 Fig. 2. Development of unit cost dependent on production output and share of fixed costs.

Fig. 4 .

 4 Fig. 4. Problem context causing obstacles within achieving VoC-related target.

Strategizing in Practice Idealized target state Synchronizing capacities and costs with demand volume Practice-oriented Applicability (O5) Outset situation Obstacles

			Approach
	Environment	Plant	Implications
	Volatility	 Capacity structure
	 Fluctuation	with high level of	 Invalid	Business cycle-continuous
	 Extreme events and disruptions	fixed costs  Demand planning	assumptions and forecasts	profitability (O1)
	comparability Uncertainty  Unknown risks  Global  Dynamics Competition  Unpredictability	global sourcing and forecasting based on historical data, experts, etc.  Relocations and benchmarks Measurement and  Performance	 Under-/Over-utilization  Variances of unit costs  Profitability and liquidity endangered	Multi-period competitiveness (O2) Multi-dimensional performance (O3) (O4) Vigorous effectiveness