Managing Complexity in Product Service Systems and Smart Services

Managing Complexity in Product Service Systems and Smart Services

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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 83 (2019) 410–414 www.elsevier.com/locate/procedia

11th CIRP Conference on Industrial Product-Service Systems 11th CIRP Conference on Industrial Product-Service Systems

Managing Complexity in Product Service Systems and Smart Services Managing Complexity in Product Service Systems 28th CIRP Design Conference, May 2018, Nantes, and FranceSmart Services Prof. Dr.-Ing. Günther Schuhaa, Dipl.-Ing. Jan Kuntzaa*, Prof. Dr.-Ing. Volker Stichaa, Dr.-Ing. Günther , Dipl.-Ing. Jan Kuntz Prof.physical Dr.-Ing. Volker Stich , aand newProf. methodology to Schuh analyze thePhilipp functional architecture Dr.-Ing. Jussen*, Dr.-Ing. Philipp Jussena

A of existing products forEngineering an assembly product55, family Insitute for Industrial at RWTH Aachenoriented University, Campus-Boulevard 52074 Aachen, identification Germany a a

Insitute for Industrial Engineering at RWTH Aachen University, Campus-Boulevard 55, 52074 Aachen, Germany

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat

* Corresponding author. Tel.: +49 24147705 224; E-mail address: [email protected] * Corresponding author. Tel.: +49 24147705 224; E-mail address: [email protected] École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France

Abstract Abstract

* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

In the context of product service systems and smart services, the huge number of possible variants and dynamic market In the contextpresent of product serviceforsystems smartwho services, thestay huge number The of possible variants and dynamic market requirements a challenge service and providers want to profitable. combination of variety and dynamic is requirements present achallenge. challenge Among for service providers who want to stay profitable. The combination of variety and dynamic is called the complexity the main difficulty is to respond to the market’s external variety and dynamic with the Abstract called the complexity Among the main difficulty is to respond to the market’s varietyon and dynamic with the right flexibility withoutchallenge. losing efficiency or effectiveness. This paper, motivated by a caseexternal study, focuses selected difficulties right flexibility without losing efficiency or product, effectiveness. This motivated case study, focuses on selected difficulties bybusiness complex markets on the the portfolio, process andpaper, resource level. Itby introduces a Due qualitative and quantitative model Inposed today’s environment, trend towards more product variety and customization isaunbroken. to this development, the need of posed complex markets on thesystems portfolio, product, process resource level. introduces a qualitative quantitative model to manage a company’s internal complexity according towith theand external complexity on all mentioned In introduction, the agile andbyreconfigurable production emerged to cope various products and Itproduct families. Tolevels. design and andthe optimize production to manage a company’s complexity according to the externalmethods complexity on all mentioned levels. the understanding introduction, most relevant challenges posed by complex be explained in detail. second section covers the of systems as well as to chooseinternal the optimal product markets matches, will product analysis are The needed. Indeed, most of theInknown methods aimthe to most relevant challenges posed by complex markets will be explained in detail. The second section covers the understanding ofa complexity management as a control loop. The third section then introduces a set of key figures that can be used to number evaluate analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the and complexity management as aimpedes control loop. The level. third section then introduces a set model ofproduct keythat figures can be used to qualitative evaluate company’s internal complexity on a quantitative In the and fourth section, a curve aimsthat at representing nature of components. This fact an efficient comparison choice of appropriate family combinations for the the productiona company’s internal complexity on a quantitative level. In the fourth section, a curve model that aims at representing the qualitative interconnections between these key figures to gain control of the complexity in product service systems and smart services be system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is towill cluster interconnections between these key product figures families to gain control of the complexity in product systems and smart services will be presented. these products in new assembly oriented for the optimization of existing assemblyservice lines and the creation of future reconfigurable presented. assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and 2019 Authors.isPublished Published by Moreover, Elsevier B.V. B.V. ©functional 2019 The Theanalysis Authors. by Elsevier a© performed. a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the © 2019 The under Authors. Published of by Elsevier B.V. Peer-review under responsibility of the scientific committee of 11th CIRP Conference on Industrial Product-Service Systems.An illustrative Peer-review responsibility the scientific committee thethe 11th CIRP Conference on Industrial Product-Service Systems similarity between product families by providing design of support to both, production system planners and product designers. Peer-review under responsibility of the scientific committee of the 11th CIRP Conference on Industrial Product-Service Systems. example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of Keywords: Smart Services; product servic systems; variety; dynamic markets; complexity management; control loop; key figures; curve model thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. Keywords: Smart Services; product servic systems; variety; dynamic markets; complexity management; control loop; key figures; curve model © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.

1. Introduction stand opposed to effective corporate action and therefore pose 1. Introduction stand opposed to effective corporate of action therefore pose a major challenge to the management smartand service providers a major challenge to the management of smart service providers When it comes to adding a service to a product, which can [1]. A company that aims at being successful in such a complex Whenasitmandatory comes to for adding service tothe a product, which can [1]. A company that aims being successful in and suchefficient a complex be seen smarta products, number of possible market environment needsat to be both flexible in be seen as mandatory for smart products, the number of possible market environment needs to be both flexible and efficient in rises exponentially. As seen in the industrial services of its the actions, a systematic approach towards 1.variants Introduction productwhich rangerequires and characteristics manufactured and/or variants rises exponentially. As seen in the industrial services its actions, which requires a systematic approach towards industry, the challenge for service providers is then assembled complexityin this management. management is system. In thisComplexity context, the main challenge in industry, for service is then complexityand management is characterized bychallenge two features, namely a highdomain variety and concerned withmanagement. finding strategies to only react to the dynamics and Due to thethe fastmain development in providers the of modelling analysis is nowComplexity not cope with single characterized by two main features, namely a high variety and concerned with finding strategies to react to the dynamics and high dynamics. and A high variety means there are many variety of a complex a way that families, reduces communication an ongoing trend that of digitization and products, a limited product market range orinexisting product high A smart high variety means thaton there are many variety complex infinda the way that tobetween reduces similardynamics. yet distinct services available the market and but ineffectiveness. Its aim optimum digitalization, manufacturing enterprises are facing important also toofbe aable toultimate analyzemarket andistotocompare products define similar yet distinct smart services available on the market and ineffectiveness. Its ultimate aim is to find the optimum between possibly even the company’s portfolio. A ahigh dynamic new the cost of diversity, andobserved flexibility in classical the smartexisting service challenges in intoday’s market own environments: continuing product families.variety It can be that possibly eventhese in the company’s own A hightimes dynamic the costfamilies ofand diversity, variety inclients the smart service implies that variants not portfolio. simply coexist, but they portfolio thearebenefit in and the form of of achievable or tendency towards reduction ofdoproduct development and product regrouped in flexibility function or prices features. implies that these variants do not simply coexist, but they portfolio and the benefit in the form of achievable prices or mutually product influence one another through thean customers’ turnover. It is often oriented seen thatproduct cost rises exponentially byto adding shortened lifecycles. In addition, there is increasing However, assembly families are hardly find. mutually influence one another through the customers’ turnover. It is often seen that cost rises exponentially by adding purchasing behaviour on being the one hand andtime possibly some more variants a portfolio, but differ on the mainly other hand the demand of customization, at the same in a global On and the more product familytolevel, products in two purchasing behaviour theall one hand some main more andrevenue more variants to anumber portfolio, on the other hand the resources onwith the competitors otheronhand. In addition, thepossibly smart realized often against a certain maximum. competition over the and world. This service trend, characteristics: (i) converges the of but components and (ii) the resources on the other hand. In addition, the smart service realized revenue often converges against a certain maximum. marketisis inducing subject to the constant and unpredictable change. These type The of target of each (e.g. business must beelectrical, a leveraged number of which development from macro to micro components mechanical, electronical). market isresults subjectinto–diminished constant andlot unpredictable These The target each business musttobefulfill amainly leveraged of two characteristics variety and dynamics – define complexity, variants andof variant changeconsidering rates thesingle cost number efficiency markets, sizes due tochange. augmenting Classical methodologies products two characteristics – variety and dynamics – define complexity, variants and variant change rates to fulfill the cost efficiency product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this variety as wellB.V. as to be able to product structure on a physical level (components level) which 2212-8271 © 2019 Theaugmenting Authors. Published by Elsevier 2212-8271 ©under 2019responsibility The optimization Authors. of Published by Elsevier B.V. Peer-reviewpossible the scientific committee the 11th CIRP Conference Product-Service identify potentials in ofthe existing causeson Industrial difficulties regardingSystems. an efficient definition and Peer-review under responsibility of the scientific committee of the 11th CIRP Conference on Industrial Systems.families. Addressing this doi:10.1016/j.procir.2017.04.009 production system, it is important to have a precise knowledge comparison of Product-Service different product Keywords: Assembly; Design method; Family identification

doi:10.1016/j.procir.2017.04.009

2212-8271©©2017 2019The The Authors. Published by Elsevier 2212-8271 Authors. Published by Elsevier B.V. B.V. Peer-reviewunder underresponsibility responsibility scientific committee of the CIRP Conference on 2018. Industrial Product-Service Systems. Peer-review of of thethe scientific committee of the 28th11th CIRP Design Conference 10.1016/j.procir.2019.03.093

Günther Schuh et al. / Procedia CIRP 83 (2019) 410–414 Author name / Procedia CIRP D-19-00272

Most of the reviewed complexity management approaches for the industrial goods production are based on the idea that there is an optimum between high stock and high capacity utilization. Complexity management then has to identify the correct point of operations under the circumstances given by the market variety and dynamic. But, Services could not be stocked due to their immateriality. As a first step, this paper uses the idea of the service production model according to Corsten [2, 3, 4] with its three different layers of product, processes and resources/potentials. Further, the present paper understands a company and its complexity management in particular as a control loop. A control loop is a closed and continuous sequence of events that aims at influencing a controlled variable through a constant succession of measuring, comparing and regulating so that the controlled variable reaches and remains at a desired value (see Fig. 1). A common control loop consists of  A control system whose output variable is changed when the input variable is altered  A controller that compares the controlled variable with the predefined target value and uses the result to determine the correcting variable and can be described by  A controlled variable that is to be maintained at a predefined target value  A target value that the controlled variable should follow  A correcting variable that can be directly regulated and in turn influences the controlled variable – used to approach the controlled variable to the target value  A disturbance variable – any variable other than the correcting variable that influences the controlled variable and is controlled outside the loop. Merging the principles of a control loop and the four levels of service production results in intertwined levels in the form of a multi-level control loop. Due to the fact that a whole portfolio instead of one single product needs to be managed in the case of complexity management, a further layer regarding the structure of the portfolio has been added to the three

Controlled variable

Disturbance variable Control system

Controller

Correcting variable

Target value

Fig. 1. Elements and key indicators of a control loop

In general, each commercial action on a market can be understood as a control loop. The market itself represents the control system, but the acting enterprises are control units with the aim to control the market. Transforming this picture into the specific complexity management case, the market remains the control system and the company under consideration represents the controller. The market complexity affects the company as an external complexity. By changing offered prices and sales volumes, the company in turn tries to affect the market. Of course, the potential prices and sales volumes are highly influenced by cost, margin and resource capacities on the other hand. To map exactly this in the presented model, the company itself is divided into the four declared levels of portfolio, products, processes and resources (for a simplified graphic representation see Fig. 2). Environment Market complexity Portfolio structure Portfolio complexity Service architecture Service architecture complexity Process complexity Cost structure

2. The company as a multi-level control loop

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existing service levels. If product service systems are covered in the evaluation according to the presented model, the physical products also need to be monitored on the portfolio level.

Price

and flexibility requirements. The present paper introduces a model that can be used for managing complexity in product service systems and smart services. For this purpose, variant and complexity management approaches from the industrial good production have been adapted to the needs in the service industry. A descriptive submodel includes key figures that can be used to describe a company’s complexity on four major levels, the portfolio, product, process and resource level. An evaluation submodel then provides curves that aim at representing the quantitative interconnections between these key figures. The four different levels allow to identify potential for optimization towards gaining the necessary flexibility without losing efficiency. Before these components of the model can be presented, however, the underlying understanding of the company as a set of intertwined control loops needs to be explained.

Market

2

Process structure Resource complexity

Resource structure

Competitors Fig. 2. Graphic representation of a control loop

The first partial control loop is a company’s portfolio. Here, the complexity of the market represents the disturbance variable. This complexity affects the actual turnover or market share of the portfolio, the controlled variable of the loop, through the customers’ purchasing behaviour. The actual turnover or market share is compared to the target value, the desired turnover or market share. Complexity management acts as the controller of the loop in the form of business development by altering the structure of the portfolio – the

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correcting variable – in a way that brings the actual turnover or market share closer to the target value. The reference point is always the variety and dynamic of the market. The second partial control loop is the architecture of individual smart services. Here, the portfolio structure acts as the disturbance variable while the structure of individual smart services within the portfolio can be understood as the control system. Like in the first partial loop, the achieved turnover or market share represents the controlled variable of the system while a predefined target turnover or market share represents the target value. Again, complexity management acts as the controller of the system by making changes to the structure of individual smart services – the service structure thus acts as the correcting variable on this level. The third partial control loop can be found on the process level. Especially in services, the processes ensure that a result is generated. Here, the correcting variable of the second level, the structure of individual services, acts as the disturbance variable. The process structure, the control system of the level, is often subject to change when the structure of individual services is changed. The actual process times represent the controlled variable, while predefined target times function as the target value of the system. Upon comparing these process times, complexity management needs to act as the controller of the system by making changes to the process structure, which can be understood as the correcting variable of this level. The fourth and last partial control loop can be found on the resource level. Like on the process level, the structure of individual services represents the disturbance variable of this loop. The control system is the operational management who selects the resources, while the controlled variable and the target value take the shape of actual or desired cost rates. Like on the previous level, complexity management acts as the controller of the system by revaluating and adapting the resource selection, which functions as the correcting variable of the system. Between the last two partial control loops and the market, prices and cost structures are two more factors that need to be included in the overall control loop. While these do not create new control loops, the costs are a product out of process time and cost rate. In addition, the product management and sales department top a margin on the cost to determine the offered price, though it is not guaranteed that the full sales volume will be sold at the target price. The control loop model of complexity management explained above forms the basis of the model for managing complexity in smart services. The model consists of three components, namely a set of key figures, a curve model and a cost accounting approach. Both the key figures and the curve model will be explained in greater detail in the following sections. 3. Key figures for managing complexity As mentioned above, companies need to act in a flexible and efficient manner in order to be able to succeed in a complex

3

market. The present paper aims at making a company’s complexity management measurable by presenting a quantitative way to express both the flexibility and the efficiency of a company on all relevant levels from portfolio to resources. For this purpose, all four levels of the control loop explained above are regarded separately, and for each level, two key figures will be defined. The first of these key figures describes a company’s efficiency on the respective level at a fixed point in time. The second key figure on the other hand quantifies the capability of change from one point in time to another – in this case, a company’s flexibility on the level in question. This distinction results in a total of eight key figures, all of which will be introduced below. The aim of the presented model is to quantify the interdependence between the efficiency indicator and the flexibility indicator in a non-linear way at a later stage. On the level of the portfolio structure, the number of smart service variants can be used to quantify a company’s complexity management. The first key figure, the portfolio efficiency, can be defined as the ratio between the numbers of requested and offered service variants. The resulting quotient reaches its best value when each variant has been sold at least once. The portfolio flexibility, on the other hand, can be quantified as the ratio between the number of new variants in the portfolio and the number of new variants on the market, scaled to the number of competitors. The resulting quotient takes values between 0 and 1, with 1 representing the greatest flexibility. Technically it is possible for the value of the flexibility indicator to become bigger than 1, but to identify weaknesses in the complexity management of a business, it is not necessary to measure such an over performance. The reason is simple: too much flexibility definitely has an impact on efficiency. η������ � η������� �

𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛

(1) (2)

On the service architecture level, key indicators can be used to quantify the flexibility and efficiency of individual physical products, services and smart services. The overarching aim here is to find out how big the share of standard partial services is and to identify possible starting points for increasing the number of standard services in order to reduce costs. Product efficiency can be defined as the ratio between the costs of standard partial services and the costs of all partial services, multiplied by the portfolio efficiency. The correcting factor in the denominator ensures that the resulting value is not influenced by the efficiency on the portfolio level. The product flexibility can be defined as the ratio between the number of changed standard partial services and the overall number of changed service variants within the portfolio.

4

Günther Schuh et al. / Procedia CIRP 83 (2019) 410–414 Author name / Procedia CIRP D-19-00272

����� �

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐�������� ������� �������� η������ 𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥��� ������� ��������

(3)

������ �

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

(4)

On the level of process structure, the overall aim is to find out how large the processing time in standard processes is and to identify starting points where more standardized processes can be used in order to reduce costs. For this purpose, process efficiency and process flexibility can be quantified using the following key indicators. Process efficiency can be defined as the ratio between the processing time of standard processes and the processing capacities for all processes, multiplied by the previously calculated product efficiency. Again, the correcting factor in the denominator ensures that the resulting value is not influenced by actions taken on the previous levels. Process flexibility, on the other hand, can be expressed as the quotient from the number of changed processes and the number of changed partial services. ����� �

𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡�������� ��������� η������ 𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥��� ���������

(5)

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

(6)

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐�������� ��������� η������ 𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥��� ���������

(7)

������ �

Finally, efficiency and flexibility can also be quantified on the resource level. The overall goal of this level is to determine the proportion of resource stagnation and to identify where more standardized resources can be used to reduce costs. Resource efficiency is defined as the ratio of the cost rate of standard resources and the cost rate of all resources, multiplied by the value obtained for process efficiency using the equation above. This correcting factor makes sure that the value obtained can be understood to represent the efficiency on the resource level only. Resource flexibility can be understood as the quotient of the number of changed resources and the number of changed processes. ����� � ������ �

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

of overlaps, this state not achievable. Instead, the real optimum needs to be found separately on each level. The four levels of portfolio-, product-, process- and resource structure may be free of overlaps, but as becomes obvious when regarding the control loop model, these levels are by no means independent from one another. This implies that the key indicators presented above are not independent from one another either. The quality and quantity of these interdependencies, however, are not instantly visible. In the following section of the present paper, a curve model that aims at representing the interdependencies between the individual key indicators will be introduced. 4. Representing interdependencies in a curve model In many sources, the interdependence between variety and costs is assumed to be linear, but it is clear that this assumption is not suitable if, as often observed, the costs exponentially explode with the number of variants. The presented model would like to open the door for the idea of using the nonlinear CNorm-function which has been developed by Nyhuis and Wiendahl [5]. |𝑥𝑥|� � |𝑦𝑦|� � �

They used this approach for describing the nonlinear interdependencies between resource efficiency and stock efficiency. To make use of the function in a two-dimensional problem, it has to be parameterized.

(8)

On each of the four levels in question, efficiency and flexibility can be understood as two dimensions of complexity management that span a plane. This plane can be used to create a graphic representation of the values obtained for the key indicators introduced above. A combination of all four planes results in a graphic overview of all key indicators (see Fig. 3). In each plane, there is an optimum between efficiency and flexibility. A hypothetical optimum that would represent a state

Fig. 3. Structure of key indicators

413

of perfect flexibility and full efficiency on all four levels lies in the centre of the graphic. However, as the four levels are free

Fig. 3. Structure of key indicators

At first, an ideal linear correlation is identified. This is divided into two sections, the first being a section of proportional growth until the maximum of efficiency. Per definition, efficiency could not get bigger than 1, so afterwards in the second section the correlation stays constantly at the same value. Both sections together form the ideal curve.

Günther Schuh et al. / Procedia CIRP 83 (2019) 410–414 Author name / Procedia CIRP D-19-00272

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Proportional section Offered variants emax

5

number of retrieved and new variants is determined in comparison to the offered variants and the average number of new variants by each competitor, the correction factors C for compression and α1 can be deduced. For optimization, exactly these two parameters need to be influenced to improve the level of complexity management.

Constant section Ideal curve for efficiency

Real curve for efficiency

Retrieved variants

Buffer is caused by:  Latency of information  Latency of planning  Latency of implementation  Scattering of implementation times Ideal curve of flexibility

minium of new variants

5. Outlook In the further research work, it will be investigated whether the two correction factors can be used in a dynamic cost calculation model or not. The whole model and its submodels will be tested in several case studies, especially in the case study that sparked the motivational impulse.

New variants Neu variants per competitor fmin

Fig. 4. The difference between ideal and real curve in the complexity model

Secondly, the nonlinear CNorm-function is placed through an actual working point of the system. By knowing that the ends of the CNorm-function and the ideal function need to be identical, correction factors for compression and glazing can be deduced. Consequently, the difference between the ideal curve and the identified curve on the basis of the CNorm-function is forming a better assumption for a realistic curve. The difference could be explained by friction losses in the system. Most common forms of appearance are latency of information, decision-making or implementation. The result of these two steps is presented exemplarily in Fig.4 for the first level of the portfolio structure. Once the

References [1] Schuh G, Springer. Produktkomplexität managen; 2005. [2] Corsten, H.: Erich Schmidt Verlag GmbH, Die Produktion von Dienstleistungen: Grundzüge einer Produktionswirtschaftslehre des tertiären Sektors. Berlin 1985. [3] Corsten, H.: Dienstleistungsmanagement. In: Lehr- und Handbücher der Betriebs-wirtschaftslehre. 4., bearb. und erw. Aufl. Oldenbourg, München 2001 [4] Corsten, H.; Gössinger, R.: Dienstleistungsmanagement. 5. Oldenbourg, München 2007. [5] Nyhuis P, Wiendahl H.-P., Springer, Loistsiche Kennlinien Grundlagen, werkzeuge und Anwendungen; 2012.