A Multi-Attribute Service Portfolio Design Problem Rico Knapper∗ , Christoph M. Flath∗ , Benjamin Blau† , Anca Sailer‡ , Christof Weinhardt§ ∗ FZI Forschungszentrum Informatik, Karlsruhe, Germany Email: {knapper, flath}@fzi.de † SAP AG, Walldorf, Germany Email:
[email protected] ‡ IBM T.J. Watson Research Center, Hawthorne, NY, USA Email:
[email protected] § Karlsruhe Institute of Technology, Karlsruhe, Germany Email:
[email protected]
Abstract—Increasing popularity of cloud-based services has led to the emergence of cloud marketplaces where services from different providers are offered, usually in the form of a catalog. The customers’ decision about buying offered services is based on idiosyncratic preferences regarding non-functional service attributes, e.g., price, provider reputation, and quality of service. Customer preferences are typically unknown to providers at the time the service portfolio (i.e. quality and price choices) is specified. Thus, from a microeconomic perspective, we have to deal with information asymmetry in markets, which complicates the challenge of finding the profit maximizing service portfolio. This paper presents a generic economic framework based on customer self-selection to address the above-mentioned optimization for a cloud service provider. The contribution is twofold: We characterize a multi-attributive customer preference function for cloud services based on a continuum of potential customers. Thereby each infinitesimal demand of a customer is characterized by a vector of minimum quality values for each of the different attributes and a maximum willingness to pay. The demand framework addresses the phenomenon of product cannibalization. We then formulate the service providers’ optimal service portfolio design. This grants the provider maximal profit through optimal combination of potential values of the chosen attributes. Keywords-Service Portfolio Design, Service Pricing, SelfSelection, Product Cannibalization
I. I NTRODUCTION With the rise of the Internet of Services, cloud platforms play a central role enabling the exchange of services. Cloud platforms are solutions on-top of a cloud infrastructure that facilitate the component-based assembly, trade, and provision of services. Instead of having to develop applications entirely from scratch, application fragments such as simple (Web) services and third-party software libraries can be dynamically retrieved from and assembled in the cloud. A. Cloud service offerings The amount and variety of cloud services offered via the Internet is already huge, ranging from infrastructure services (IaaS) such as Amazon’s Simple Storage Service and
SimpleDB to business applications (SaaS) as, for instance, offered by Salesforce or NetSuite.1 Situated in betweeen IaaS and SaaS, the former model of Sun Microsystem’s network.com platform2 offered so-called “published applications” for re-use. Morph Labs and Google App Engine provide platforms for the deployment and management of Grails, Ruby on Rails and Java in the cloud enabling developers to write their applications, upload their code into the cloud and run in a web-based manner.3 Developers do not have to care about issues like system scalability as the usage of their applications grows. Further platform examples from BungeeLabs, Salesforce, and Microsoft enable managing the whole tailored business applications lifecycle from the cloud.4 Leading on from this development, cloud ecosystems, where buyers and suppliers come together to buy and sell IT services, start to emerge, although today still being in their infancy. Zimory5 provides software that enables multiple enterprises to offer and share services for dynamic IT infrastructures. These services can then be composed with services from other providers for a richer set of cloud-based services. For example, a buyer can purchase compute services from provider A, a management service from provider B, while data backup and restore service is from provider C. StrikeIron6 provides Web-based marketplace for delivering business data offered by diverse providers to any Internetconnected system, including SaaS. B. Economics of cloud services From a micro-economic perspective, cloud marketplaces are an environment that enables the trade between market participants, i.e., the exchange of services between service 1 http://aws.amazon.com/, http://www.salesforce.com/, http://www.netsuite.com/ 2 http://www.sun.com/service/sungrid/ 3 http://www.mor.ph, http://www.code.google.com/appengine/ 4 http://www.bungeeconnect.com/platform/, http://www.salesforce.com/ 5 http://www.zimory.com/ 6 http://www.strikeiron.com
providers and service customers, similarly to the exchange of goods on ‘traditional’ physical goods markets. Information (e.g., required service quality, willingness to pay for a particular service) is not common knowledge in such markets but dispersed among and private to the market participants. More precisely, suppliers hold private information regarding their cost structure and capacity but lack the information on the customers’ preferences and willingness to pay. Conversely, service customers hold private information on their preferences for service quality and the price they are willing to pay. Given this uncertainty with respect to customer quality requirements and product valuations the supplier offerings are designed based on average expectations about customer preferences. Given the high costs of developing additional physical products they are likely to only offer average quality at an average price. This lack of quality differentiation leads to the loss of various customer types, especially those seeking very high quality or very low price. This phenomenon is commonly known as the adverse selection problem. Cloud service markets, as well, are characterized by asymmetric information and heterogeneous customer preferences. However, it is much simpler for service providers to offer multiple quality versions of its service products [1]. But with product variety arises the problem product cannibalization: low cost versions may attract new customer segment but may also attract customers away from more expensive versions. Hence, service providers are faced with a problem of strategic product line design. In this paper we develop and formalize the service component selection problem for cloud service providers. Assuming individually rational customers, we model market demand for functionally similar service products as a continuum of infinitesimal customers characterized by probability distributions over quality requirements and reservation prices. Service quality is represented as an abstract scalar but build from different non-functional attributes such as bandwidth, latency or security level. This demand model endogenously incorporates product cannibalization and allows us to characterize an optimal offer policy for a cloud service provider. Our model enables service providers to design an optimal menu regarding their service offerings, i.e. a service offering catalogue that maximizes the service providers’ revenue given infinitesimal number of customers characterized by probability distributions over quality requirements and reservation prices.
demand model framework for quality-differentiated services. Using these primitives we describe the arising product cannibalization and characterize the provider’s profit for a given portfolio. This allows to formulate the service provider’s product line design optimization program. Finally, Section V concludes by summarizing our contribution and outlining future research opportunities.
C. Outline
At the economic core of our problem stands the idea of companies exercising price discrimination between customers to extract profit. We will provide a quick overview on the subject manner and refer for an in-dept treatise to the extensive industrial organization literature in this field, e.g. Varian (1989) [7]. There are three generic types of price discrimination:
The remainder of this article is structured as follows: Section II reviews the related information systems and economics literature on service composition, price discrimination, product line design and multi-attributive product utility. In section III we then characterize the properties of the service product portfolio and describe the corresponding
II. R ELATED W ORK A. Service composition The field of service composition is traditionally a technical domain that is dominated by computer science research, which is underpinned by corresponding related work: For determining suitable service compositions a wide range of different methods has been proposed. Most of these approaches rely on AI planning algorithms and apply backward chaining to derive suitable compositions from a certain goal. Such an approach is, for example, presented in [2] for stateful and in [3] for stateless services. Often such approaches are based on formal descriptions of service functionality as proposed by the W3C recommendation SAWSDL, and the W3C submissions OWL-S and WSMO. Composition that additionally include information about the (temporal) behavior of a service is presented in [4]. All these approaches consider service functionality as the only composition criteria and largely disregard other non-functional (and particularly business-related) service properties used for service differentiation (e.g. quality of service or prices) as postulated by the next requirement. There are several algorithms for QoS-based composition such as presented in [5]. However, these approaches do not provide declarative representations of service offers and requests as required in a Web scenario. An approach for a compact representation of service requests and offers with complex pricing and preference functions is presented in [6]. Although this approach supports multiple service configurations and features a service selection algorithm, the approach is restricted to the selection of single services and not applicable for service networks. Nevertheless, the presence of asymmetric information and rational opportunistic behavior of service providers and customers is always ignored in the body of work that deals with service composition from a purely technical perspective. B. Price discrimination and product line design
First-degree price discrimination (perfect price discrimination): all surplus from customers is extracted by the company • Second-degree price discrimination (customer selfselection): by offering different price-quantity/ pricequality pairings the company induces customers to selfselect the product most suitable for them • Third-degree price discrimination (spatial price differentiation): customers are grouped into distinct segments without possibility of transition (e.g., local separation, age discounts) Given the openness of cloud and service markets only second-degree price discrimination can be applied in this domain. Versioning and quality discrimination are the key instruments for this approach. The extra revenue from applying them will, however, always go hand in hand with revenue cannibalization between different product versions. This poses the challenge of which versions/ products to offer to the company. In the economics and marketing science literature this trade-off between extra market coverage and lost revenue is traditionally referred to as a product line design problem. Prior contributions typically differ with respect to the customer segments considered and the number of versions. While the more applied articles [8], [9], [10] consider discrete product quality offerings for a discrete number of customer segments, [11] develop a model for continuous product qualities offered to a continuum of customers. Clearly the discrete cases separate into two distinct subproblems where either m = n or m > n. In the former each customer class gets its version while in the latter case some segments are pooled with corresponding firm profit losses.7 The challenge of designing cloud service portfolios gives rise to a similar problem. In the information systems and cloud service domain an increasing number contributions have considered price discrimination and product line design problems [12], [13], [14]. However, these typically follow the classic economic literature assuming a discrete number of customer segments. This does not resonate well with the vast heterogeneity of cloud service customers. Therefore, we characterize customer quality requirements as probability distributions thus creating a continuum of customers. This poses a new challenge to service providers — offering a finite number of products to an infinite number of customer types (see Table I). •
C. Modeling service quality In the product line design literature quality is typically assumed to be scalar, i.e. reflected by a single dimension. By design cloud service products are characterized by an 7 In the continuous case a similar problem can arise if customer willingness-to-pay is not monotone in quality.
Number of customer types
1
m≥n
Number of products n
∞
[8], [9], [10] standard profit maximization problem
∞
our focus
[11]
Table I OVERVIEW OF PRODUCT LINE DESIGN MODELS
inherent product complexity — after all, it is the possibility of being able to offer many differentiated versions that creates the attractiveness of cloud service markets. Hence, cloud service customer preferences are hardly captured by a single quality value but are rather driven by the combination of non-functional quality attributes. Typically, cloud service utility is modeled as linear multiattributive utility functions over non-functional quality attributes which yield a user’s willingness to pay for the product [6], [15], [16]. In this paper we suggest an alternative approach. We assert that customers formulate minimum level for the non-functional attributes and that product feasibility (functionality) is governed by meeting these requirements. This approach truncates some of the expressiveness of multi-attributive utility functions but allows to formulate the service portfolio problem in a tractable fashion. III. M ODEL In this section we present our generic economic framework based on customer self-selection to achieve profit maximization for a cloud service provider. We thereby deal with the question how service providers should design their offerings (quality and price) on a cloud service platform to maximize their profit. Offering more than one single version of the service (different quality-price-pairs) obviously leads to product cannibalization. First we describe the cloud service design including all attributes relevant for the optimization. We focus on formalizing the non-functional attributes of a ‘service product’ in our setting. Using this formalization we then describe and derive the market demand for a single service product based on a continuum of potential customers. Then we evaluate service portfolios offerings and characterize the effect of the resulting product cannibalization. Finally, we formulate the mathematical optimization problem
for finding the maximum profit service portfolio recognizing both product cannibalization and complexity costs. A. Service composition and design The service provider offers n ∈ N (functionally) substitutable service products xi , i ∈ I = {1, ..., n} defined by multiple quality attributes qij j ∈ J = {1, ..., m}, e.g.: response time, bandwidth, availability or security level. Let qi = (qi1 , ..., qim )T denote the vector representing all m ∈ N quality values of service xi . The qij are normalized to [0, 1] with 1 representing an ideal realization. Moreover, the provider quotes a price pi for each product. Maximizing the providers’ profit based on customer selfselection can then be reformulated as the problem to determine • • •
the number n ∈ N of different services xi (i ∈ I) the quality attributes qi of the n offered services xi (i ∈ I) the price pi of the n offered services xi (i ∈ I).
We assume that variable cost differences between two offered versions are negligible. Therefore, the problem of service portfolio design reduces to balancing extra revenue potential against the cost of complexity and product cannibalization. Hence, building a framework for optimally designing a service portfolio mainly depends on the magnitude of complexity costs of additional versions as well as the available data on customers’ expectations and preferences regarding quality and their willingness to pay. B. Demand characterization In our model framework a customer k’s demand is based on a feasibility set Fk which consists of all services that are functional to the customer. Membership of this feasibility set is governed by a vector of minimum quality values for each of the m different attributes q jk and n a maximum willingness o
to pay p¯k and it obtains Fk = xi | pi < p¯k , qi ≥ q k with q k = (q 1k , q 2k , · · · , q m )T being the vector representing k the minimum quality values of customer k. Hence, for a service to be functional the non-functional attributes must meet minimum requirements.8 1) Feasibility sets and individual rationality: To properly characterize customer behavior we need to specify it in a fashion that is fulfills individual rationality (IR). Propositon 1: For customer k it is IR to purchase a service xi ∈ Fk . Each service xi ∈ Fk fulfills the customer’s minimum level for all non-functional attributes and its price pi is below the maximum willingness to pay. Thus, the customer obtains strictly positive utility from purchasing this service which makes this purchase decision IR. 8 Remark:
We define that qi ≥ q k ⇔ qij ≥ q jk ∀j ∈ J.
2) Customer choice function: For the characterization of the customers’ choice behavior we need to recognize that the functional utility of all members of Fk is identical and the concrete realization of attribute levels is no longer decision-relevant, that is over-fulfillment of non-functional attribute requirements is not valuable to customers. Then, choosing the cheapest sufficient service is the unique utilitymaximizing decision of a customer. In our modeling framework the resulting bang-bang behavior of such fully rational customer choice decisions is somewhat undesirable. Moreover, the neo-classic assumption of fully rational customers has been disputed in more recent economics research focusing on bounded rationality [17], [18]. We circumvent this problem by applying a moderated customer choice function following the logit choice theory [19], [20]. In our context the only difference between products in Fk is product price. Hence, the choice function translates price differences into corresponding purchase probabilities. We obtain for each customer k the purchase probability of each service product xi as follows: P e−λpi−λp if xi ∈ Fk j j∈Fk e (1) Pk (xi ) = 0 otherwise In this formulation λ ∈ [0, ∞) describes the rationality of the decision maker: λ = 0 reflects irrational random choice with uniform choice probabilities over the feasible services while for λ → ∞ we approach a perfectly rational decision maker choosing the cheapest service product in Fk . C. Aggregate market demand As noted before we acknowledge that aggregated market demand is spanned by preferences over non-functional attributes and price sensitivity. Contrary to most existing approaches we do not try to cluster the continuum of potential customers into n discrete, distinct groups of customers (customer types) but rather deal with a continuum where the infinitesimal customers exhibit the choice behavior described before. 1) Single service case: Let f (q, p) denote the multidimensional probability density function describing the distribution of the threshold levels of the whole customer population.9 The set containing all potential customers is denoted by Ω with the total number of potential customers being given by |Ω|. Denoting the maximum willingness to pay by pmax demand Di for a single product xi can be expressed as Z pmax Z qi1 Z qim f (q, p)dq m · · · dq 1 dp · |Ω| . (2) Di = ··· pi
0
0
9 In this work we assume the threshold levels to be distributed independently. A relaxation of this assumption will be part of future research.
From Equation (2) we readily obtain the resulting monopolist revenue as Z pmax Z qi1 Z qim Πi = pi ··· f (q, p)dq m · · · dq 1 dp·|Ω| . (3) pi
0
Price
=
Attribute 1
0
Dik =
k X
Di,j
(4)
=
Attribute 2
Figure 1. Since it holds that p1 ≤ p2 ≤ . . . ≤ pn we only have to regard the case that the price pk+1 of product k + 1 is greater or equal that pk . The values of the attributes can either increase, decrease or stay constant.
this second product, that is demand/revenue of the second product treated as single product minus the cannibalized demand/revenue of product one. Using the minimum of the quality attributes of both products as upper integral bounds leads to a solution covering all imaginable cases depicted in Figure 1 (so far in the two product case). Therefore the demand for product two is D22 =
pmax
Z
q21
Z
q11
10 This
simplification eliminates ordering problems within the model’s demand structure. We could alternatively structure the problem as a product line expansion problem choosing the optimal extension product.
f (q, p)dq m · · · dq 1 dp · |Ω| (6)
q1m
and accordingly the revenue Π22 = p2 · D22 = Z Z pmax Z q21 ··· p2 · q11
p2
q2m
f (q, p)dq m · · · dq 1 dp · |Ω| . (7)
q1m
Obviously this formalization can be transfered easily to the n-product case (i ∈ {2, ..., n} – for i = 1 refer to Equations (2) and (3)): Z
pmax
Z
qi1
Z
qim
··· pi
(5)
That means we need to iterate over the demand regions of the k products to determine the fraction of the customer population that is attracted by products i. For the new product each of these attributes can increase, decrease or stay constant as depicted in Figure 1. For the readers’ convenience we first introduce the case of adding a second product. Depending on the different possibilities regarding the quality attributes (increase, decrease, stay constant) as depicted in Figure 1 we have to calculate the actual added demand (and revenue) of
q2m
Z ···
p2
Din = Di,j = Pj (xi ) · Dj .
=
Attribute m
j=1
where
= ...
Given negligible variable costs the maximization of Equation (3) with respect to pi and qi directly yields the optimal single product offering. As noted in section II this is equivalent to a standard monopolist revenue maximization problem. 2) Service portfolios and product cannibalization: In a product setting without variable costs quality differentiation serves as a means for price discrimination. That is, the service provider introduces additional versions to profitably attract additional customer segments. To maximize profits, the service provider needs to balance the gains from an additional version against its costs. However, given our demand characterization product cannibalization arises endogenously whenever an additional service product is offered and needs to be taken into account when optimizing service portfolio as wells. To understand the impact of product cannibalization we need to generalize Equation (2) to the multi-product case. We assume without loss of generality that p1 ≤ p2 ≤ . . . ≤ pn , that is product prices are increasing in version number. Going from n to n + 1 service products we need to evaluate the demand Din+1 for service n+1 based on the cannibalized and non-cannibalized demand of the other services offered, labeled 1 to n. Moreover, we assume that a higher version cannot be worse in any attribute level.10 Then, by combining Equations (1) and (2) demand for single product xi — the subscript denotes the product evaluated , the superscript the number of products in the service portfolio considered — within service portfolios obtains using the m non-functional attributes to partition the relevant demand choice regions:
1 qi−1
f (q, p)dq m · · · dq 1 dp·|Ω| (8)
m qi−1
and accordingly the revenue Πni = pi · Din = Z pmax Z qi1 Z pi · ··· pi
1 qi−1
qim
f (q, p)dq m · · · dq 1 dp · |Ω| . (9)
m qi−1
Hence, we are able to formulate the profit maximization program. IV. P ROFIT M AXIMIZATION Based on the above described multidimensional probability density function describing the distribution of the threshold levels of the whole customer population and the
formalisation of resulting demands and revenues, a service provider is able to maximize his profit. IR is implicitely part of the formalization due to Proposition 1 and has not to be added as constraints in the optimization program. Taking into account the costs for offering a product with quality qi , cproduct (qi ) and the complexity costs for offering n products ccompl (n), the resulting maximization program can be represented as
max q,p,n
n X
(Πni − cproduct (qi )) − ccompl (n)
(10)
i=1
subject to: 0 ≤ qij ≤ 1 ∀i, j
(11)
0 ≤ pi ≤ pmax ∀i
(12)
Since the maximizing character of our solution (cf. Equation (10)) obviously leads to the optimal solution from an analytic perspective we do not have to evaluate the framework regarding its results compared to other approaches. However, deeper insights into the actual realization of the optimization and its solution is regarded as future work. V. C ONCLUSION We developed a formal model for describing a cloud service providers product portfolio together with an appropriate, individually rational demand specification. Unlike prior work we specifically apply a multi-attributive quality representation to a quality discrimination model. Moreover, we do not assume a discrete customer population but rather represent a continuum of customers by means of probability distributions on minimum requirements on non-functional attributes. This allows us to represent the service demand as a continuum facilitating mathematical analysis and optimization procedures. Our model endogenously reflects the product cannibalization effect arising in portfolios of partially substitutable products and we are able to characterize the strategic service product line optimization problem. Opportunities for future research This article provides a theoretical framework for economic analysis of service product portfolios. On the modeling level we will have to address the question of characterizing appropriate probability distributions as well as characterize or approximate the optimal portfolio in a more concrete fashion. Similarly, relaxation of distributional independence requirements would allow us to obtain more general results. At the same time this framework is meant to serve as a base for future work in this domain. Potentially, the screening type self-selection setup could be extended by a signaling component. Moreover, a practical evaluation in the context of a case study may shed light on the real-world usefulness of the model.
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