Module-based pricing

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INOM

EXAMENSARBETE INDUSTRIELL EKONOMI,

AVANCERAD NIVÅ, 30 HP STOCKHOLM SVERIGE 2021,

Module-based pricing

Towards pricing of configurable products MARTIN BYSTRÖM

KTH

SKOLAN FÖR INDUSTRIELL TEKNIK OCH MANAGEMENT

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Module-based pricing

Towards pricing of configurable products

by

Martin Byström

Master of Science Thesis TRITA-ITM-EX 2021:85 KTH Industrial Engineering and Management

Industrial Management SE-100 44 STOCKHOLM

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Modulbaserad prissättning

Vägen mot prissättning av konfigurerbara produkter

av

Martin Byström

Examensarbete TRITA-ITM-EX 2021:85 KTH Industriell teknik och management

Industriell ekonomi och organisation SE-100 44 STOCKHOLM

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Master of Science Thesis TRITA-ITM-EX 2021:85 Module-based pricing

Martin Byström

Approved

2021-04-15

Examiner

Bo Karlsson

Supervisor

Pernilla Ulfvengren

Commissioner

Cytiva

Contact person

Pasi Juntikka

Abstract

Modularity has the possibility to fulfil a wide range of customer requirements by using relatively few input components. The benefits of modularization from an engineering perspective have been

confirmed repeatedly by multiple researchers, but less attention has been drawn to the question of how to effectively price the large number of variants of top-level configurations. In terms of pricing, a common approach is to add a contribution margin to the production cost, but there are problems associated with this method. In general, there should be possibilities to: i) base price on value, not cost (i.e., price structure); ii) ensure consistency in pricing between configurations (i.e., pricing policy);

and iii) maintain the prices over time (i.e., price maintenance). Contribution margin on production cost approach does not effectively fulfill these three criteria. This thesis aims to contribute to filling this research gap by introducing the concept of module-based pricing: a top-level configuration’s list price should be the sum of the prices of its modules. The model, MBPN, developed in this thesis minimizes the difference in the outcome of any existing and a new, modular based model as a neutral starting point. The model uses applied least squares method with an option to set variable limits on the module prices to achieve e.g., value-based module pricing. The results present a case of a successful transition from a contribution margin on production cost approach to module-based pricing for a configurable product.

Key-words

Modularization, Configurability, Module-based Pricing, Pricing Strategy, Value-based Pricing.

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Examensarbete TRITA-ITM-EX 2021:85 Modulbaserad prissättning

Martin Byström

Godkänt

2021-04-15

Examinator

Bo Karlsson

Handledare

Pernilla Ulfvengren

Uppdragsgivare

Cytiva

Kontaktperson

Pasi Juntikka

Sammanfattning

Modularisering har möjligheten att uppfylla ett stort antal kundkrav med utgångspunkt i relativt få komponentvariationer. De ingenjörsmässiga fördelarna med detta tillvägagångssätt har bekräftats upprepade gånger i olika studier, men mindre uppmärksamhet har riktats mot hur man effektivt kan prissätta de olika varianter av konfigureringar som uppkommer med modulariseringsstrategier.

Gällande prissättning av konfigurerade produkter är det vanligt att använda en bidragsmarginal på produktionskostnaden, men det finns problem associerade med denna metod. Generellt bör det finnas möjligheter att: i) basera pris på värde, inte kostnad (dvs. prisstruktur); ii) säkerställa enhetlighet i prissättningen mellan konfigurationer (dvs. prissättningspolicy); och iii) upprätthålla priserna över tid (dvs. prisunderhåll). Bidragsmarginal på produktionskostnaden uppfyller inte dessa tre kriterier. Detta examensarbete introducerar därför konceptet modulbaserad prissättning: konfigureringens listpris utgörs av summan av dess modulers priser. Modellen, MBPN, utvecklad i detta examensarbete minimerar skillnaden i utfallet av en befintlig och en ny, modulbaserad modell som en neutral utgångspunkt. Modellen är en tillämpad minsta kvadratmetod med möjligheter att applicera

variabelgränser för att uppnå t.ex. värdebaserad modulprissättning. Resultatet visar på en framgångsrik övergång från en prissättningsmodell baserad på bidragsmarginal på produktionskostnad till

modulbaserad prissättning för en konfigurerbar produkt.

Nyckelord

Modularisering, Konfigurerbarhet, Modulbaserad prissättning, Prissättningsstrategi, Värdebaserad prissättning.

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I

List of Figures

Figure 1: Modular product architecture. ... 6

Figure 2: Customer value vs. company value. Adopted from Sköld (2017). ... 6

Figure 3: Mass product vs. Configurable product vs. One-of-a-kind product in relation to price and adaptability to customer preferences. Adopted from Tiihonen and Soininen (1998). ... 7

Figure 4: Two configurable mixers: (a) 500L and (b) 200L. ... 9

Figure 5: Geometric interpretation of the residual vector. ... 13

Figure 6: Graphic representation of " = "$%" (a) and " = "$&' (b). ... 14

Figure 7: Geometric interpretation of the KKT conditions in ℝ². ... 16

Figure 8: Two configurable mixers: (a) 500L and (b) 200L. ... 19

Figure 9: Four different mixer configurations of total 96 possible. ... 29

Figure 10: Percentage price difference for the different top-level variants. All differences are between -1.76% and 0.93%. ... 31

Figure 11: Percentage price difference for the different top-level variants for the example with 40% contribution margin on nominal volume is 1000L. All differences are between -4.95% and 3.92%. ... 34

Figure 12: Data consistency. (a) smaller difference and thus better data fit. (b) larger difference and thus worse data fit. ... 37

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IV

List of Tables

Table 1: A business model for modularization strategy after Tongur and Engwall (2014). ... 7

Table 2: Cost for two mixers (500L and 200L) with their top-level prices based on contribution margins. ... 9

Table 3: Cost for two mixers with their modules and list prices based on contribution margins used in the first test. ... 19

Table 4: Minimum allowed prices for modules in the second test. ... 19

Table 5: The modules used in testing more complex configuration design-space in the third test. ... 20

Table 6: Cost and price for modules based on margins. ... 23

Table 7: MBPN model outcome; module prices with minimum allowed price $0 for each module. ... 23

Table 8: MBPN model outcome; module prices with minimum allowed price equal to production cost for each module. ... 24

Table 9: Price difference between "contribution margin on production cost" and MBPN model. The price difference is zero and modules have the same price for both systems. ... 24

Table 10: MBPN model outcome; module prices with minimum allowed price of five times production cost for each module. ... 24

Table 11: Price difference between "contribution margin on production cost" and MBPN model with allowed minimum price of five times production cost for each module. ... 25

Table 12: MBPN model outcome; module prices with minimum allowed price equal to the production cost for each module. ... 25

Table 13: Price difference between "contribution margin on production cost" and MBPN model with allowed maximum price equal to the production cost for each module. ... 25

Table 14: Mixer configurability. ... 26

Table 15: The module prices as a result of MBPN model run on the mixer design-space. ... 30

Table 16: The two configurations with the highest errors from MBPN run compared to their initial prices using contribution margin on production cost. ... 30

Table 17: MBPN model outcome for module prices. Tank Mtrl B 100 has a fixed price $540.5. ... 32

Table 18: New contribution margins to demonstrate challenge for module-based pricing. ... 33

Table 19: MBPN model outcome for module prices. The contribution margin is now 40% if nominal volume is 1000L. ... 33

Table 20: The two configurations with the highest errors from MBPN run compared to their initial prices using contribution margin on production cost. Contribution margin is now 40% if nominal volume is 1000L. ... 34

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V

Acknowledgements

There are several people who have contributed with invaluable expertise and insights during this project. I would like to express special gratitude to a couple of you who have been crucial for me when finalizing the thesis.

Firstly, from the KTH Royal Institute of Technology side, I would like to thank my supervisor Pernilla Ulfvengren as well as seminar leader Pontus Braunerhjelm for reviewing the thesis from an academic perspective. Your feedback made it possible to improve consistency and quality of the text throughout the report. I would also like to show gratitude to Gustav Melander for assisting me with the

programming – my conceptual ideas would not have been realized into concrete results without your help. Also, I would like to thank Albin Eriksson Östman for supporting me with the mathematical dilemmas I encountered during the project. Lastly, I would like to direct major gratitude to my master thesis class peers for repeatedly providing rigorous feedback.

Secondly, from the Cytiva side, a special thanks to Mikael Johansson, Pasi Juntikka and Philip Nilsson. You provided me with a challenging project and good support throughout the process. It has been truly rewarding to be a part of a project where curiosity is encouraged, and established ways of thinking are challenged.

Martin Byström, Stockholm, April 2021

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1 Background

Pricing configurable products are a challenge for many producing industries; manly due to the high number of product variants that can be created. For example, Sköld (2017) outlines the fact that six Lego pieces with eight knobs can be combined in 915 103 765 different ways. Consequently, few numbers of standardized modules have the possibility to create large variants of customer specific products. A challenge is therefore the ability to effectively price all possible configurations, i.e., module combinations built to a top-level functioning system.

There are many scholars presenting different criteria to consider regarding pricing strategies even though they have similar undercurrents. Firms often want the possibility to charge a premium on high value-adding products to effectively capture the value created for its customers, but also price

differently depending on customer segment. The latter is a key for configurable product offerings:

customers can design their own products and consequently decide on a suitable price level. Utilization of information systems such as “configure-price-quote” (CPQ) tools have the possibility to

communicate the price and value directly to customers and is often used for modularized products.

Nagle and Müller’s (2017) are using two different concepts to describe this: price structure, i.e., how to effectively capture the value created for its different customer segments, as well as pricing policy, i.e., the customer expectation on pricing. The latter refers to as “a rule or habit, consistently applied, that defines the criteria under which a company will change a price for an individual customer, for a limited period of time or for particular transactions” (Nagle & Müller, 2017, p. 108). Furthermore, a crucial dimension regarding pricing of configurable products is the price maintenance of the high variability of final products. Price structure and pricing policy are two important dimensions to consider, but in the context of configurability, a firm could offer billion of different products utilizing shared modules. In fact, this is one of the main objectives for modularized system product offerings.

Consequently, a third dimension to consider when settling for a pricing strategy for configurable products is the price maintenance: how can a firm maintain the prices of the large number of product variants?

Baldwin and Clark (2006) states that “modularizing a system involves specifying its architecture, that is, what its modules are; specifying its interfaces, i.e., how the modules interact” (p. 180). Thus, modules are part of a larger system but designed to function together as a whole. A common approach for pricing such modularized systems is through a contribution margin on the production cost. Each module has its cost and the configuration’s cost is the sum of its module’s costs, and the list price for the system is then decided on a contribution margin on the sum of the module’s costs. However, does

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2 a cost-plus model effectively fulfil the three criteria of price structure, pricing policy and price

maintenance?

A contribution margin on production cost of the modules means that there is no differentiation on value, only cost. Some modules have a higher cost of production and will drive a higher list price even though they not necessarily increase the proposed value, or the profit margin needs to be decreased.

On the contrary, modules with lower production costs that increases the proposed value might not be effectively captured as the contribution margin is set on the system level. Consequently, the price structure is not effectively fulfilled. Furthermore, pricing policy is neither effectively fulfilled as shared modules between configurations with different contribution margins will contribute differently to the list price. I.e., there are inconsistencies in the pricing between configurations. Lastly, the maintenance of prices remains a challenge as there is a need to maintain contribution margins for each possible configuration.

This line of thought reveals that there are improvement opportunities to be gained by refining the price strategy from a contribution margin on production cost approach. However, refining a pricing strategy for already established price levels are risky as firms typically have established customer relationships and market price equilibriums. Consequently, there is a need to not change the existing price levels for the configurations, but there are many internal benefits to gain by refining the pricing strategy to effectively fulfill price structure, pricing policy and price maintenance.

Modularization and platform architecture have reached significant research attention from an engineering perspective; see e.g., Baldwin & Clark (2006) and Martin & Ishii (2002). However, less attention has been drawn in connecting modularization strategies and pricing strategies for the

configuration possibilities. This thesis aims to act gap-filling in the modularization research realm and discuss modularization from a pricing strategy perspective.

1.1 Purpose

The purpose of this study is to develop a module-based pricing concept of operations for configurable products. Questions that support this study are:

1) What requirements are central to fulfil price structure, pricing policy and price maintenance?

2) How can a pricing strategy be formulated that fulfil those requirements?

3) What challenges does this transformation of pricing model have for alteration from the established list prices?

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3 1.2 Research delimitation

The research has it focal point in transferring to a new pricing strategy that effectively fulfill price structure, pricing policy and price maintenance for configurable products with established price levels. Consequently, the research requires that the prices of the configurations are known. The rationale behind this is that the project aim is not to determine competitive market prices for

configurable systems. The neoclassical economics theories state that the quantity demanded of a good is dependent on its price. Established manufacturers have their existing customer base with established relations and market-agreed prices. Thus, it is important to not radically change the price based on internal rationales: the refinement of the pricing strategy is meant to increase internal efficiency and not affect the proposed product value. Before adjusting price levels, it is important to first analyze possible effects of this action, e.g., by analyzing the price elasticity of demand. However, this is not part of this study.

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2 Theoretical foundations

The theoretical foundations section aims to outline the theoretical fundamentals for the problem statement. Firstly, a discussion about modularization is conducted: the trade-off between volume vs.

variation is presented as well as modularization’s ability to bring the two together. Secondly,

modularization is described from a business model perspective. Thirdly and lastly, the rational for the key idea “module-based pricing” is presented.

2.1 Volume vs. variation vs. modularization

Already in 1980, Michael Porter outlined that it is vital for any firm not to get “stuck in the middle”

(Porter, 1980, p. 41) and compete neither through price nor product differentiation. This competitive strategy philosophy is still present as many firms focusses on economies of scale to compete by keeping costs down, or through customization to ensure tailored customer offerings. However, philosophies of modularization aim to bring the two together: produce customized products at low costs (Baldwin & Clark, 2006; Dahmus et al., 2001; Henderson & Clark, 1990; Robertson & Ulrich, 1998). Practically, this is achieved through platform strategies where modules with specific interfaces in an architecture are combined to a system. See Figure 1. Modularization of products play an

important role for many modern producing industries to effectively fulfil a wide range of customer requirement without endangering production control. In fact, modularization is determined as a key factor for competitive advantage in terms of mass customization, production cost, lead time and product development. As modules are part of a larger system but designed to function together as a whole, they can be produced and developed independently without risking the functionality of other modules (Baldwin & Clark, 2006). This enables parallel work and efficiency in product development.

Furthermore, Henderson and Clark (2006) argued that modularization does not only affect product engineering and development, but the firm’s information filters and communication channels. Thus, they argued that once a stable product architecture has emerged, the organization are built around it (Brusoni & Prencipe, 2011). This highlights the magnitude of the internal consequences of

modularization. Furthermore, modularization helps companies with increased opportunities to fulfil mass customization efficiently. Robertson & Ulrich (1998, p. 21) states that “customers care about distinctiveness; costs are driven by commonality”, arguing that modularization enable a balance between fulfilling customized products at low costs. This is practically achieved by e.g., limiting the number of predefined modules with specified interfaces that can be configured into many variations of systems (Hvam et al., 2008).

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5 Figure 2 is adopted from Sköld (2017), where customer value is outlined in relation to company value.

Relating back to the quote by Robertson and Ulrich (1998, p. 21): “customers care about

distinctiveness” (i.e., bottom-right quadrant in Figure 2), while “costs are driven by commonality”

(i.e., top-left quadrant in Figure 2). Ideally, modularization enables high values for customers through tailored products as well as high value for companies through high volume and resource utilization (i.e., top-right quadrant in Figure 2). It is thus a utopian state for many firms to achieve this double efficiency.

Even though strategies of modularization can be applied on e.g., services (Voss & Hsuan, 2009) or programming, this thesis focal point is physical products. However, modularization does not only have impact on the product design. Henderson and Clark (1990) argued that once a dominant design has emerged, this design becomes embedded in the organization. They also argued that platform strategies give companies an edge on the profitability over their competitors. On the cost side, Meyer and Lehnerd (1997) demonstrated through extensive case studies the possibilities to achieve cost leadership by platform and modularization strategies. Furthermore, Baldwin and Clark (2006) examined modularization from an engineering perspective, highlighting that modularity enables parallel work as well as the ability to improve modules independently of each other. One area that have not reached significant interest is how to price configurable products, which is an important part of a firm’s business model. Next subsection 2.2 will conduct a deeper discourse on modularization from a business model perspective and relate it to pricing strategies.

2.2 Modularization from a business model perspective

The business model concept has been widely discussed in academic research (Bidmon & Knab, 2018;

Teece, 2010; Tongur & Engwall, 2014; Zott et al., 2011). Commonly, it relates to how customer’s needs are fulfilled by firm’s technological capabilities (Chesbrough & Rosenbloom, 2002). Tongur and Engwall (2014) conducts an examination of various researcher’s interpretation of the concept and concludes that it consists of following three dimensions (p. 3):

“1. Value proposition, i.e., the value of the products and services that the company offers to its customers;

2. Value creation, i.e., how this value is created; and

3. Value capture, i.e., how the company retains the value it has created for its customers.”

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6 I.e., a business model is how a firm propose and create value for its customers as well as how this value is captured and retained to profit. Aligning the information from section 2.1, it can be concluded that the value proposed for modularized products is products tailored to customer preferences at lower price and faster production speed (Sköld, 2017), and the creation of the proposed value is through platform strategies (Henderson & Clark, 1990; Martin & Ishii, 2002). See Table 1 which format is adapted from Tongur and Engwall (2014) and their discussion on business model dilemmas in

technology shifts, and Figure 3 adopted from Tiihonen and Soininen (1998). However, how to capture the value has not received equal attention from a modularization perspective even though it plays an important role for a successful modularization strategy. Value capture relates to strategies of how to earn money on the produced goods, which often is achieved through concepts such as “revenue models” or “pricing strategies” (Magretta, 2002). Consequently, from a cost standpoint, the benefits of modularity are highly supported from researchers; from a revenue standpoint, the possible high volumes to produce compared to “one-of-a-kind product” is also highly supported from researchers.

Yet, the other important part of revenue is pricing, but this have had seldom interest in research for configurable products. A common approach to price configurable products is described by e.g., Farm (2020), which is utilizing a contribution margin on the cost of production shared between some product characteristics, e.g., products with a specific chassis has a shared contribution margin for the sole purpose of avoiding individual contribution margins for individual products.

Nagle and Müller (2017) highlights four important aspects when deciding for a pricing strategy:

1) Price structure, i.e., how to effectively capture the value created for its different customer segments.

2) Pricing policy, i.e., customer expectation on pricing.

3) Price competitions, i.e., how to manage conflict between competitors.

4) Price sensitivity, i.e., how price sensitive the customers are.

These four dimensions are a foundation to capture the value effectively and increase internal efficiency. However, point 3) and 4) are not in depth discussed in this thesis as this thesis presumes

Figure 1: Modular product architecture. Figure 2: Customer value vs. company value. Adopted from Sköld (2017).

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7 established price levels for the products. A criteria not mentioned by Nagle and Müller (2017) is the ability to maintain the prices over time, which is crucial for configurable products as the aim is to offer a high volume of different products utilizing shared modules. Consequently, a fifth important aspect to consider when pricing configurable products is the price maintenance as the number of possible configuration variants could be several millions. Still, the common way to price configurable products is through a contribution margin on production cost which has its weaknesses in fulfilling price structure, pricing policy as well as price maintenance.

2.3 Pricing using contribution margin on production cost

A common pricing strategy approach for configurable products is to utilize a contribution margin on production cost to obtain profit. As an example, Figure 4 shows two modularized products: one mixer with a volume of 500L and one mixer with a volume of 200L. The only module that varies between them is the tank itself – one has a volume of 500L while one has a volume of 200L – and the other modules are shared between them; e.g., Control 1, Sensor AB, Control 2 as well as Base plate as

Table 1: A business model for modularization strategy after Tongur and Engwall (2014).

Business model

Strategy Value proposition Value creation Value

capture Modularization

strategy

Products tailored to customer preferences at lower price and

faster production speed.

Platform strategy with predefined modules that can be combined into many variants of

top-level systems.

Ambiguous.

Figure 3: Mass product vs. Configurable product vs. One-of-a-kind product in relation to price and adaptability to customer preferences. Adopted from Tiihonen and Soininen (1998).

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8 outlined in Table 2. If “volume is the driver of value”, then the 500L mixer could have a higher contribution margin than the 200L mixer – in the example 10% and 7.5%, respectively.

The contribution margin on production cost approach sums the individual modules’ production costs and adds a contribution margin (CM) percentage on the cost. I.e.,

"#$% '(#)* +,( ),-+#./(0%#,- = ∑^!_"#$3,4/5* #′$ '(,4/)%#,- ),$%

1 − 93 ;

where the configuration contains m number of modules. The final price for the 500L mixer is approximately $8 056 (based on 10% contribution margin on a production cost of $7 250), while the final price for the 200L mixer is $4 597 (based on 7.5% contribution margin on a production cost of

$4 250)¹. These price levels for the mixers might be an appropriate market price, but there are some problems associated with pricing configurable products using contribution margin on production cost approach with regards to price structure, pricing policy and price maintenance as explained per next subsections.

2.3.1 Price structure

The price structure refers to the strategy of capturing the value effectively from different customer segments (Boyaci & Ray, 2003). Individual customers value features differently and could

consequently be charged differently. Therefore, there is a need to effectively capture the value that has been created for each customer segment and price it correctly, i.e., charge a premium for functions – or modules – that deliver high value to customers who are willing to pay for it; and of course, vice versa, lower the price for the features that deliver limited customer value. There is a possibility to increase volume as well as revenue from sales by doing so.

As a contribution margin on production cost derive price only from cost and not value, this is not effectively fulfilled. For example, if the Control 1 module has a high customer value, the contribution margin for that module could arguably be higher than e.g., the Base plate module which deliver lower customer value. As the contribution margin is determined on the top-level system, all modules will have a shared contribution margin within a specific configuration. Consequently, when price is derived from a contribution margin on cost approach, it is impossible to effectively capture the value from different customer segments. The price is determined from cost – not value.

1 Note: the prices and the contribution margins are fictive and do not represent Cytiva’s data.

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9 2.3.2 Pricing policy

Pricing policy relates to the expectation customers have on pricing. For example, customers that are aware of quarterly sales might hold their purchase until that time, even though they are willing to purchase at the regular price. Customers try to maximize their own utility and has expectations on the price (now and in the future) and will make their decision based on these expectations (Bils, 1989; Lal

& Staelin, 1984). Nagle and Müller (2017) states:

(a) (b) Figure 4: Two configurable mixers: (a) 500L and (b) 200L.

Table 2: Cost for two mixers (500L and 200L) with their top-level prices based on contribution margins.

500L JTKD Mixer 200L JKTD Mixer

Module cost of production

Module price (10% CM)

Module cost of production

Module price (7.5% CM)

Tank $5 000 $5 555.6 $2 000 $2 162.2

Control 1 $700 $777.8 $700 $756.8

Sensor AB $400 $444.4 $400 $432.4

Control 2 $300 $333.3 $300 $324.3

Base plate $850 $944.4 $850 $918.9

TOTAL: Total cost:

$7 250

Total price:

$8 055.6

Total cost:

$4 250

Total price:

$4 594.6

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10

“A customer’s willingness-to-pay an offered price is not determined solely by whether that price is fair or reasonable when compared to economic value. If customers come to expect that some change in their purchasing behavior will enable them to get the same product or service at an even better price, then the regular price becomes no longer acceptable.” (Nagle

& Müller, 2017, p. 107)

Having an adequate pricing policy (e.g., price negotiations) is crucial for all firms to not lose power and keep desirable margins. Pricing of configurable products is no exception. The example in Figure 4 and Table 2 shows the different modules used to build two mixers. The only module that differs between the mixers is the tank, but as they have different contribution margin on the production cost, each individual module contributes differently to the final price. For example, Control 1 module with a production cost of $700 will have a price of approximately $777.8 for the 500L mixer example with 10% contribution margin, and a price of $756.8 for the 200L mixer example with 7.5% contribution margin as following:

!"#$%"& 1 )%"*+,$-"# ,".$ = $700 3 ⟶ 10% CM: $700

1 − 0.1= $777.8 ⟶ 7.5% CM: $700

1 − 0.075= $756.8

This means that the contribution to the final list price would be different if Control 1 is added to the 500L compared to the 200L mixer (assuming that the Control 1 module is optional, i.e., it can be selected or de-selected from the configuration depending on customer preferences). From a pricing policy perspective, this means that there are inconsistencies in the pricing: Control 1 module does not have the same price even though it is the same module with the same function in both mixers.

Consequently, this opens the door for observant customers to gain scepsis by questioning the pricing consistency between configurations. To avoid scepsis, shared module should be priced consistently through the product portfolio.

2.3.3 Price maintenance

A crucial outcome of the price strategy is to settle for a suitable price level. In complex manufacturing industries dealing with configurable products, the possible number of final products could be several billions. Therefore, there could be a question of maintaining billions of price levels and individual contribution margins. Nevertheless, as exemplified in subsection 0, individual contribution margin between shared product platform would result in an inconsistent pricing policy. There is thus a need to reduce the number of price maintenance points to make the maintenance manageable.

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11 2.4 Framework for module-based pricing

To be able to effectively fulfil price structure, pricing policy and price maintenance, there is a need to refine the pricing strategy. From a price structure perspective, there should be a possibility to price based on value; from a pricing policy perspective, there should exist pricing consistency between configuration features; from a price maintenance perspective, there should be fewer price points to maintain without impacting the price structure or pricing policy. A pricing strategy that fulfils these criteria is to let predefined modules carry prices of the configuration without necessarily be saleable items. Hence, the modules are “carriers of prices” for the system they are part of. The principle is that the price of a top-level system will be the sum of the prices of its modules, i.e.:

;<$%*= '(#)* = > ?_"

!

"#$

;

where ?_" is the price of module # of a system consisting = modules. As a result, an effective price structure is fulfilled as modules with higher economic value can be charged a premium, while modules with lower economic value have a lower margin (i.e., ?_" can be set individually independent of cost of production). Furthermore, the pricing policy is consistent as an assigned module price would not change dependent on what system it is used in. Lastly, the price maintenance is eased as the number of modules are fewer than the number of ways they can be combined into a top-level system (for a successful modularization strategy). Thus, module-based pricing fulfils the three important criteria for effective pricing.

Module-based pricing does not change the value proposition but has the possibility to realize an effective value capture strategy. Consequently, it is important to not change the established price levels. The transformation from e.g., contribution margin on production cost approach to module- based pricing must minimize the difference in the outcome of any existing and a new, modular based model as a neutral starting point. Hence, established manufacturers have a pricing strategy problem that can be solved by mathematical optimization: minimizing the difference between price levels for contribution margin on production cost and module-based pricing by solving an overdetermined equation system.

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3 Method

The method section concretizes the objective function to achieve module-based pricing from any existing pricing model for configurable systems. Firstly, the mathematical model selection is outlined.

Secondly, the mathematical model to transfer to module-based pricing is outlined. Thirdly and lastly, the model testing approach is presented.

3.1 Mathematical model selection

As repeatedly emphasized in this text: one benefit of a modularized system is the possibility to create many top-level systems using relatively few modules. However, if the top-level systems have targeted prices and the modules within these systems are defined, how can the modules’ prices be determined if the system price equal the sum of the price of its modules? In a mathematical context, the problem can be outlined as an overdetermined equation system in the general form @ABB⃗ ≈ !BB⃗, where @ ∈ ℝ^% ' !, ABB⃗ ∈ ℝ^! and !BB⃗ ∈ ℝ^% with - > =. The general form of the equation system would be²:

⎩⎪

⎨

⎪⎧

0_$$?_$+ ∙ ∙ ∙ + 0_$!?_! = N_$

∙

0_%$?_$+ ∙ ∙ ∙ + 0_%!?_! = N_%

The coefficient 0_"( is the quantity of a specific module with price ?_", and N_" is the targeted list price for the specific configuration. Consequently, each row in the equation system corresponds to a specific configuration.

In general, there is no solution that satisfies all the equations simultaneously for overdetermined systems, but there are methods to find approximate solutions. The most common method for finding approximate solutions is the least squares method. The aim of the least squares method is to minimize the Euclidian 2-norm of the residual vector OB⃗ = !BB⃗ – @ABB⃗, i.e., min

)**⃗ ∈ ℝ^!T!BB⃗ − @ABB⃗T^.= min

)**⃗ ∈ ℝ^!‖OB⃗‖^.. The norm of residual vector OB⃗ is minimized when orthogonal to the vector

@ABB⃗ ∈ range(@) = span(^BB⃗_$, ^BB⃗_.… ^BB⃗_!), where ^BB⃗_$, ^BB⃗_.… ^BB⃗_! are linearly independent column vectors in

2 Note that it is appropriate to assume >_"> 0 as the price for top-level systems are sold by strategy of profitability. Thus, the equation system is inhomogeneous with >_"> 0.

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13

@. Consequently, the solution of the least squares problem min

)

**⃗ ∈ ℝ^!T!BB⃗ − @ABB⃗T^. can be solved by the normal equations as they are orthogonal to every vector in range(@). See the geometric interpretation in Figure 5. Note that !BB⃗ ∉ range(@) in Figure 5, but if the equation system has a solution ABB⃗_/ then OB⃗(ABB⃗_/) = !BB⃗ – @ABB⃗_/ = bBB⃗ and !BB⃗ ∈ range(@).

There is a global minimum when !BB⃗ − @ABB⃗ is orthogonal to range(@), i.e., when:

@⁰c!BB⃗ − @ABB⃗d = bBB⃗ ⟺ @⁰!BB⃗ = @¹@ABB⃗ ⟺ ABB⃗ = (@¹@)^2$@¹!BB⃗

This means that the minimization problem can be solved by solving the normal equations. Note that ABB⃗ = (@¹@)^2$@¹BB⃗ can be solved uniquely provided that (@! ¹@)^2$ exists, i.e., @ has linearly

independent columns. However, if @ is rank deficient and has linearly dependent columns then the solution @⁰!BB⃗ = @¹@ABB⃗ can be provided by the augmented matrices and an infinite number of solutions ABB⃗ = fB⃗ + %gBB⃗, where % ∈ ℝ.

3.1.1 Boundary conditions

Minimizing the Euclidean 2-norm might provide a solution ABB⃗ that has “unfavorable” elements from a module pricing focal point. Profitable operating businesses want to ensure that modules have margins corresponding to the overall pricing strategy, as well as the important possibility to achieve an effective price structure. Therefore, it is desirable to ensure higher control of the outcome and apply constraints on the optimization variables, i.e., the variables which can be controlled to solve the objective function. The variable limits on ABB⃗ can be written as ABB⃗₃₄₅≤ ABB⃗ ≤ ABB⃗₃₆₎, where ABB⃗₃₄₅ and ABB⃗₃₆₎ are vectors representing the allowed upper and lower values for ABB⃗, respectively.

The variable limits might result in undesirable outcomes. For example, if the Euclidean 2-norm is minimized when ABBB⃗ = ABB⃗₃₆₎ (where ABB⃗₃₆₎ is the upper limits for ABBB⃗), then it might result in an

Figure 5: Geometric interpretation of the residual vector.

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14 undesirably high “error³” T!BB⃗ − @ ABB⃗₃₆₎T. See Figure 6a. Conversely, Figure 6b depicts the situation applying ABBB⃗ ≥ ABB⃗₃₆₎ resulting in that T!BB⃗ − @ABB⃗T is minimized for ABBB⃗ = ABB⃗₃₄₅. In the same line of thoughts, variable limits on individual elements in ABBB⃗ might affect the other elements in ABBB⃗ for which T!BB⃗ − @ABB⃗T is minimized.

3.1.2 Objective function

Using the mathematical theory from presented, main problem can be phrased to a constrained objective function (OF):

) min

**⃗_#$% 7 )***⃗ 7 )**⃗_#&' | )**⃗ ∈ ℝ^!T!BB⃗ − @ABB⃗T^. (OF)

The refined OF fulfils the desired characteristics for the focal point of module-based pricing.

3.1.3 Trust region methods and Karush-Kuhn-Tucker conditions

As outlined: a least squares problem can be solved by the normal equations. However, applying variable limits on the solution ABB⃗_/ makes the problem becomes an optimization constrained problem.

Generally, the objective of minimization of an unconstrained problem is to find a vector Aj ∈ ℝ^! such as a local minimum to a scalar function +(ABB⃗) is obtained, i.e.:

min)**⃗ +(ABB⃗)

3 Error is in this thesis referred to as “the 2-Euclidian norm of the residual vector”.

(a) (b) Figure 6: Graphic representation of @AAA⃗ = @AA⃗_#&' (a) and @AAA⃗ = @AA⃗_#$% (b).

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15 Thus, +(ABB⃗) use vector arguments and return a scalar + ∶ ℝ^! ⟶ ℝ .

For a given point Aj₉ ∈ ℝ^!, the objective is to move a step mB⃗ such as +(Aj₉+ mB⃗) < +( Aj₉). The idea is to approximately describe function + around a point Aj by a simpler function o (e.g., Taylor approximation) that becomes a trust region p around +(Aj). The sub-problem then becomes to minimize o(mB⃗) where mB⃗ ∈ p. I.e.,

min:*⃗ o(mB⃗)

If +( Aj₉+ mB⃗) < +( Aj₉), then the current point is updated to Aj_;= Aj₉+ mB⃗, and a new trust region is found around +( Aj_;) and the process is repeated. However, if +( Aj₉) < +( Aj₉+ mB⃗), then the current point remains Aj₉ and the trust region p is shrunk and the step process repeats for a new trial step.

The main concern in the trust region approach is to find suitable description function o around +(Aj), how to refine the trust region p and then solve the sub-problem min

:*⃗ o(mB⃗). There are different methods, and this thesis will not conduct a deeper discourse about different computations of trust regions. However, the traditional trust region method by Moré and Sorensens (1983) utilizes second- order Taylor approximation of + around Aj, while the Trust-region Interior Reflective approach by Branch et al. (1999) utilizes diagonal affine scaling matrices. Moré and Sorensen as well as Branch et al. methods are also applicable for non-linear equation systems and references to their respective papers are found in the reference list for the interested.

So far, the theory only discussed the unconstrained problem. However, if the objective is to find an optimum of a function subjected to variable limits, then a common approach is to utilize the Karush- Kuhn-Tucker (KKT) conditions for optimization. This thesis is not meant to outline a full deep dive in optimization theories, but it is necessary to lay out the foundation of the KKT conditions. An example with geometric interpretation of the KKT condition will be outlined below, but the full description could be found in e.g., Kuhn and Tucker (1951).

In the general form, KKT first order conditions are at a candidate for solution Aj that optimizes +(ABB⃗) (assuming + is continuously differentiable and concave function) by the constraint functions .(ABB⃗):

∃r BBB⃗ ∈ ℝ_<^! at a Aj such as:

∇+ ≤ ∑^!_"#$t_"∇.^" and Aj ∙ c∇+ − ∑^!_"#$t_"∇.^"d = 0;

.(Aj) ≤ !BB⃗ and r BBB⃗ ∙ c.(Aj) − !BB⃗d = 0

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16 Geometrically, this can be explained as the example depicted in Figure 7 (in ℝ^. to make it possible to draw the image) for the objective function:

)**⃗ ∈ ℝmax₍⁾+(ABB⃗) $. %. .^$(ABB⃗) ≤ N_$ and .^.(ABB⃗) ≤ N_..

Thus, the constraint on the optimization variables is that they must be non-negative, and the objective function must fulfill the constraint linear functions .^$(ABB⃗) ≤ N_$ and .^.(ABB⃗) ≤ N_.. The gradient of the functions shows in what direction the functions are increasing in; thus, the constraints give the feasible area marked as light blue in Figure 7. Furthermore, the level curve of f is intersecting the intersection of .^$(ABB⃗) = .^.(ABB⃗), and this level curve represents +(ABB⃗) = +(Aj). Consequently, the direction of ∇+

reveals that the intersection point .^$(Aj) = .^.(Aj) at a candidate for solution Aj is the maximizer of the objective function (i.e., a unique solution). All vectors in ℝ^. can be written as a linear combination of

∇.^$ and ∇.^.; thus, ∇+ = t_$∇.^$+ t_.∇.^.. Furthermore, as geometrically interpreted from Figure 7:

t_$, t_. ∈ ℝ_<. Consequently, all KKT first order conditions are fulfilled and there exists a unique solution Aj that maximizes the example objective function.

The example of the KKT conditions demonstrates how it works for a linear programming problem when finding a maximum point subjected to constraints. It was meant to concretize the KKT conditions by a general problem in an interpretative nature in ℝ^..

Figure 7: Geometric interpretation of the KKT conditions in ℝ^*.

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17 3.2 The MBPN model

Using the optimization formula derived in the 3.1.2, following least squares objective function (OF) can be outlined:

) min

**⃗_#$% 7 )***⃗ 7 )**⃗_#&' | )**⃗ ∈ ℝ^!T!BB⃗ − @ABB⃗T^. (OF) where:

i. !BB⃗ ∈ ℝ^% are the list prices for all configurations;

ii. @ ∈ ℝ^% ' ! is the configuration matrix defining all the different possible configurations, where each row corresponds to a configuration and each column corresponds to the module quantity for each configuration;

iii. ABB⃗ ∈ ℝ^! be the module prices; and

iv. ABB⃗₃₄₅ and ABB⃗₃₆₎ are the vectors representing the allowed upper and lower price for elements in ABB⃗ set by the modeler.

3.2.1 Computing the MBPN model using Python

There are multiple numerical computing software available to solve overdetermined linear equation systems by least squares method. For example, Matlab™, General Algebraic Modeling System (GAMS) or Python™ all have built-in algorithms that can both exactly and approximately solve constrained least squares problems. Usually, if @ is quadratic, then a process of Gauss elimination is conducted to solve @ABB⃗ = !BB⃗; if @ is rectangular, then @ABB⃗ ≈ !BB⃗ is solved by least squares method. Thus, there are no need to explicitly state the normal equations in the software. One way – not the only way – to solve the OF is to use Scipys’ least squares method in Python (lsq_linear solver), which will be used in this thesis. The solver aims to solve a linear least-squares problem with variable limits. The algorithm first solves the unconstrained least-squares problem by minimizing the Euclidian 2-norm.

The solution is returned as optimal if the elements in ABB⃗ lays within the set limits ABB⃗₃₄₅ and ABB⃗₃₆₎. If the solution does not lay within limits, then a process of trust region reflection and KKT examination occurs as outlined in Branch et al. (1999) to make sure that a solution of minimizing the Euclidian 2- norm that satisfy the variable limits is returned. A script for the MBPN model is outlined fully in

The model is from now called MBPN model, an abbreviation of “module-based-pricing- negotiation”.

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18 Appendix, where Scipys’ least squares method lsq_linear solver is utilized. This script is used in the empirical results section 0.

3.3 MBPN model testing

The MBPN model was tested with regards to five different aspects. Firstly, a simple case example when converting from a contribution margin on production cost approach to module-based pricing was conducted. The purpose was to assure applicable pricing model. Secondly, using the same case as the previous point, the modeler responsibility was tested by applying variable limits. Thirdly, the MBPN model was applied on an overdetermined system with a greater number of configurations than number of modules. The purpose was to test the MBPN model for a common industry situation. Fourthly, the MBPN model was tested by applying value-based pricing on specific modules. Fifthly and lastly, the MBPN model was tested in a situation of large differences in contribution margin between products (e.g., “two different product families with shared modules”). These five tests aimed at proving that the transformation to module-based pricing from an existing pricing model can be successful using the MBPN model. In each test, the script outlined in Appendix was used.

The MBPN model testing was conducted on a mixer platform with its fictive modules and fictive established list prices. The five testing aspects will be described in detail in the following subsections.

3.3.1 Conversion to module-based pricing for two simple systems

In the first MBPN model test, a simple case example for two configurable mixers (see illustrative image in Figure 8) with fictive modules making configuration matrix @ and fictive prices making price vector !BB⃗ = [8 0556.6 4 594.6]¹ was considered, see Table 3. The quantity of each module was one in respective system. This test was run with respect to two different minimum prices for the modules:

i) ABB⃗₃₄₅> bBB⃗, i.e., only positive module prices; and ii) ABB⃗345 equal to the production cost for the different modules. There was no upper limit for module prices in the tests.

3.3.2 Modeler responsibility

In the second MBPN model test, the configuration matrix @ and price vector !BB⃗ was the same as presented in section 3.3.1. This test was run with two different constraints on the module prices: i) a minimum module price ABB⃗₃₄₅ price corresponding to five times the respective module’s production cost (no upper limit for module prices); and ii) a maximum allowed module price ABB⃗₃₆₎ equal to each module’s production cost (no lower value for the module prices). See Table 4.

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19

Table 4: Minimum allowed prices for modules in the second test.

Module Production cost

Test i)

ABB⃗₃₄₅

(5 x Production cost)

Test ii)

A BB⃗₃₆₎

(equal to production cost)

Tank Mtrl A 500 $5 000 $25 000 $5 000

Tank Mtrl A 200 $2 000 $10 000 $2 000

Sensor AB $400 $2 000 $400

Control 1 $700 $3 500 $700

Control 2 $300 $1 500 $300

Base plate $850 $4 250 $850

(a) (b) Figure 8: Two configurable mixers: (a) 500L and (b) 200L.

Table 3: Cost for two mixers with their modules and list prices based on contribution margins used in the first test.

500L Mixer 200L Mixer

Tank $5 000 $2 000

Sensor AB $400 $400

Control 1 $700 $700

Control 2 $300 $300

Base plate $850 $850

TOTAL COST $7 250 $4 250

Contribution margin (CM) 10% 7.5%

LIST PRICE $ 8 055.6 $ 4 594.6

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20 3.3.3 Conversion to module-based pricing when number of modules are greater than number

of possible configurations

In the third MBPN model test, the number of possible configurations was greater than the number of modules. The configuration matrix @ is presented in Appendix 8.2 and the list price vector !BB⃗ is outlined in Appendix 8.3. The different modules and their respective production costs used in the tests are outlined in Table 5. The vector ABB⃗₃₄₅ was set equal to the production cost for each module (no upper limit for module prices).

3.3.4 Value-based module pricing

In the fourth MBPN model test, @ and !BB⃗ were the same as in section 3.3.3, but the module Tank Mtrl B 100 was assigned the value-based price ?_!"% = ?_!=> = 540.5.

Table 5: The modules used in testing more complex configuration design-space in the third test.

Module Production cost ABB⃗₃₄₅ ABB⃗₃₆₎

Tank Mtrl A 1000 $7 500 $7 500 Inf

Tank Mtrl B 1000 $4 000 $4 000 Inf

Tank Mtrl A 500 $5 000 $5 000 Inf

Tank Mtrl B 500 $2 500 $2 500 Inf

Tank Mtrl A 200 $2 000 $2 000 Inf

Tank Mtrl B 200 $1 000 $1 000 Inf

Tank Mtrl A 100 $1 000 $1 000 Inf

Tank Mtrl B 100 $500 $500 Inf

Sensor AB $400 $400 Inf

Sensor A $250 $250 Inf

Sensor B $250 $250 Inf

Control 1 $700 $700 Inf

Control 2 $300 $300 Inf

Base plate $850 $850 Inf

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21 3.3.5 MBPN model outcome for large difference in contribution margins

In the fifth and final MBPN model test, @ was set as the same as in section 3.3.3, but the list price vector !BB⃗ was changed according to the data outlined in Appendix 8.4.

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22

4 Empirical results

The empirical results section outlines MBPN model testing as outlined in section 3.3.

4.1 Conversion to module-based pricing for two simple systems

A 500L mixer has a production cost of $7 250 and a contribution margin of 10%, which results in a list price of $8 056. Another mixer with a volume of 200L – with all modules identical to the 500L mixer except for the tank itself – has a lower contribution margin due to the different targeted list price (e.g., because the smaller volume is less valuable for customers); more specifically, the contribution margin for the 200L mixer is 7.5%⁴. This is outlined in Figure 8 and Table 3. Implicitly, this means that the modules have different prices depending on where they are used, as outlined in Table 6.

The MBPN model aims to harmonize the module prices in such a way that they are consistent across the two systems. Applying the MBPN model⁵ to the mixers, as described in section 3.3.1, results in the outcome as presented in Table 7. As shown, the module prices have been harmonized, i.e., a specific module has an assigned price. More importantly, there is no difference between the list prices in the conversion to module-based pricing from contribution margin on production cost, as outlined in Table 9. However, as displayed in Table 7, the contribution margin is negative for some modules (the only constraint on the module prices was the fact that the prices were set to be greater than or equal to zero in this MBPN model run). One way to avoid negative contribution margins on module prices is to set the minimum allowed price equal to the production cost for each module. Rerunning the MBPN model with these price limits results in the outcome shown in Table 8. Thus, the price difference is still 0%, but the contribution margins turn out to be positive for all modules when assigning prices to the modules using the MBPN model.

4.2 Modeler responsibility

Table 10 outlines the results when using the previous example of the 200L and 500L mixers but applying a minimum price as five times the modules’ production costs. As shown, the proposed module prices from the MBPN model are equal to their minimum allowed prices which means that the

4Note: the prices and the contribution margins are fictive and do not represent Cytiva’s data.

5 The MBPN model Python script used in the empirical result section is outlined in Appendix.

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23 error is minimized when the module prices are equal to the minimum allowed price. Consequently, the list prices for the mixers with the module prices in Table 10 will result in a price difference between the two pricing models as outlined in Table 11: 350% and 363% for the 500L and 200L mixer, respectively. Similarly, applying a maximum allowed price for the modules equal to the production cost would result in module prices from the MBPN model equal to their maximum allowed prices, see Table 12 and Table 13. This example connects to the constraint theory discussion in section 3.1.1.: the MBPN model requires the user to apply variable limits for the module prices with care and

furthermore, examine the outcome to make sure that the module prices are aligned with the overall pricing strategy.

Table 6: Cost and price for modules based on margins.

Cost Price

500L 200L 500L

(10% CM)

200L (7.5% CM)

Tank $5 000 $2 000 $ 5 555.6 $2 162.2

Sensor AB $400 $400 $444.4 $432.4

Control 1 $700 $700 $777.8 $756.8

Control 2 $300 $300 $333.3 $324.3

Base plate $850 $850 $944.4 $918.9

TOTAL $7 250 $4 250 $8 055.6 $4 594.6

Table 7: MBPN model outcome; module prices with minimum allowed price $0 for each module.

Module Production cost

Minimum allowed price for

module

Proposed module price from MBPN

model

Contribution margin (%)

Tank Mtrl A 500 $5 000 $0 $4 171.0 -19.9

Tank Mtrl A 200 $2 000 $0 $710.1 -181.7

Sensor AB $400 $0 $971.1 58.8

Control 1 $700 $0 $971.1 27.9

Control 2 $300 $0 $971.1 69.1

Base plate $850 $0 $971.1 12.5

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24

Table 8: MBPN model outcome; module prices with minimum allowed price equal to production cost for each module.

Module Production cost Minimum allowed price for

module

Proposed module price from MBPN

model

Contribution margin (%)

Tank Mtrl A 500 $5 000 $5 000 $5 589.6 10.5

Tank Mtrl A 200 $2 000 $2 000 $2 128.7 6.0

Sensor AB $400 $400 $464.4 13.9

Control 1 $700 $700 $745.2 6.1

Control 2 $300 $300 $370.8 19.1

Base plate $850 $850 $885.6 4.0

Table 9: Price difference between "contribution margin on production cost" and MBPN model. The price difference is zero and modules have the same price for both systems.

Product Old mixer price using contribution margin on

production cost

New mixer price sum of module price from MBPN

model outcome Price difference (%)

Mixer 500L $8 055.6 $8 056.0 0.0

Mixer 200L $4 594.6 $4 595.0 0.0

Table 10: MBPN model outcome; module prices with minimum allowed price of five times production cost for each module.

Module Production cost Minimum allowed price for module (5 x Production cost)

Proposed module price

from MBPN model Contribution margin (%)

Tank Mtrl A 500 $5 000 $25 000 $25 000 80

Tank Mtrl A 200 $2 000 $10 000 $10 000 80

Sensor AB $400 $2 000 $2 000 80

Control 1 $700 $3 500 $3 500 80

Control 2 $300 $1 500 $1 500 80

Base plate $850 $4 250 $4 250 80

Module-based pricing

Module-based pricing

Towards pricing of configurable products MARTIN BYSTRÖM

Module-based pricing

Towards pricing of configurable products

by

Martin Byström

Modulbaserad prissättning

Vägen mot prissättning av konfigurerbara produkter

av

Martin Byström

Table of Contents

List of Figures

List of Tables

Acknowledgements

1 Background

2 Theoretical foundations

3 Method

4 Empirical results