University of Augsburg Prof. Dr. Hans Ulrich Buhl Research Center Finance & Information Management Department of Information Systems Engineering & Financial Management Discussion Paper WI-99 Prouct Differentiation for Software-as-a-Service Proviers by Arne Katzmarzik appears in: Business & Information Systems Engineering (011) 1 Universität Augsburg, D-86135 Augsburg Visitors: Universitätsstr. 1, 86159 Augsburg Phone: +49 81 598-4801 (Fax: -4899) www.fim-online.eu
Prouct Differentiation for Software-as-a-Service Proviers Abstract The market for the new provisioning type Software-as-a-Service (SaaS) has reache a significant size an still shows enormous growth rates. By varying size of SaaS proucts, proviers can improve their market position an profits by successfully acting in the tension area of customer acquisition, pricing an costs. We firstly elaborate ifferences concerning prouct ifferentiation between classic software provisioning moels an SaaS. Seconly, we introuce a micro-economic base ecision moel to maximize the return of a provier by fining an optimal granularity, i.e. by varying the size of services. This paper makes two contributions in this context: (1) it provies a conceptual founation for prouct ifferentiation within the scope of SaaS an () it presents the first implementation of variable reprouction costs for web base software offers. The moel is illustrate by a real worl case with ata from a SaaS provier. Keywors Software-as-a-Service, Prouct ifferentiation, Service granularity, Decision moel Prouktifferenzierung für Software-as-a-Service-Anbieter Keywors Software-as-a-Service, Prouktifferenzierung, Service-Granularität, Optimierungsmoell Teaser Prouct ifferentiation for SaaS base offere software bears potential for both customers an proviers. We present a micro-economic base moel to show the effects of prouct ifferentiation for this new type of software provisioning. By formalizing concepts of prouct ifferentiation for SaaS, this article shall establish basic unerstaning an form the founation for further research. Furthermore, the moel provies evience that reprouction costs, which have mostly been neglecte in relate quantitative software versioning literature so far, can have significant influence on both the optimal sales volume an service size in the context of SaaS. 1
1 Introuction Progress in information technology (IT) such as the service-oriente architecture (SOA) paraigm an avances in web base communication facilitate new types of software provisioning such as web services (Papazoglou et al. 007). Enable by web services technologies, the service-oriente software provisioning (SSP) moel Software-as-a-Service (SaaS) allows integrating stanar software into online service infrastructure (Cheng et al. 006, p. 51; Lehmann an Buxmann 009). Customers may easily rent functionality an use this software via web clients instea of running license software on their own IT infrastructure. SaaS bears avantages for both proviers an customers. SaaS proviers can primarily profit from economies of scale by aressing more customers (Walsh 003; Sääksjärvi et al. 005). Avantages for customers are e.g. lower IT procurement costs or faster access to new technology, functionality an upgraes (Walsh 003; Susarla et al. 009, p. 07). Thus, this emerging market will attract more an more customers an has alreay reache a significant size of $ 9.6 bn, still shows two-igit annual growth rates an is preicte to grow up to $ 16 bn in 013 (Gartner 009). In particular proviers can profit from this market evelopment. However, they must iversify their offer to be attractive for both existing an new customers. The concept of prouct ifferentiation may lea to a win-win situation for both proviers an customers. Therefore, a ecision support moel consiering both customers an proviers nees as well as the characteristics of SaaS is crucial. The objective of this paper is to contribute to close this ientifie gap by eveloping a normative approach to support ecisions starting out with the perspective of a monopolistic SaaS provier. In the introuce moel, a provier can maximize its return by changing the granularity of its offere services, i.e. it can sprea the functionality on several smaller services instea of offering all in one monolithic service. Starting out with micro-economic theory an the information systems (IS) research stream of software versioning - or in the following just versioning, our scientific contribution is two-fol: First, base on the ieas of versioning, we iscuss if moels from this stream can be applie to SaaS an lay a conceptual founation for prouct ifferentiation for SaaS by introucing a moel base on the eman curve which is extene by characteristics of SaaS. Secon, we elaborate from literature that variable reprouction costs in contrast to classic software provisioning (CSP) cannot be neglecte for SaaS an integrate these costs into our moel, what has not been state of the art so far. To improve comprehensibility, the moel is illustrate by stuying a real worl case with ata from a major provier. The remainer of this text is organize as follows: In section, we give an overview of relate literature. Aitionally, this section lays the conceptual funament for this paper (incluing the efinition of important terms). In section 3, the ecision moel is presente, analyze an illustrate by an operationalization. After a iscussion in section 4 we conclue in section 5. Prouct ifferentiation of software goos Prouct ifferentiation can be separate into two imensions, vertical an horizontal ifferentiation (Cremer an Thisse 1991). Vertical ifferentiation refers to offering a goo in multiple versions each iffering in size an price (Bhargava an Chouhary 001). Horizontal ifferentiation refers to offering a goo isjoint in parallel inepenent versions to aress customers who request only specific parts (Weber 008). As SaaS inclues charateristics of both imensions as we shall see below, we provie an integrate view on both imensions an generally speak of prouct ifferentiation. This concept has been applie in the stream of version-
ing for IS goos, an there mostly for CSP, i.e. where customers purchase software from a provier as installation package an are themselves responsible for running it (Phillips 009). Thus, we start our examination with an overview of effects an literature on application of prouct ifferentiation for CSP in.1. We iscuss their applicability on SSP moels an in particular SaaS in.. We conclue this section with a review of relate work an point out the nee for further research on ecision support in.3..1 Effects of an literature on prouct ifferentiation Demaners of software functionality are heterogeneous in eman for functionality an willingness to pay (WTP) (Jing 000). By ifferentiating software proucts, proviers may try to ajust their software to be more customer specific an thus may aress more iffering emaners to exten sales (Shapiro an Varian 1998). Due to the characteristics of stanar software, customers usually o not require all functionality inclue in an offer (Raghunathan 000). As prouct ifferentiation enables purchasing only parts of the functionality instea of the whole, customers who woul have purchase the whole if this is offere exclusively, but only have eman for parts of the functionality, can purchase only the parts they actually require (Bhargava an Chouhary 001). This may result in a ecreasing total amount of sol functionality. Pricing is another important aspect when being face with customers of heterogenous eman an WTP. Stanar software usually contains parts of functionality which customers o not require, but customers are force to buy these not require parts (Raghunathan 000). Hence, available buget has to be spent both on require an not require functionality. Though, customers are only willing to pay for require functionality as using this generates ae value. Prouct ifferentiation allows offering functionality in smaller parts instea of one holistic version. This ieally allows customers to obtain exactly the functionality requeste, i.e. which is perfectly fitte to their specific eman (Chouhary et al. 005). As the WTP of customers epens on their specific eman (Weber 008), the total buget is (nearly) not affecte if not requeste functionality is not inclue. Therefore, proviers may attain higher prices per piece of functionality if an offer is more eman specific. Thus, proviers must carefully trae off between the effects of attainable prices an acquisition of new customers against the possibility of selling in sum less functionality. Prouct ifferentiation also has effects on costs. First, software proucts have to be mae accessible for customers an thus proviers have reprouction costs (Varian 1997). As prouct ifferentiation may positively affect the number of customers, reprouction costs usually increase. Furthermore, the total functionality has to be cut into inferior or parallel versions which causes effort for splitting up functionality an offering new packages (Weber 001). Therefore, a higher egree of prouct ifferentiation is leaing to increasing costs. Literature on ifferentiating CSP proucts goes even beyon fining an optimal number of versions in the tension area of the mentione basic effects: Examinations have been conucte in more specific contexts such as competition (Jones an Menelson 005; Wei an Nault 006), licensing in software contracts (Zhang an Seimann 00), interorganizational systems (Nault 1997), free ownloa policies (Cheng an Tang 010), network externalities (Jing 000), an fighting igital piracy (Chellappa an Shivenu 005). In the following, we iscuss if the basic effects can be simply transferre to SaaS.. Special Charateristics of SaaS: Moeling Issues To elaborate ifferences between CSP an the SSP moel SaaS, we have to give our perception of this uprising provisioning type: SaaS refers to a software provisioning moel where a 3
stanar software application is hoste on an internet accessible server (Lehmann an Buxmann 009). Thereby, customers rent an application from a provier on a per-use or perperio basis, an the provier itself is responsible for elivering, securing an managing application, ata an unerlying infrastructure (Kaplan 007). Thus, SaaS bunles software functionality with infrastructure services (Fan et al. 009, p. 661). At this point, we have to clarify that we o not examine the effects of splitting the bunle of functionality an infrastructure, instea we want to examine effects of splitting functionality into its parts. Valente an Mitra (007) state that there are enormous ifferences in customer access to software functionality an responsibility of proviers. Therefore, the presente moels from the stream of versioning as well as the effects elaborate in versioning literature cannot simply be transferre to SaaS. We iscuss ifferences between both provisioning types below an elaborate moeling issues that have to be consiere in a ecision moel. Decision problem: In moels for CSP, proviers offer a flagship version containing the total functionality an also inferior versions which are create by removing functionality from the flagship version (Bhargava an Chouhary 001), or they offer several smaller parallel versions as inepenent proucts which coul be re-bunle to a flagship version (Weber 008). In SSP moels, functionality is offere as service. A (web) service is a software artifact containing certain business functionality (Papazoglou an van en Heuvel 007). Accoring to the SOA paraigm, services can be integrate into applications an/or re-combine to applications. If functionality is offere very granular, i.e. it is split up into many small services, customizability an flexibility increase as many versions are possible. In those terms, Anerson (006) escribes the ieal of a highly granular SaaS offer: Customers may select exactly the functionality they require an so customize their own service by compiling it from all available artifacts. At this point, we have to mention that prouct ifferentiation for SaaS is situate both in the vertical an the horizontal imension since splitting allows on the one han several inferior versions with less functions or features, but also on the other han parallel versions with isjoint functions or features. However it still epens on characteristics of the functionality, if a prouct ifferentiation problem is situate in only one or both imensions. Thus, the service granularity (or just granularity), which refers to the size of a service, is a viable instrument for iffentiation of SaaS proucts (Haesen et al. 008, p. 383). This leas to Moeling Issue 1: Ajusting granularity has to be consiere in a moel for SaaS instea of fining a number of versions to ensure full flexibility in ifferentiating SaaS proucts. Sales Volume: Prouct ifferentiation allows aressing aitional customers that are only intereste in parts of the offere functionality. In versioning literature, this effect with impact on sales volume, i.e. the amount of sol functionality, is hanle in two ways. Moels of the first type such as Bhargava an Chouhary (001) are built on assumptions that the sales volume will increase as aitional customers buy inferior versions an the sale of the flagship version is not affecte. Moels of the secon type such as Nault (1997) consier that customers which woul buy the flagship version coul choose an inferior version instea. The moels of the latter type argue that the number of customers increases, but it is not guarantee that the overall sales volume increases as only few customers may buy the flagship version an many customers only inferior versions. Since highly granular SaaS offers allow very high customizability, assumptions of the secon type of moels are more realistic an shoul be inherite: Therefore, both positive an negative variation of the sales volume shoul be consiere in a moel (Moeling Issue ). Pricing: In versioning moels, pricing is base on WTP an specific eman of customers (Weber 008, p. 448). These moels usually have assumptions that aitional value generate 4
for a customer may ecrease with every further piece of functionality (Ghose an Sunararajan 005), since the amount of not require functionality increases with larger offers. As SaaS is also stanar software like the regare software in versioning moels, we postulate - referring to pricing aspects of versioning moels (cp..1) - that this assumption has to be inherite leaing to Moeling Issue 3: The higher the granularity of SaaS offere functionality the more flexibly customers can select parts accoring to their specific eman. Customers can now irectly spen their buget on requeste functionality leaing to higher attainable prices per piece of functionality. Costs: Moifying proucts requires technical effort that also has to be consiere in a holistic economic view. In versioning moels, costs are separate into prouction an reprouction costs. Prouction costs on the one han consist of costs for implementing functionality an maintenance (Banker et al. 1991), an on the other han of costs for granularity: With increasing granularity, proviers offer more services, i.e. functionality has to be cut into several moules, an also interfaces have to be provie. Interfaces must ensure that services can be accesse by customers or by other services which require their functionality (Krafzig et al. 005). Futhermore, granular services must be compose in a way that they can work together in orer to rebuil business processes (Arsanjani et al. 008). Heinrich an Frigen (005) m ( m 1) state that for m services at least m, i.e. a single interface per service, but up to interfaces, i.e. all services are connecte with each other, have to be provie. Thus, more services make implementing interfaces an their composition more complex an costly (Haesen et al. 008) resulting in Moeling Issue 4: Costs for granularity increase with granularity, whereas costs for implementing functionality an maintenance are mostly inepenent of granularity. Reprouction costs come up for making functionality accessible for customers. For CSP, venors usually provie a copy on a ata transfer meium or a ownloa server, whereby these costs are of insignificant size an usually neglecte in ecision moels (Bhargava an Chouhary 001; Varian 000). In contrast, a SaaS provier is responsible for hosting an running computations. The more functionality a provier sells, the more computations have to be conucte an there are higher are call frequencies of services an ata transfer resulting in costs for infrastructure (Boerner an Goeken 009). This causes communication an computing costs which are for SaaS of significant size (Lehmann an Buxmann 009) resulting in Moeling Issue 5: Reprouction costs must be consiere in a moel for SaaS. Since varying the granularity of SaaS shows enormous ifferences in contrast to versioning for CSP, we concentrate on the ientifie moeling issues in the following. Summarizing, Tab. 1 compares CSP an SSP base on the iscussion above an gives examples for practical application. 5
Tab. 1 Comparison between CSP an SSP base on the iscussion CSP SSP Sub-category Web service SaaS Definition Stanar software offere as installation package. Running an hosting is inepenent of sales. Functionality that can be integrate into applications accoring to the SOA paraigm. It is offere on an internet accessible server. Running an accessibility is ensure by the provier. Examples Microsoft (MS) Office Query of creit rating provie by rating agency Implementation of prouct ifferentiation Examples of prouction ifferentiation Versioning: Proviers offer ifferent versions to acquire new customers with a more eman specific offer. Reprouction costs per customer are neglectable small. Vertical: MS Office Professional, MS Office home Horizontal: MS Wor, MS Excel Provisioning strategy base on web service technology: Stanar software (incl. fronten) is run, hoste an provie via internet. SAP-CRM-On-Deman, NetSuite ECOMMERCE (NSE) Granularity: Proviers offer inepenent, but combinable services. With higher granularity, i.e. smaller an more services, customers may select functionality fitting to their specific eman, an thus more customers are aresse. Costs for cutting functionality, interfaces an service composition increase with higher granularity. Reprouction costs epen on communication an computing, an can be of significant size. Vertical: Query is base only on ata of few perios Horizontal: Query elivers aitional information about subject Vertical: NSE with constraine analysis functionality Horizontal: NSE Web Shop, NSE BB.3 Relate work on prouct ifferentiation of SSP an granularity A lot of quantitative moels for CSP stemming from the relate research area of versioning exist, but cannot be applie to SaaS as iscusse. With respect to the special characteristics of SaaS, Lehmann an Buxmann (009) state there is a nee for new pricing moels for SaaS an following ecision support. Though most articles ealing with SaaS are still of qualitative manner such as Benlian (009), Benlian et al. (009) or Mietzner an Leymann (008), there are only few quantitative ecision moels concerning SaaS an the highly relate area of web services, we analyze below. Most of the existing research of this upcoming research stream is about competition an factors for offering services successfully on the market. For SSP, Cheng et al. (006) an Fan et al. (009) have examine the effects of provisioning strategies. Cheng et al. (006) analyze three ifferent SSP strategies for proviers an investigate uner which conitions these strategies are profitable. Fan et al. (009) examine short- an long-term competition between proviers of SaaS an CSP. With a game theoretical approach, the authors fin that SaaS proviers have to face high introuction costs in the short, but have avantages in the long run ue to an increasing customer base. Both papers show the economic potential of SSP from a strategic perspective, but o no focus on etails. Another important success factor for SSP is the service level, i.e. the availability of offere functionality, as proviers have to guarantee access to their functionality (Fan et al. 009, p. 66). Zhang et al. (009) examine effects on sales volume an pricing ue to increasing service levels. Bhargava an Sun (008) show how contingency pricing can be applie to IT services an fin that customers are willing to pay higher prices epenent on the provie 6
service level. The mentione papers provie evience how proviers can positively affect prices, but o not consier the granularity of services. Erl (005, p. 557) outlines that ajusting granularity is an important economic factor for web services an SOA. In a more etaile research on granularity, Haesen et al. (008) elaborate three imensions of ecisions on granularity. The functionality imension is about reucing prouction costs ue to higher re-use share. The ata imension refers to reucing communication costs ue to the amount of transfere ata. Whereas the objective of both imensions is reucing costs, the business value imension is about increasing sales volume an aressing more clients. Holschke et al. (009) consier granularity as ecision variable in the functionality imension. They examine which granularity is cost minimizing in reconstructing an existing IT system. In the business value imension, Lee et al. (006) present a versioning approach for web services. They examine how sales volume, aspire quality of a flagship service an the total costs are affecte by a free inferior version, but the authors o not consier effects of chargeable inferior services. These papers focus on sizing an granularity, but consier only single of the relevant aspects (cp. Moeling Issues) instea of a holistic view. Granularity of software has also been subject of research concerning the relate area of components. Base on Parnas (197) work on moulization, an Szysperski s (1998) analysis on component technologies, research was about fining a suitable size of software moules. Such approaches on granularity either have a functional focus (Albani et al. 003), i.e. clustering similar functionality, a technical focus (Kim an Chang 004), i.e. how can a composition of moules or services to an application be mae, an an economic focus (Wang et al. 005), which aim to fin a granularity in orer to reuce costs in implementing systems. The economic approaches primarily focus on the cost imension, but not the sales imension. Summarizing, we can state that there is a lack of quantitative research consiering SaaS. Aitionally, to the best of our knowlege, there is no publication that takes a holistic quantitative approach examining the granularity of SaaS consiering sales volume, pricing an technical aspects. Thus, we aim to fill this research gap by eveloping a moel consiering the elaborate moeling issues. 3 A moel supporting prouct ifferentiation ecisions for SaaS proviers We now present a micro-economic moel to support granularity ecisions on SaaS proucts. We introuce the general form of our moel an the unerlying basic assumptions in subsection 3.1. This is followe by a simplifie moel with assumptions concerning behavior of the market an prouction costs to show funamental relationships in subsection 3.. Here, we present an analytical solution an operationalize our moel with a real worl case serving as running example in the following. In subsection 3.3, we exten the simplifie moel by variable reprouction costs (cp. Moeling Issue 5). 3.1 General form of the moel Basic assumptions an notation The theoretical funament of the moel is forme by the eman curve representing the relation between prices an sales volume (Varian 009) as well as the ientifie Moeling Issues base on the literature review. To set up the eman curve, we have to make two assumptions: 7
Assumption 1: In our one-perio moel, a monopolistic SaaS provier offers functionality, namely the amount F measure in size units (SU) 1. Originally, the functionality is implemente as coherent block an offere in one piece to N customers. Each customer may either buy or not. In aition, there is a technical moule require to run the functionality. This technical moule is not inclue in F an its price is inclue in using the functionality. Thus, the maximum eman Q, i.e. the quantity of salable functionality, is the prouct of offere amount an maximum number of customers (Q=FN). For reasons of simplicity, we consier Q instea of its calculation (FN) in the following. Assumption : The market for selling one single service comprising the whole functionality is given by a eman curve epening on the price p. The eman curve is continuous an linear, has a negative slope, is characterize by the maximum eman Q, an the market parameter β. With both assumptions, the price for each possible eman x from 0 to Q can be calculate. This relation is now enhance by granularity aspects elaborate in the literature review. Accoring to Moeling Issue 1, the provier also can offer the functionality in several more granular services to improve profits: Assumption 3: The functionality can be cut into M services of same size FS (= M F ). Services are not overlapping. The technical moule can be use with any service combination without moification. Base on this assumption, we can introuce the ecision variable egree of granularity g є [0;1[ as normalization an measure of the functional size, whereby g=0 refers to no granularity an higher values of g refer to more granular services. As ientifie in Moeling Issue, offering not all SU in one, but in several more granular services, may help to acquire new customers (N increases). As services become smaller, this bears the risk that customers may only purchase services containing actually require functionality (less than all offere F SU). Assumption 4: The maximum eman may vary epenent on granularity. With higher granularity the more flexible customers can select functionality an the better is the fit to the specific eman. Thus customers can more irectly spen their buget on require functionality as they only want to pay for this. Accoring to Moeling Issue 3, following relation between prices an granularity is assume: Assumption 5: The price per SU increases with higher granularity. We now can introuce the function h(g) representing the increase in price per SU subject to the egree of granularity. Accoring to Assumptions 4 an 5, the provier can influence the market, namely the maximum eman an the attainable price, by moifying the granularity of its services. These moifications have effects on the total costs (enote by C) consisting of prouction an reprouction costs. Prouction costs consist of costs for implementing an maintaining functionality (enote by C p ) an costs for granularity (enote by C g (g)), i.e. for splitting the functionality up into more services an for interfaces. To satisfy Moeling Issue 4, we assume: 1 Let a SU be a general measure for a size of software. Applying the moel, this measure shoul be replace by a software metric such as the Function Point Analysis or COCOMO. 8
Assumption 6: Implementation an maintenance costs are fixe. Costs for granularity increase with higher granularity. To ensure Moeling Issue 5, we consier reprouction costs C r (x) ue to higher communication an computing effort: Assumption 7: Reprouction costs epen on the amount of sol functionality. With these assumptions on market an costs, we can evelop a moel in which a provier can etermine the optimal egree of granularity in orer to maximize its return. Moel Development In the first part of this subsection, we evelop our optimization moel for etermining the optimal number of SU to sell. In the secon part, we integrate effects of granularity into the moel. The actual number of sol SU can be written by the eman curve. Accoring to mircoeconomic theory, this figure can be calculate as ifference of the maximum eman, an the prouct of price per SU an market parameter β measuring the impact of the price. Thus, prices an sales volume correlate negatively (Varian 009): 1) x( p) = Q β p By inverting, the price can be written as function of the eman: Q x ) p( x) = β Though it is more intuitive from an entrepreneur s point of view setting price instea of setting eman, we take the latter perspective (equation )) as it is mathematically easier to process an the moel evelopment is easier to follow. The return can be calculate as a prouct of price an sol SU minus costs: Q x 3) R( x) = x C β Equation 3) can be employe to calculate the return, if all functionality is offere in one single service, i.e. FS=F. Now we moel the effects of granularity, i.e. FS<F. Accoring to Assumption 3, we introuce the egree of granularity, which can be calculate in two ways: as a relation of the offer share, i.e. the size per service over the total amount of offere functionality, an alternatively, epening on the number of services. To be more intuitive, g=0 shall refer to no (zero) granularity. 4) FS g = g( FS) = 1 F 1 g = g( M ) = 1 M FS g {1 F 1 g {1 M FS IN} M IN} In contrast to factual correct values as written by eq. 4), we moel g to take every value in the interval [0;1[, i.e. 0<g<1. This mathematical simplification allows a continuous objective function an thus an analytical analysis. In the following, we issolve this conflict in the operationalization by showing factual correct optimal results accoring to eq. 4). The egree of granularity has effects on the parameters of the return function. Accoring to assumptions 4-7, the fixe maximum eman Q is replace by the granularity epenent maximum eman Q(g). The price (equation )) is multiplie with the price avance function 9
h(g). The total costs are the sum of prouction an reprouction costs an are written as C=C p +C g (g)+c r (x). As granularity has effects on the mentione parameters an as these parameters are multiplie with the eman x in the return function, eman an egree of granularity are epenent. Thus, there is a return maximizing eman which itself epens on the granularity an is enote by x(g). In the following, this relation is always employe instea of the variable x. By integrating these effects, the return function (equation 3)) can be written epening on g an is use as objective function: 5) R( x 0 =< g < 1 Q( g) x ( g), g) = β ( g) h( g) x ( g) C p C g ( g) C r ( x ( g)) max! By concretizing this general form of the objective function, we will now examine the effects of granularity. 3. Basic ecision moel Base on the general form, we efine a simplifie setting that enables an analytical examination of the funamental effects cause by granularity. We therefore assume that granularity causes linear changes on the moel parameters eman, price an costs for granularity. Aitionally, in this stage of the moel, we still assume that reprouction costs are fixe as in CSP moels. Base on the ancestor assumptions of the previous subsection an replacing them, we make new simplifie assumptions: Assumption 4.1: The maximum eman may increase, stagnate or ecrease, an is expecte to vary linearly on the moification factor η with increasing egree of granularity. 6) Q( g) = Q (1 + η g) Assumption 5.1: The price per single SU increases linearly by the moification factor γ>0 with increasing egree of granularity. 7) h( g) = 1+ γ g Assumption 6.1: Costs for implementing an maintaining functionality are fixe (enote by PC). Costs for granularity increase linearly up to the maximum extent GC. 8) C = PC C ( g) = GC g p g Assumption 7.1: Reprouction costs consist of a fixe cost block RC an neglectable variable costs. 9) C r ( x ( g)) = RC With these new assumptions, the objective function can now be written as: 10) R( x 0 =< g < 1 Q (1 + η g) x ( g), g) = β ( g) (1 + γ g) x ( g) PC GC g RC max! To obtain a relation x(g) between optimal eman an granularity, we set the 1 st partial erivative of the return function with respect to the eman to 0. By solving the resulting equa- 10
tion for the eman an checking the n orer conition, we can write the return maximizing eman as a function of the egree of granularity (Simon an Blume 1994, cp. App. A): Q (1 + η ) 11) x ( g) = g Inserting this relation into equation 10), the optimization problem is written as: 1) Q R( g) = 0 =< g < 1 (1 + η g) 4 β (1 + γ g) PC GC g RC max! Moel analysis We now examine the moel analytically an euce general statements on the moel parameters. As the maximum eman may increase, stagnate or ecrease ue to changes of granularity, two cases have to be consiere. Before stepping into the analysis, we can state that proviers shoul abstain from offering granular services, if costs for granularity are very high an excee possible aitional income. This is true for both of the following cases. Case 1: Maximum eman increases or stagnates with increasing granularity (η>0) Very simple an intuitive statements can be euce for this case. With increasing granularity, prices will increase an the eman will stagnate or increase. As income (as prouct of prices an eman) will always increase, if more granular services are offere, proviers shoul always pick the maximum egree of granularity. Case : Maximum eman ecreases with increasing granularity (η<0) With increasing granularity, prices will increase an the maximum eman will ecrease. Thus, in contrast to Case 1, the maximum income an thus the egree of granularity may be situate anywhere in the feasible interval. We now erive the optimal egree of granularity, whereby a more etaile erivation is shown in App. B. To optain a possible optimal egree of granularity, which we enote with ĝ, the 1 st orer conition for ĝ is: R η Q (1 η g) (1 + γ g) γ Q (1 η g) 13) = + GC! = 0 gˆ g β 4 β The n orer conition also has to be satisfie for ĝ to etermine a unique return maximum: R η γ Q (1 η g) η Q (1 + γ g) 14) = +! 0 g g = gˆ β β < Base on the 1 st erivative, we can etermine two possible optima, of which this one satisfies the n orer conition: 1 15) gˆ = 3 η 3 γ 4 3 GC β + 1 9 Q η γ Q ( η + η γ + γ ) The parameter η has been substitute by η =-η. As now all parameters in the following equation are positive, the analysis is easier to follow. 11
As the ecision variable is efine in an interval, the possible optimum has to be prove for feasibility an the position of ĝ has to be examine. If ĝ is situate within the interval, it is the optimal g. If g ˆ => 1, one shoul select the maximum granularity. In case of g ˆ < 0 the return maximizing granularity is either at the lower or upper bounary (no or maximum granularity), thus both points have to be examine (cp. App. B). These erivations an formulas (especially equation 15)) form the founation for analyzing the real worl case. At this point, we can euce the following general statements concerning the behavior of the egree of granularity ue to variations of the parameters. The first finings concerning the parameters, that are irectly conjunct with granularity, are very intuitive: Lower costs for granularity (lower GC) an a higher WTP for more specific functionality (γ increases) may lea to an increasing egree of granularity. In contrast, the more customers only request few specific moules (η increases (or η ecreases)), the more shoul the egree of granularity ecrease. Thus, by offering services of lower granularity, proviers can ensure to sell a critical mass of SU by offering larger parts an by this force customers to buy more SU than requeste. This is also true if large parts of the functionality are requeste by the majority of customers an customers requesting only small parts must not be given much attention. Even more interesting are general statements on given market parameters: A larger β, i.e. lower general WTP an more inelastic eman coming up with lower customers reservation prices, woul lea to lower granularity. This is generally ue to lower attainable prices. Proviers may try to compensate this with selling larger services containing more SU. Secon, a larger market/higher maximum eman (larger Q) causes not only higher sales volume an prices (Varian 009), but also higher granularity. This is ue to rising income (since more functionality can be sol an prices woul increase) in contrast to constant costs for granularity. Therefore, proviers shoul try to influence the market size in a positive manner: Starting points woul be e.g. a higher focus on customer relationship management (CRM) to support customer retention an acquisition, or expaning the amount of offere functionality to sell more SU per customer. However, it must be overhaule if there is eman for such expansions an if this eman is not alreay covere by another provier. Operationalization: Introuction of the real worl case This case will serve as a running example to further illustrate the application of the moel an is base on ata of the SaaS provier IESP. Names as well as all ientifying etails are omitte an the business case ata have been anonymize an slightly abrige for reasons of confientiality. Besies SaaS suites for CRM an financials, IESP offers an inepenent suite for employee resource management (ERM). Furthermore, there is a technical moule running in the backgroun an is require for all three suites. The real worl case is base on ata of this ERM functionality. Due to the very high functional maturity its ERM software nearly has an exclusive position on its SaaS market. The suite contains the moules self services for employees/managers, human resources management an ocument management. IESP employs the software metric Function Point Analysis to measure the size as this metho allows a etaile analysis (Albrecht 1979, Jones 007). The functionality has been estimate to 0,000 function points with this metho base on content an complexity of inclue functions. Base on historical ata, implementation costs for function upates an maintenance are estimate to.6 mn. Costs for proviing incl. user support are estimate to 400,000. 1
IESP has offere the ERM suite recently in a single service, but overthinks to change its strategy: By offering the functionality within more granular services, new customers shall be acquire emaning only certain parts of the whole ERM suite. The potential of such a strategic change has been evaluate with a market stuy which is base on internal ata an purchase ata from a market research institute. IESP has internal ata about recent customers, an potential customers which have been subject to acquisition in the last two years. This ata comprises the number of requeste user licenses, requeste parts of the suite an WTP. The ata from the institute was base on a questionnaire in which evelopments of SaaS markets an its segments (e.g. CRM, ERM) were estimate an which was sent wiely sprea to large an meium-size companies. For each segment, the questionnaire containe a list of functionalities that the requeste software shoul provie. Participating firms were aske to mark functionality they require an to estimate the number of licenses. Furthermore, they shoul quantify the extent of WTP if they woul buy software satisfying their requirements in large extent (e.g. stanar software) or fully (e.g. customize software). Concerning the ERM functionality, the external ata gives information about customers, potential sales volume of ERM subfunctions an attainable prices. From the external ata, IESP selecte ata concerning its target groups. This ata was matche with internal ata. Concerning eman, potential customers are segmente into five clusters (cp. Tab. ), whereby clusters C1-C3 consist of potential customers for the alreay offere full version, C4 an C5 of new potential customers which are intereste in parts of the suite an only coul be aresse with services of higher granularity. For estimating the eman of C1-C3 primarily internal ata was taken. As the external ata shows higher sales potential, estimations were raise by a certain extent, but for reasons of safety not up to the full extent as preicte by the external ata. For C4 an C5 external ata was taken an moifie by a safety reuction. Concerning WTP, lower an upper ranges result from ata for each cluster. As the reservation price (RP) is erive from the maximal WTP, an resulting market prices in monopolies are usually lower than RP, for reasons of clearness only the upper range of the WTP is liste in Tab.. IESP now has evience about the potential number of users an their specific amount of require functionality as well as their maximum WTP for using the functionality. We also label every attribute with a symbol, as these figures are use to calculate the moel parameters an the calculation is easier to follow. Costs for granularity, i.e. for spreaing functionality on more services, are estimate to rise up to a maximum sum of 175,000. 13
Tab. Annual market potential Attribute Symbol/ Calculation Cluster c C 1 C C 3 C 4 C5 Number of customers [users/year] Require functionality [%] Require functionality [SU] Maximum WTP per customer [ ] Maximum WTP per SU an customer [ /SU] N c 1,000 1,500,500 3,000 4,000 REQ c 100% 65% 50% 5% 15% REQ c F 0,000 13,000 10,000 5,000 3,000 WTP c 3,000,00 1,750 900 570 WTP c F REQ c 0.15 0.169 0.175 0.18 0.19 Together with experts of IESP, we took these figures to quantify the moel parameters. First, iniviual emans an WTP ha to be aggregate to the eman curve. For a monopoly (Varian 009), the RP equals the maximum iniviual WTP, an maximum eman is an aggregation of all iniviual emans, i.e. potential salable SU of relevant clusters are ae. Secon, we assume that varying the granularity influences the market, an hence eman curve an its parameters. As we assume linear progression ue to granularity, we ha to quantify the maximum eman, reservation prices an costs for minimum (all recent customer clusters C1-C3 are relevant) an maximum (all clusters are relevant) granularity. Base on eman an prices, we coul etermine moification factors an market parameters as liste in Tab. 3. Due to changing granularity, other customer clusters with ifferent require SU an WTP may become relevant for etermining β resulting in another value for β. However, β is kept fixe an these effects were moele by the factor γ which itself is multiplie with β in the objective function. 14
Tab. 3 Parameters of the moel Parameter Formula Value Q(0) [SU] Q( 0. 9 ) [SU] 3 c= 1 5 c= 1 N N c c F REQ c F ( 1,000 + 1,500 +,500) 0,000 = 100,000,000 (1,000 1.0 +1,500 0.65 +,500 0.5 + 3,000 0.5 + 4,000 0.15) 0,000 = 91,500,000 Maximum PR per SU an customer for g=0 [ /SU] Maximum PR per SU an customer for g= 0. 9 [ /SU] β WTP max( c 3,000 ) = 0. 15 F 0,000 WTPc max( F REQ Q(0) PR(0) PC [ ] -,600,000 c ) 570 = 0.19 0,000 0.15 100,000,000 = 666,666,666 0.15 RC [ ] - 400,000 GC [ ] - 175,000 η γ Q(0.9) 91,500,000 1 1 = 0. 085 Q(0) 100,000,000 PR(0.9) 1 PR(0) 0.19 1 = 0.667 0.15 Applying the moel base on these parameters, it suggests an optimal granularity an a market price, an aherent amount of sol SU 3. Optimization Inserting the parameters of Tab. 3 into equation 15), the optimal egree of granularity can be calculate analytically. Fig. 1 an Tab. 4 show the optimal results with relevant economic ata. To show the effects of granularity, we also list the values for no granularity. 3 Due to characteristics of a monopoly, both market price an sol SU will be lower than maximal RP an eman. Thus, resulting prices an eman may iffer from the estimations. 15
Tab. 4 Optimization results g Return [ ] Income [ ] Costs [ ] Number of Services Offer share [%] Sol SU Price per SU [ ] g = 0.69 813,788 3,935,01 3,11,33 3. 31 47,055,777 0.084 g int = 0.667 813,701 3,930,367 3,116,666 3 34 47,166,666 0.083 g = 0 (no granularity) 750,000 3,750,000 3,000,000 1 100 50,000,000 0.075 R [ mn] 810000 800000 0.80 790000 780000 0.78 770000 theoretical maximum integer maximum 760000 0.76 0. 0.4 0.6 0.8 1.0 Fig. 1 Graphical representation of the results g First, this result has to be prove for feasibility. Examining the result of ĝ = 0.69 (cp. Moel Analysis; App. B) reveals that this ĝ is also the optimal theoretical g representing 3. services. The next g with an integer number of services (cp. eq. 4)), which also has the highest return, is g int = 0.667 implying the functionality shoul be split on three services, an now calle integer maximum. This new allocation causes significant changes in the amount of sol functionality ecreasing by 6% an prices attaine per SU increasing by 11%. These effects are ue to a change in the customer structure. Though, the customer base can be enlarge, the sales volume ecreases as services are smaller an more specific an customers only buy require functionality. In the context of this example, the propose egree of granularity woul imply in particular customers of clusters C an C3 an limite C4 coul be provie with services more specific to their eman. Furthermore, customers WTP can be better skimme resulting in higher prices per SU since the offere smaller services are more specific to their eman. This results in higher income. Compare to the origin state, where only a single service was offere, the income increases by 180,367. The costs only increase by 116,666. In sum, return woul increase by 63,701 or 8%, respectively. We can state in the context of this example that a provier can enlarge its return by offering granular services, though the amount of sol functionality may ecrease. This positive eco- 16
nomic effect is ue to a win-win setting for customers an provier enable by granularity: Customers can purchase functionality highly specific to their eman an spen the amount they are willing to pay for require functionality. Proviers can realize higher prices per moule an enlarge the business value of their functionality. This effect is even enlarge by the charateristics an payment moalities of SaaS, since customers pay per use or per perio for a bunle of infrastructure an functionality an o not have to install software on own servers. Therefore, customers are very flexible an variable in costs since they only have little fixe costs for initial investments (Sääksjärvi et al. 005, p. 183). As the impact of upfront cost ecreases, fine grane SaaS functionality is in particular attractive for customers with little or meium eman. Thus, proviers shoul use granularity as instrument to be attractive to new customers an attain higher income. 3.3 Moel extension reprouction costs In this stage, we examine effects of reprouction costs as postulate (cp. Moeling Issue 5). Until now, we assume fixe reprouction costs. As communication an calculation costs increase with the amount of sol functionality (Lehmann an Buxmann 009), we replace Assumption 7.1 by: Assumption 7.: Reprouction costs increase linearly with the amount of sol functionality. Thus, the more functionality is sol an following customers are acquire, the higher are reprouction costs. They can be calculate as prouct of costs per single sol SU RC SU an actual eman. 16) C ( x ( g)) = RC x ( g) r SU With this aitional assumption, the objective function is now written as follows: 17) R( x 0 =< g < 1 Q (1 + η g) x ( g), g) = β ( g) (1 + γ g) x ( g) PC GC g RC SU x ( g) max! This enhancement complicates the return function an now solving the maximization problem analytically is not possible anymore. We have to solve the problem numerically. We implemente an solve equation 17) with the NMaximize function of the program Mathematica. Operationalization: Continuation of the real worl case In the previous stage, we unerlie fixe reprouction costs of 400,000. Together with experts of IESP, we analyze the relevant costs an estimate the maximum reprouction costs, in case the eman woul be fully covere, to 600,000 (best case) or 800,000 (worst case), respectively. This is resulting in a parameter value for RC SU of 0.006 or 0.008 [both in /SU]. To examplify the effects of reprouction costs, we calculate both cases. Tab. 5 lists the results of the optimization. 17
Tab. 5 Optimization results RC SU [ /SU] g 0.006 g = 0.79 g int = 0.8 Return [ ] Income [ ] Total costs Reprouction costs [ ] of Servic- Number [ ] es Offer share [%] Sol SU Price per SU [ ] 938,495 3,947,036 3,008,541 69,89 4.8 1 44,98,00 0.088 938,45 3,948,164 3,009,71 69,71 5 0 44,977,000 0.088 g = 0 850,000 3,750,000,900,000 300,000 1 100 50,000,000 0.075 0.008 g = 0.8 g int = 0.833 849,16 3,947,69 3,098,530 354,53 5.6 18 44,316,571 0.089 849,149 3,949,198 3,100,049 354,16 6 17 44,78,300 0.089 g = 0 750,000 3,750,000 3,000,000 400,000 1 100 50,000,000 0.075 Fig. shows the curve progressions an maxima for both scenarios. 900000 850000 800000 0. 0.4 0.6 0.8 1.0 Fig. Graphical representation of the results As both g are feasible an granularity is also attractive like in the previous section, an even with increases in return up to 13%, we focus in our analysis on one leaing question: Which ifferences occur if reprouction costs are consiere (which is usually neglecte in moels for CSP)? We can see that reprouction costs foster higher granularity an return can also be increase. This is also epicte in Fig. where the maximum of the return curve moves towar higher granularity for both cases. This is for two reasons, reprouction costs ecrease with higher granularity, an proviers can parallel exploit the value of their services ue to higher attainable prices. This is economically sensible as long as the reuction of reprouction costs an the increase in income excee costs for granularity. Thus, proviers shoul carefully outweigh the characteristics of these factors. By comparing both cases, one can say that 18
higher reprouction costs result in higher granularity. If a provier has functionality with high ata traffic or intensive computations, it might be interesting to reuce reprouction costs by higher specialization of the offer with more granular services. Another aspect is the evelopment of harware prices which are steaily ecreasing resulting in reuce reprouction costs (cp. best case). Here we can state that lower reprouction costs have ecreasing effects on the egree of granularity. Summarizing, we have to point out that consiering variable reprouction costs for SSP moels is of crucial importance. As implication for scholars, we have to point out that reprouction costs cannot be neglecte in moels for SaaS as one in moels for CSP. 4 Discussion on limitations an practical application The introuce moel is base on a set of assumptions. We explain why the moel elivers vali results though built on rigi assumptions an iscuss how their relaxation can improve practical impact. Furthermore, these limitations at the same time bear extension potential. We assume a monopoly as this market form is often employe in theory since it allows a goo analysis of effects on the market. Other market forms such as a uopoly or competition are also conceivable as proviers may offer similar software an thus have to compete for market shares. Concerning other market forms, it seems that firms having certain market power, e.g. price leaers, may profit from similar effects like a monopolist. In this case, finings may be partially transferre. In contrast, if firms have no influence on the market, transferability of finings is hinere. Thus, other market forms coul be subject to further research. We introuce a rigi assumption that the functionality has to be cut into services of same size. This implies that regare functionality ha to consist of several functional blocks that can be offere inepenent of each other, whereby cuts have to be mae along these blocks. Though in reality, moules are usually not of same size, the moel may eliver a guie value which granularity shoul be chosen for software of concurrent moules. Tab. 6 shall illustrate how the egree of granularity can be mappe to cutting functionality. Tab. 6 Interpretation of granularity Granularity Description Number of Services Interval for g No granularity One service comprising all SU. 1 [0.0;0.5[ Low granularity Meium granularity High granularity The functionality is split into its major parts: employee self services, HR management an ocument management. Major parts are split up into their main functionalities. For instance, HR management coul be split up into employee aministration, acquisition, reporting, an payroll. The functionality is split into services up to an economically reasonable minimal size. -3 [0.5;0.667[ 4-1 [0.667;0.917[ >1 [0.917;1.0[ 19
A relate problem is fining a sufficient size that provies still enough value for customers. For instance, it might be not reasonable to offer functionality which only returns a list of employees. Instea a minimum size woul be to combine this listing function at least with timesheet tracking or expense reports. In sum, though ecision makers have to efine a minimum size, the moel can support them in fining a size equal to or above this efine lower boun. Increasing granularity is followe by increasing prices. However, customers requesting all functionality woul have to pay more with higher granularity, though they woul purchase the same amount of functionality. This bears risk of movement of such customers. Incluing volume iscounts for customers requesting all or most functionality may be a starting point for this extension. The moel captures basic effects in an aggregate approach which enable showing funamental aspects of the problem in a comprehensible way. But, income an costs may iffer from service to service as e.g. some services cause a larger ata transfer than others (Boerner an Goeken 009) or some parts of the functionality have higher eman. In practice, a more etaile analysis with a isaggregation to single services may be appropriate. These parameter estimations base on single services can be aggregate an then employe to our moel. Further research coul be occupie with other analysis methos such as two-(or more-)part pricing schemes to consier heterogeneity of services. Finally, we assume linear changes ue to varying granularity. While this allowe a meaningful analysis by an analytical solution, the applicability of linear changes is limite. This is especially true for granularity costs as the number of interfaces may crucially increase (Heinrich an Frigen 005). Such an enormous increase woul result in exponentially rising costs. In this case, our moel woul propose a lower egree of granularity compare to linear progression. However, the general form can be easily substantiate with arbitrary realistic, e.g. exponential relations, or with more etaile input ata as mentione in the previous paragraph. 5 Conclusion SaaS bears much economic potential, but there are only few quantitative ecision support moels for this uprising provisioning type. In particular, there is a lack of research concerning prouct ifferentiation of SaaS. To contribute to fill this gap, we presente a formal approach consiering aspects of prouct ifferentiation for SaaS, in particular effects on prices, sales volume an costs were consiere. Therefore, we iscusse applicability of existing CSP versioning moels to SaaS an ientifie moeling issues, in particular that varying the service granularity is a viable instrument of prouct ifferentiation for SaaS. Starting out with microeconomic moels base on the eman curve, we elaborate which effect varying granularity has on the market an hence on parameters of the eman curve. Then, we inclue these effects into the parameters of the eman curve an presente a ecision moel base on this extene eman curve. Furthermore, we inclue variable reprouction costs which have mostly been neglecte in quantitative research so far. Finally, we illustrate our approach with a real worl case. The article formalize concepts of prouct ifferentiation for SaaS an shoul help to establish basic unerstaning in this area. Thus, our approach provie insights into the economic trae-off between the major influence factors. In analyzing the presente moel, relations between these major influence factors an varying a SaaS prouct coul be eucte. Furthermore, the moel provies evience that reprouction costs may have significant influence on granularity an profits. Thus, they shoul be consiere necessarily for SSP moels. This is contrary to prior versioning approaches for CSP. Summarizing, the propose moel for 0
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Appenix A. Relation between the egree of granularity an the actual eman This appenix contains a etaile erivation of the relation between the egree of granularity an the actual eman. The actual eman x an the egree of granularity g are mathematically epenent, as they are multiplie in the objective function: A_1) R( x 0 =< g < 1 Q (1 + η g) x ( g), g) = β ( g) (1 + γ g) x ( g) PC GC g RC max! To allow an analysis an resulting general statements base on an analytical solution, one has to etermine a relation x(g) between optimal eman an granularity to option an objective function epening one a single variable. Therefore, the 1 st partial erivative of the return function (equation 10) in the paper or here A_1)) with respect to the eman has to be set to 0: R ( Q (1 + η g) x ( g)) (1 + γ g)! A_) = 0 x ( g) = x ( g) β By solving the resulting equation for the regare case, we receive the return maximizing relation between actual eman an egree of granularity (cp. equations 11) or A_3)): Q (1 + η ) A_3) x ( g) = g Finally, this resulting relation has to be checke with the n orer conition: R + γ g A_4) =! 0 ( x ( g)) β < The n orer conition is true for the calculate relation, thus it can be use as maximizing relation between actual eman an egree of granularity an further employe in the objective function. B. Detaile erivation of the optimal egree of granularity This appenix contains a etaile erivation of the optimal egree of granularity in case of ecreasing maximum eman with increasing granularity (cp. 3. Case ). Starting out with the objective function (equation 1)), the possible optimal egree of granularity, which we enote with ĝ, can be calculate over the 1 st orer conition. B_1) R g η Q = (1 η g) (1 + γ g) γ Q + β (1 η g) 4 β GC! = 0 gˆ 4
Base on the 1 st erivative, two possible optima can be etermine. For reasons of simplicity, we also substitute the parameter η by η =-η as now all parameters in the following equation are positive an the erivation is easier to follow. B_) gˆ gˆ 1 1 = 3 η 3 γ 1 = + 3 η 3 γ 4 3 4 3 GC β + GC β + 1 9 1 9 Q η γ Q Q η γ Q ( η ( η + η γ + γ ) + η γ + γ ) The next step is to analyze the calculate extrema. As the objective function for this case is a polynomimal of 3 r egree, there is always one local maximum an one local minimum (Simon an Blume 1994). Thus, to etermine a unique return maximum the n orer conition has to be satisfie for the possible optima ĝ : R η γ Q (1 η g) η Q (1 + γ g) B_3) = +! 0 g g = gˆ β β < As all parameters are positive, ĝ is always greater than ĝ 1. By inserting both possible optima into the n erivative, one can state that the value of the n erivative at ĝ is always greater than the value at ĝ 1. Accoring to the n orer conitions, the local maximum must be situate at the lower value, i.e. ĝ 1, an the local minimum at the greater value, i.e. ĝ. Thus, the possible return maximum which has to be examine for feasibility, is: g ˆ = gˆ 1. As the ecision variable is efine in an interval, the position of the possible maximum has to be prove for feasibility, i.e. lying in [0;1[ or not. This examination be mae from the perspective of the number of services (0<M<F) for gˆ [0;1[: g = gˆ B_4) for for gˆ => 1: g gˆ < 0 : g = lim M F = 0, g( M ) if R(0) => R( lim g( M )) + M 1 g = lim M F g( M ), if R(0) < R( lim g( M )) + M 1 or the size per service (F>FS>0) for gˆ [0;1[: g = gˆ B_5) for for gˆ => 1: g gˆ < 0 : g = lim g( FS) + FS 1 = 0, if R(0) => R( lim g( FS)) + FS 1 g = lim g( FS), + FS 1 if R(0) < R( lim g( FS)) + FS 1 5
Now ifferent cases may occur an have to be examine: If ĝ is situate within the feasible interval, the calculate value is also the return maximum, i.e. g = gˆ. If g ˆ => 1, i.e. it situate even beyon the maximum feasible granularity, the return maximum is at g = lim g( FS)) = lim g( M ). Thus, the maximum granularity shoul be chosen, i.e. services + FS 1 M F shoul be of a minimal size, or a maximum possible number of services shoul be provie, respectively. + FS 1 M F More complex is the case g ˆ < 0, as the local maximum occurs at a negative value. Thus, the local minimum ĝ may be situate within the feasible interval [0;1[. Hence, the attainable maximum return occurs either at the lower ( g = 0, one service comprising the total functionality) or upper bounary ( g = lim g( FS)) = lim g( M ), services have an economically reasonable minimum size, maximum possible number of services). Therefore, both points have to be examine an the one with higher return shoul be selecte. 6