3.1 PS channel design decisions

For modeling a PS channel, the key trade-offs in PS channel design decisions need discussion. A simple example helps illustrate the interconnectedness of the service and product design optimization problems. When a product is launched, the producer must determine its price, which can be approached with standard techniques (e.g., conjoint and a time-discounted or finite-horizon profit model). For PS channels, the product price setting must consider the demand for associated services, in addition to what might happen if a lower initial product price spurs demand not only for the producer’s own services, but also for the competitors’ services that can be accessed through its device. If the channel is exclusive (the producer’s customers can only access its services on its devices), the lower product price may translate into greater demand for costly services down the road – the inspiration behind the saying ‘give away the razors and get them on the blades’ (Anderson Reference Anderson2009). In a non-exclusive channel, one might give away the razors and see a competitors’ sales surge for the blades, in effect, leading to a double loss. Yet the seemingly simple solution of ensuring no competitor’s services are available makes the core product less versatile, and therefore placed at a disadvantage to more open platforms, a situation reminiscent of the early debates between the Apple (closed) and Microsoft (open) Operating System development platforms. This additional source of consumer freedom in the PS channel renders PS choice and demand far more complex to model. Since the particular PS channel availability is a shared decision variable, firms need to understand how the PS channel decisions affect not only their own service and product demand levels, but also those of competitors’ shared channels.

The PS channel design problem is well exemplified by eBook service and tablet designs, the specific application examined later in this article. For example, Kindle/Amazon Books (Amazon), Nook/B&N (Barnes & Noble), iPad/iBook (Apple), and Nexus/Google Play (Google), supply both eBook services, and associated core tablet products. Assuming that all PS channels were exclusive, Kindle users could avail only Amazon eBooks, and Amazon can supply eBooks only to Kindle users; iPad users are limited to iBook; and iBook can supply iPad users alone. Yet in reality, PS channels are non-exclusive and, importantly, asymmetric: at the time of data collection (see Section 4.1), a Kindle user is limited exclusively to the Amazon eBook market, as Amazon’s App Store lacks an iBook app; yet Amazon supplies eBook services not only to Kindle, but also the iPad (via the Kindle app in Apple’s App store). That is, iPad users can use not only iBooks but also Amazon eBooks, but iBooks supplies eBook services to only the iPad users (Bläsi & Rothlauf Reference Bläsi and Rothlauf2013; Ritala, Golnam & Wegmann Reference Ritala, Golnam and Wegmann2014).

3.2 Market setting

This section details the market setting for the integrated PS business model addressed in this study. Figure 1 depicts several representative PS channel structures involving two producers. Service choice examples are also shown according to their PS channel structures.

Figure 1. Examples of market settings.

The key properties of the types of systems depicted in Figure 1:

1. (1) A producer supplies a service and product together. Producer $A$ supplies product $p_{A}$ and associated service $\mathbf{s}_{A}$ ; producer $B$ supplies product $p_{B}$ and associated service $\mathbf{s}_{B}$ .

2. (2) A service consists of multiple subservices, e.g., $\mathbf{s}_{A}$ includes $\{s_{Ai}\}=\{s_{A1},s_{A2},s_{A3},s_{A4}\}$ , while $\mathbf{s}_{B}$ includes $\{s_{Bi}\}=\{s_{B1},s_{B2},s_{B3},s_{B4}\}$ . [For example, these could be items in a web store, such as a particular book or app, as long as they are potentially purchasable from different providers.]

3. (3) Subservices can be unique to a particular provider or similar across providers. In the case of similar services, pairs such as, $(s_{A1},s_{B1}),(s_{A2},s_{B2})$ , $(s_{A3},s_{B3}),(s_{A4},s_{B4})$ may have different prices and qualities while providing functionally equivalent benefits to the user. [Given any set of subservices from A and B – partly overlapping or not – one can always conjoin them to create a key list with matched indices, and this will be done later.]

4. (4) Because the products are presumed to provide similar core benefits, each customer who buys a product, chooses exactly one, either $p_{A}$ or $p_{B}$ ; customers may elect to choose the ‘outside good’ (i.e., no product at all, that is, waiting), but not more than one. [This will be explicitly incorporated in the forthcoming conjoint simulation.] S/he then chooses a service – either $s_{Ai}$ or $s_{Bi}$ . Elected services correspond to a subset of all available services.

5. (5) There are three cases, in general, for two producers:

   1. (i) Case 1, exclusive channels: $p_{A}$ users can use subservices from only $\mathbf{s}_{A}$ ; $p_{B}$ users can use subservices from only $\mathbf{s}_{B}$ .

   2. (ii) Case 2, non-exclusive and asymmetric channels: $p_{A}$ users can use subservices from only $\mathbf{s}_{A}$ ; but $p_{B}$ users can use subservices from both $\mathbf{s}_{A}$ and $\mathbf{s}_{B}$ , so that $p_{B}$ users can choose some subservices from pairs such as $(s_{A1},s_{B1})$ , $(s_{A2},s_{B2})$ , $(s_{A3},s_{B3})$ , $(s_{A4},s_{B4})$ . For example, $p_{B}$ users can choose $\{s_{B1},s_{A2},s_{B3}\}$ , that is, two items from their own product manufacturer, $B$ , and one from $A$ .

   3. (iii) Case 3, non-exclusive and symmetric channels: regardless of product choice, customers can choose any subservices.

6. (6) Adding a channel requires acceptance from competitors, whereas removing a channel can be decided by only one partner (unless contractually disallowed). For example, when producer $A$ wants to add a channel between $p_{A}$ and $\mathbf{s}_{B}$ , or a channel between $\mathbf{s}_{A}$ and $p_{B}$ , acceptance by producer $B$ is required.

The assumption is that a customer chooses a product based on product price, product attributes, and the PS channel; and chooses a service based on service price and attributes. Taking the example of the tablet and eBook service market, $p_{A}$ and $\mathbf{s}_{A}$ can be the Kindle and Amazon market, respectively; $p_{B}$ and $\mathbf{s}_{B}$ can be the iPad and iBooks markets, respectively. That is, $\{s_{A1},s_{A2},s_{A3},\ldots ,s_{AM}\}$ are eBooks in the Amazon market and $\{s_{B1},s_{B2},s_{B3},\ldots ,s_{BM}\}$ are eBooks in the iBooks market. In practice, $M$ , the number of total potential books, can number in millions. Note that $s_{At}$ and $s_{Bt}$ are the same book, where $t=1,2,3,\ldots ,M$ , and can either take on a value of 1, if the book is available, or 0 if it is not. In the service and product market, the book price and shopping methods can be different. Each customer can purchase a different number of eBooks for a different period of product ownership.

3.3 Demand and profit modeling under the PS channel

Services and products are modeled based on the market set-up described above, with a demand model that can be modified for different market settings. This study adopts the latent (to the researcher) consumer utility concept underlying random-utility-based discrete choice models (Green & Krieger Reference Green and Krieger1996), which have come to dominate both theoretical and applied work in the marketing field, as has the Hierarchical Bayes (HB) choice-based conjoint (Rossi & Allenby Reference Rossi and Allenby2003; Gustafsson, Herrmann & Huber Reference Gustafsson, Herrmann and Huber2013) for estimating heterogeneous customer preferences (often referred to as ‘part-worths’ for discrete or discretized attributes).

Product demand modeling follows recent design research using the HB approach (e.g., Michalek et al. Reference Michalek, Ebbes, Adigüzel, Feinberg and Papalambros2011), which itself builds upon decades of research in preference elicitation and measurement (see, for additional detail, Green et al. (Reference Green, Krieger and Wind2001) or Gustafsson et al. (Reference Gustafsson, Herrmann and Huber2013)). The basic process can be summarized as follows: (i) Data are gathered using a choice-based conjoint task; (ii) HB choice model parameters (i.e., individual-level part-worths) for the preference function are estimated; (iii) splines interpolate across (discrete) part-worths, enabling efficient optimization over a continuous design space; (iv) market demand is predicted, based on choice probabilities and potential market size.

The individual-level discrete utility, $v_{ip_{j}}$ , of individual $i$ and product $p_{j}$ takes the usual form with respect to discrete attributes levels, as

(1) $$\begin{eqnarray}\displaystyle v_{ip_{j}}=\mathop{\sum }_{k=1}^{K}\mathop{\sum }_{l=1}^{L_{k}}\unicode[STIX]{x1D6FD}_{ikl}z_{jkl}, & & \displaystyle\end{eqnarray}$$

where $z_{jkl}$ are binary dummy variables indicating if alternative product $j$ possesses attribute $k$ at level $l$ ; $z_{jkl}$ represent product price, product attributes, and service compatibility; $\unicode[STIX]{x1D6FD}_{ikl}$ are the part-worth coefficients of attribute $k$ at level $l$ for individual $i$ .

Service compatibility is determined by the structure of the PS channel decisions made by producers. For example, in Figure 1, there are four PS channel decision variables: potential linkages between $p_{A}$ & $\mathbf{s}_{A}$ , $p_{A}$ & $\mathbf{s}_{B}$ , $p_{B}$ & $\mathbf{s}_{A}$ , and/or $p_{B}$ & $\mathbf{s}_{B}$ . Channel decision variables are binary: 1 indicates that a channel is connected (as depicted by lines in Figure 1), while 0 indicates that it is not. Note that $p_{A}$ & $\mathbf{s}_{A}$ , and $p_{B}$ & $\mathbf{s}_{B}$ should always be connected, since producers will by necessity make their services available using their own product platforms. In this case, customers can avail three levels of service compatibility: $\mathbf{s}_{A},\mathbf{s}_{B}$ , and $(\mathbf{s}_{A},\mathbf{s}_{B})$ , according to their product choice. In our forthcoming empirical example, there will be four producers, and therefore $2^{4}-1=15$ levels of service compatibility, as shown later in Table 2.

The HB choice model estimates the conjoint part-worths via a two-level process. At the ‘upper level,’ we assume individuals’ part-worths, $\boldsymbol{\unicode[STIX]{x1D6FD}}_{i}$ , follow a multivariate normal distribution, $\boldsymbol{\unicode[STIX]{x1D6FD}}_{i}\sim N(\boldsymbol{\unicode[STIX]{x1D703}},\boldsymbol{\unicode[STIX]{x1D6EC}})$ , where $\boldsymbol{\unicode[STIX]{x1D703}}$ indicates a vector of mean individual preference and $\boldsymbol{\unicode[STIX]{x1D6EC}}$ is their covariance matrix; that is, the former ( $\boldsymbol{\unicode[STIX]{x1D703}}$ ) suggests what a ‘typical’ consumer would like, whereas the latter suggests how much variability there is in consumer preference (diagonal elements of $\boldsymbol{\unicode[STIX]{x1D6EC}}$ ), as well as how preferences for one attribute help predict those for a different attribute (off-diagonal elements of $\boldsymbol{\unicode[STIX]{x1D6EC}}$ ). At the ‘lower level,’ choice probabilities have a logit form, which is particularly amenable to gradient and elasticity computation:

(2) $$\begin{eqnarray}\displaystyle Pr_{i}(p_{j})=\exp (v_{ip_{j}})/\mathop{\sum }_{j^{\prime }\in \mathbf{J}}\exp (v_{ip_{j^{\prime }}}), & & \displaystyle\end{eqnarray}$$

where $Pr_{i}(p_{j})$ is the probability that individual $i$ chooses product option $p_{j}$ from a set of product alternatives $\mathbf{J}$ .

Product demand can be calculated, for various market scenarios, based on heterogeneous customer preference models. Either the total or average demand across participants can be used for optimization (as these contain identical information); the latter is given by:

(3) $$\begin{eqnarray}\displaystyle q_{p_{j}}=\frac{1}{I}\mathop{\sum }_{i=1}^{I}\unicode[STIX]{x1D707}Pr_{i}(p_{j}), & & \displaystyle\end{eqnarray}$$

where $q_{p_{j}}$ is the product demand of product option $p_{j},\unicode[STIX]{x1D707}$ indicates the potential product market size (i.e., number of users), and $I$ indicates the total number of participants.

Next, service demand is calculated via conditional probability, given product choice and demand. A choice-based conjoint survey can be conducted (as described previously) to gather service preference data; the estimation of service attributes part-worths proceeds analogously to that of products. Note, however, that the setting is somewhat more complex, due to the following reasons: (1) service alternative options depend on product choice; (2) services consist of subservices; and (3) service choices occur on multiple occasions.

The individual-level discrete utility, $v_{is_{h_{t}}}$ , of individual $i$ and service $s_{h_{t}}$ , can be expressed in linear form with respect to discrete attribute levels as

(4) $$\begin{eqnarray}\displaystyle v_{is_{h_{t}}}=\mathop{\sum }_{m=1}^{M}\mathop{\sum }_{n=1}^{N_{m}}\unicode[STIX]{x1D6FD}_{imn}z_{h_{t}mn}, & & \displaystyle\end{eqnarray}$$

where $h$ is a service platform, $t$ indicates subservice, $z_{h_{t}mn}$ are binary dummy variables representing service price, and attributes $m$ at level $n$ , and $\unicode[STIX]{x1D6FD}_{imn}$ are the part-worth coefficients of service attribute $m$ at level $n$ for individual $i$ . Using the HB choice model, $\unicode[STIX]{x1D6FD}_{imn}$ are estimated, and then service choice probabilities can be calculated using the logit-based expression

(5) $$\begin{eqnarray}\displaystyle Pr_{i}(s_{h_{t}}|p_{j})=\frac{\exp (v_{is_{h_{t}}})}{\mathop{\sum }_{h^{\prime }\in \mathbf{H}_{p_{j}}}\exp (v_{is_{h_{t}^{\prime }}})}, & & \displaystyle\end{eqnarray}$$

where $Pr_{i}(s_{h_{t}}|p_{j})$ is the conditional probability that individual $i$ , after choosing product $p_{j}$ , will then choose service option $s_{h_{t}}$ from the set of service alternatives $\mathbf{H}_{p_{j}}$ of product $p_{j}$ . The service alternatives available to a consumer who has selected a particular product are dictated by the PS channel decision made by its producer. Equations (4) and (5) represent, for simplicity of exposition, single choices of subservices (e.g., one eBook choice). Service demand can be calculated by summing all subservice choices over all products during the product’s life cycle.

As before, the averaged (across consumers) demand value is used for profit optimization:

(6) $$\begin{eqnarray}\displaystyle q_{\mathbf{s}_{h}}=\frac{1}{I}\mathop{\sum }_{i=1}^{I}\mathop{\sum }_{t\in \mathbf{T}_{i}}\mathop{\sum }_{j^{\prime }\in \mathbf{J}}\unicode[STIX]{x1D707}Pr_{i}(p_{j^{\prime }})Pr_{i}(s_{h_{t}}|p_{j^{\prime }}), & & \displaystyle\end{eqnarray}$$

where $q_{\mathbf{s}_{h}}$ is service demand of service option $\mathbf{s}_{h}$ , $\unicode[STIX]{x1D707}$ indicates the potential product market size, $Pr_{i}(p_{j^{\prime }})$ is choice probability of product $p_{j^{\prime }}$ , $Pr_{i}(s_{h_{t}}|p_{j^{\prime }})$ is conditional probability of service $s_{h_{t}}$ given $p_{j^{\prime }}$ , $\mathbf{J}$ is a set of product alternatives, $\mathbf{T}_{i}$ is a set of service choices of individual $i$ , and $I$ indicates total number of individuals. The set $\mathbf{T}_{i}$ is can be determined by foreknowledge, an additional survey, or inferred from market statistics (e.g., eBook purchase history).

To illustrate, Equations (1) to (6) are applied to Case 2, that is, a non-exclusive and asymmetric channel (as in Figure 1), for two products, $A$ and $B$ :

(7) $$\begin{eqnarray}\displaystyle & \displaystyle q_{p_{A}}=\frac{1}{I}\mathop{\sum }_{i=1}^{I}\unicode[STIX]{x1D707}\left[\frac{\exp (v_{ip_{A}})}{\exp (v_{ip_{A}})+\exp (v_{ip_{B}})+\exp (v_{ip_{0}})}\right] & \displaystyle\end{eqnarray}$$

(8) $$\begin{eqnarray}\displaystyle & \displaystyle q_{p_{B}}=\frac{1}{I}\mathop{\sum }_{i=1}^{I}\unicode[STIX]{x1D707}\left[\frac{\exp (v_{ip_{B}})}{\exp (v_{ip_{A}})+\exp (v_{ip_{B}})+\exp (v_{ip_{0}})}\right] & \displaystyle\end{eqnarray}$$

(9) $$\begin{eqnarray}\displaystyle q_{\mathbf{s}_{A}} & = & \displaystyle \frac{1}{I}\mathop{\sum }_{i=1}^{I}\quad \mathop{\sum }_{t\in \mathbf{T}_{i}}\left[\unicode[STIX]{x1D707}\left[\frac{\exp (v_{ip_{A}})}{\exp (v_{ip_{A}})+\exp (v_{ip_{B}})+\exp (v_{ip_{0}})}\right]\right.\nonumber\\ \displaystyle & & \displaystyle \times \left[\frac{\exp (v_{is_{A_{t}}})}{\exp (v_{is_{A_{t}}})+\exp (v_{is_{0}})}\right]\nonumber\\ \displaystyle & & \displaystyle +\,\unicode[STIX]{x1D707}\left[\frac{\exp (v_{ip_{B}})}{\exp (v_{ip_{A}})+\exp (v_{ip_{B}})+\exp (v_{ip_{0}})}\right]\nonumber\\ \displaystyle & & \displaystyle \times \left.\left[\frac{\exp (v_{is_{A_{t}}})}{\exp (v_{is_{A_{t}}})+\exp (v_{is_{B_{t}}})+\exp (v_{is_{0}})}\right]\right]\end{eqnarray}$$

(10) $$\begin{eqnarray}\displaystyle q_{\mathbf{s}_{B}} & = & \displaystyle \frac{1}{I}\mathop{\sum }_{i=1}^{I}\mathop{\sum }_{t\in \mathbf{T}_{i}}\left[\unicode[STIX]{x1D707}\left[\frac{\exp (v_{ip_{B}})}{\exp (v_{ip_{A}})+\exp (v_{ip_{B}})+\exp (v_{ip_{0}})}\right]\right.\nonumber\\ \displaystyle & & \displaystyle \times \left.\left[\frac{\exp (v_{is_{B_{t}}})}{\exp (v_{is_{B_{t}}})+\exp (v_{is_{0}})}\right]\right].\end{eqnarray}$$

Here, $q_{p_{A}}$ and $q_{p_{B}}$ are product demands of producers $A$ and $B$ , respectively, $q_{\mathbf{s}_{A}}$ and $q_{\mathbf{s}_{B}}$ are analogous service demands, and ‘0’ indicates that the customer ‘chooses the no-choice option,’ that is, refrains from choosing entirely. Note that Eq. (9) has one term more than Eq. (10) because service $\mathbf{s}_{A}$ can be used by both $p_{A}$ and $p_{B}$ .

Based on this demand model, the product profit and service profit are calculated as

(11) $$\begin{eqnarray}\displaystyle & \displaystyle \unicode[STIX]{x1D6F1}_{p_{j}}=q_{p_{j}}(P_{p_{j}}-C_{p_{j}}), & \displaystyle\end{eqnarray}$$

(12) $$\begin{eqnarray}\displaystyle & \displaystyle \unicode[STIX]{x1D6F1}_{\mathbf{s}_{h}}=\frac{1}{I}\mathop{\sum }_{i=1}^{I}\mathop{\sum }_{t\in \mathbf{T}_{i}}\mathop{\sum }_{j^{\prime }\in \mathbf{J}}\unicode[STIX]{x1D707}Pr_{i}(p_{j^{\prime }})Pr_{i}(s_{h_{t}}|p_{j^{\prime }})(P_{s_{h_{t}}}-C_{s_{h_{t}}}\!), & \displaystyle\end{eqnarray}$$

where $\unicode[STIX]{x1D6F1}_{p_{j}}$ is the profit of product $p_{j}$ , $q_{p_{j}}$ is product demand, $P_{p_{j}}$ is product price, $C_{p_{j}}$ is product cost, $\unicode[STIX]{x1D6F1}_{\mathbf{s}_{h}}$ is the profit of service $\mathbf{s}_{h}$ , $P_{s_{h_{t}}}$ is price of service $s_{h_{t}}$ , $C_{s_{h_{t}}}$ is cost of service $s_{h_{t}}$ , and other symbols retain their definitions from Eq. (6). Our goal is to optimize the sum of the service and product profits.

3.4 Product–service design framework

Based on the demand system above, a framework to optimize profits for PS design is proposed and depicted schematically in Figure 2. Following a predetermined order, one firm is selected as the focal firm among producers who optimizes its profit. Then, the next producer is selected as the focal firm who maximizes profit, while the previous focal firm becomes one of its competitors. This sequential optimization proceeds until the optimization result converges to the equilibrium.

Figure 2. Profit maximization framework for PS design.

Before optimization, the current PS channel structure and competitors’ service and product prices/attributes are set. Decision variables are the PS channel structure, product price, product attributes, service prices, and service attributes. Note that the product attributes and service attributes for optimization are selected by the designer. This selection is beyond the scope of the research reported here and it is challenging in its own right.

These variables are set for the competitor, then optimized for the focal firm. Note that all decision variables are optimized at the same time and a producer can access all other previous decisions during its turn. This framework is used for the design of a single product and multiple services for each producer. (Extension to product family or line design would require a straightforward modification of the present optimization framework with a concomitantly higher-order dimensional optimization; see Michalek et al. (Reference Michalek, Ebbes, Adigüzel, Feinberg and Papalambros2011) for additional details.)

The optimization problem for the focal firm, in each iteration, is stated as follows:

(13) $$\begin{eqnarray}\displaystyle \max _{\mathbf{x}_{p_{j}},\mathbf{x}_{\mathbf{s}_{h}},\mathbf{c}\mathbf{h}_{\!jh}}\unicode[STIX]{x1D6F1}_{p_{j}}+\unicode[STIX]{x1D6F1}_{\mathbf{s}_{h}} & & \displaystyle\end{eqnarray}$$

with respect to

(14) $$\begin{eqnarray}\displaystyle & \displaystyle \mathbf{x}_{p_{j}}=[p_{p_{j}},\mathbf{a}_{p_{j}}\!] & \displaystyle\end{eqnarray}$$

(15) $$\begin{eqnarray}\displaystyle & \displaystyle \mathbf{x}_{\mathbf{s}_{h}}=[\mathbf{p}_{\mathbf{s}_{h}},\mathbf{a}_{\mathbf{s}_{h}}] & \displaystyle\end{eqnarray}$$

(16) $$\begin{eqnarray}\displaystyle & \displaystyle \mathbf{c}\mathbf{h}_{\!jh}=[ch_{\!jh_{1}},ch_{\!jh_{2}},\ldots ,ch_{\!jh_{2n-2}}],\mathit{c}\mathit{h}_{\!jh}\in \{0,1\}. & \displaystyle\end{eqnarray}$$

subject to

(17) $$\begin{eqnarray}\displaystyle & \displaystyle lb\leqslant [\mathbf{x}_{p_{j}},\mathbf{x}_{\mathbf{s}_{h}}]\leqslant ub & \displaystyle\end{eqnarray}$$

(18) $$\begin{eqnarray}\displaystyle & \displaystyle \mathbf{g}_{ch}(\mathbf{x}_{p_{j}},\mathbf{x}_{\mathbf{s}_{h}},\mathbf{c}\mathbf{h}_{\!jh},\boldsymbol{\unicode[STIX]{x1D6F1}}_{p_{j^{\prime }\in \mathbf{J}}},\boldsymbol{\unicode[STIX]{x1D6F1}}_{\mathbf{s}_{h^{\prime }\in \mathbf{H}}})\leqslant 0. & \displaystyle\end{eqnarray}$$

The objective of Eq. (13) is to maximize the overall profit which is the sum of the product profit $\unicode[STIX]{x1D6F1}_{p_{j}}$ , of product $p_{j}$ , and the service profit $\unicode[STIX]{x1D6F1}_{\mathbf{s}_{j}}$ of service $\mathbf{s}_{h}$ . As introduced in Section 3.3, the product demand is calculated based on product price, product attributes, and service compatibility as per Eqs. (1) to (3). Using individuals’ potential services sets, service demand is calculated based on service prices, service attributes, the PS channel, and product demand, using Eqs. (4) to (6). Product and service profits are calculated using price, cost, and demand for services and products, using Eqs. (11) and (12).

In Eq. (14), $\mathbf{x}_{p_{j}}$ is the vector of product design variables, where $p_{p_{j}}$ is the product price and $\mathbf{a}_{p_{j}}$ is the vector of product attributes. In Eq. (15), $\mathbf{x}_{\mathbf{s}_{h}}$ is the vector of service design variables, where $\mathbf{p}_{\mathbf{s}_{h}}$ is the vector of service prices and $\mathbf{a}_{\mathbf{s}_{h}}$ is the vector of service attributes. In Eq. (16), $\mathbf{c}\mathbf{h}_{\!jh}$ is the vector of channel design variables.

As discussed earlier, the PS channel is a binary design variable. So, if a channel links a product and a service platform, its value is 1, otherwise, 0. When there are $n$ producers in the market, the PS channel can be described as an $n\times n$ matrix, as shown in Table 1. Optimization amounts to a producer’s choosing values from within this matrix for its service and product options; note that diagonal values are 1 because services and products from the same manufacturer are always connected. Therefore, the number of channel design variables for the focal firm is $2\times (n-1)$ , where the firm decides whether to supply its product to ( $n-1$ ) competitors’ service platforms and whether to supply its service platform to ( $n-1$ ) competitors’ products. Eq. (17) shows bound constraints on the product and service design variables, and Eq. (18) shows inequality constraints for PS channels acceptance. $\unicode[STIX]{x1D6F1}_{p_{j^{\prime }\in \mathbf{J}}}$ and $\unicode[STIX]{x1D6F1}_{\mathbf{s}_{h^{\prime }\in \mathbf{H}}}$ indicate product profits and service profits of competitors, respectively.

Table 1. Market setting for eBook / tablet applications

a Prices and figures in parentheses refer to the average prices and standard deviations, respectively, across 20 bestseller books.

A notable feature of the proposed framework is that it uses a competitor’s profit change as a constraint: when a given producer wants to add channels with a competitor’s product or service, if its design decision affects the competitor’s profit positively, it is taken to be a feasible design decision; otherwise, it is not. In other words, a producer can only reasonably propose channels to a competitor that will enhance that competitor’s profit. However, when more than three producers make decisions sequentially, some channels can oscillate between two producers by repeatedly adding and deleting. In our research, it is assumed that adding oscillated channels is not permitted after all other channels have converged. Deleting an oscillated channel has priority over adding one. For feasibility constraints (e.g., whether a product’s components can fit in its case), engineering and operations simulation models (Kang, Feinberg & Papalambros Reference Kang, Feinberg and Papalambros2015, Reference Kang, Feinberg and Papalambros2017) that consider uncertainties (Kang, Bayrak & Papalambros Reference Kang, Bayrak and Papalambros2018; Lee, Kang & Lee Reference Lee, Kang and Lee2019) can be applied.

The optimization proceeds iteratively across producers. After maximizing the overall profit of a focal producer, other competitors optimize their profit using the same process that the ‘optimized’ producer followed. These sequential optimizations proceed until no players (producers) can find a better design (i.e., one that increases profit). This results in a Nash equilibrium, a ‘solution concept’ widely deployed in marketing and engineering design research (Luo et al. Reference Luo, Kannan and Ratchford2007; Shiau & Michalek Reference Shiau and Michalek2009b ; Kang et al. Reference Kang, Ren, Feinberg and Papalambros2016). Here during the initial iteration, it is assumed that producers decide on all decision variables; for subsequent iterations, they decide only on product/service prices and channels. In other words, because product design decisions are slow and costly to alter, it is presumed that producers first decide product attributes, and then engage in (iterative, sequential) optimization for prices and channels for both services and products.

4.1 Market setting

The proposed framework is demonstrated via tablet (product) and eBook (service) designs. Because the main purpose of this study is illustrative, market assumptions are deliberately generic, transparent, and simple, as follows. First, four main producers are selected, each of which operates in both the tablet and eBook markets: (1) Kindle/Amazon Kindle books, (2) Nook/Barnes & Noble (B&N), (3) iPad/iBooks, and (4) Nexus/Google Play books. The study focuses on single product designs (as opposed to product family designs), and therefore assumes that each producer optimizes for a single ‘flagship’ tablet with full-color display. For eBook services, price distributions across the four eBook markets are based on the real observed prices of 20 bestseller eBooks in each market available from a verified, published source (Gilbert Reference Gilbert2012); the PS channel structure is based on the market situation at the time price data collection. In addition, the assumption is that when a customer shops for an eBook from her or his tablet’s producer, she or he does so via an in-tablet app but uses a web-based interface for eBooks from other competitors (Bläsi & Rothlauf Reference Bläsi and Rothlauf2013; Ritala et al. Reference Ritala, Golnam and Wegmann2014).

Table 1 summarizes the market setting for the study, with four flagship tablets and four eBook markets. The eBook prices shown are averages of 20 bestsellers. For example, Amazon’s price of $9.78 compares favorably with those for B&N ($9.98), iBooks ($10.41), and Google Play ($10.14). The binary indicators listed in Table 1 indicate whether a channel exists between tablet and eBook markets. Note, for example, that the PS channel is asymmetric: iPad users can access all four eBook services (Row 3 of 4), while iBooks does not supply eBook services to competitors (Column 3 of 4).

4.2 Demand modeling

Two choice-based conjoint surveys were conducted, for the tablet and eBook, sequentially. 152 respondents in the United States (US) were surveyed using Amazon’s Mechanical Turk (Amazon 2012a ) in conjunction with Sawtooth Software’s CBC (Choice-Based Conjoint) Hierarchical Bayes Module (Orme Reference Orme2013); this sample size is comparable to those used in prior studies in the area (e.g., Michalek et al. Reference Michalek, Feinberg and Papalambros2005, with $n=184$ ). Respondent demographics were broadly consistent with the US in general: 41% male, 59% female; 20% were 15–24 years of age, 49% 25–34, 16% 35–44, and 15% older than 45; 72% and 58% of the respondents reported tablet and eBook use experiences, respectively. Analogous figures for the US (Census 2012; Pew Research 2013) are: tablet users are 47% male and 53% female; 18% are 15–24 years of age, 19% 25–34, 24% 35–44, and 40% are over 45. These deviations between sample and population demographics are non-significant.

For the tablet choice-based conjoint survey, five attributes – compatible eBooks, tablet brands, price, display size, and storage – were included, as shown in Table 2. Respondents were asked to suppose that they were considering purchasing a tablet, with the specific objective that they could read eBooks, and that their tablet choices would determine which of the multiple compatible eBook services would be available to them. The survey began with an ‘education’ page that ensured participants understood the nature of the eBook/tablet format, co-branding, and other key elements of the market system; for example, when the tablet brand is Kindle HD, the compatible eBook options always included Amazon (i.e., ones along the diagonal in Table 1). As is typical, each choice set included a small number (in this case, three) of tablet profiles along with a ‘none’ option (that is, the ‘no-choice option’ in which the customer chooses none of the PS options).

Table 2. Part-worths for tablet attribute levels

Previous respondents from the tablet survey were surveyed again. They were told to suppose that they had bought a tablet, and then wanted to purchase an eBook. For the eBook choice-based conjoint survey, three attributes of known importance were included – eBook market, eBook price, and ease of shopping – and shown in Table 3. Subjects were told that the prices for the same book can vary across markets. As mentioned earlier, customers can buy a book from their tablet producer’s market via an in-tablet app, or from another seller using a web-based store. This reflects the reality that using your tablet brand’s eBook market is simply more convenient than buying from a competitor. As in the tablet conjoint, each choice set included three eBook profiles, and the option of choosing ‘none.’

Table 3. Part-worths for eBook attribute levels

a When tablet and eBook market are from the same producer, eBooks can be purchased using an in-tablet app.

Using HB estimation (as per Section 3.2), individual preference functions were quantified for each of the 152 respondents. Markov Chain Monte Carlo (MCMC) draws were ‘thinned’ to every tenth; the burn-in was 50,000 (these were discarded); and the inference proceeds from the final 50,000 draws, which were used to obtain preference part-worths. Tables 2 and 3 list estimated part-worths for each level, and the average relative importance for each attribute. Cubic spline interpolation allows the estimation of continuous preference functions from the discrete part-worths used in the study (see Michalek et al. Reference Michalek, Ebbes, Adigüzel, Feinberg and Papalambros2011). Lastly, the profit values are calculated using the means of the market response distribution based on the preference parameters of these 152 customers.

The conjoint survey was supplemented by follow-up questions aimed at assessing eventual service demand, e.g., ‘Suppose you buy a new tablet now. How long do you intend to use it?’ and ‘Suppose you use the eBook service, how often are you likely to purchase eBooks?’ The mean and standard deviation of the period of product ownership were 4.4 years and 2.7 years, respectively; analogous values for the frequency of eBook purchase were 19.2 and 15.8 books per year, respectively. These data were used in calculating individual-level service demand.Footnote ¹ Recall that the price data of 20 eBooks were used (Gilbert Reference Gilbert2012), some of which were the same across the four markets, while others differed. Average prices were used for optimization purposes.

Since tablets are multi-purpose products, estimating the market ‘share’ and size for tablets among eBook users is challenging. Summary statistics can provide benchmarks: 457 million eBooks were sold in 2012 (Wilson Reference Wilson2014), 25% of the eBooks are read on tablets (BWMBooks 2012), and the average number of eBooks read (among those who read electronically) is 24 books per year (Rainie Reference Rainie, Zickuhr, Purcell, Madden and Brenner2012). Based on this data, a rough estimate of the projected tablet demand used for eReading is 4.76M (i.e., $457\text{M}\times 25\%/24$ ). Because this is an input figure that ‘scales linearly’ within the model, improved estimates of the market size can be easily included in the methodology.

4.3 Cost and optimization modeling

To put our method to use, producers must build their own costing models. To this end, prior studies of tablet cost modeling are adapted (Wang, Kannan & Azarm Reference Wang, Kannan and Azarm2011) focusing on display and memory storage costs:

(19) $$\begin{eqnarray}\displaystyle & \displaystyle C_{d_{j}}=C_{d_{0}}q_{d_{j}}^{b_{1}}z_{d_{j}}^{b_{2}} & \displaystyle\end{eqnarray}$$

(20) $$\begin{eqnarray}\displaystyle & \displaystyle C_{m_{j}}=C_{m_{0}}z_{m_{j}} & \displaystyle\end{eqnarray}$$

where $C_{d_{j}}$ is the cost of LCD display $j$ , $C_{d_{0}}$ is $50 (of variable cost, used as a basis value), $q_{d_{j}}$ is overall demand for displays, $z_{d_{j}}$ is display size in inches, $b_{1}$ and $b_{2}$ are parameters (estimated in prior work at $-$ 0.1032 and 0.7965, respectively), $C_{m_{j}}$ is cost of flash memory $j$ , $C_{m_{0}}$ is $4 (of variable cost), and $z_{m_{j}}$ is memory size in Gigabytes (GB); any of these values can be updated as newer information becomes available. Display costs follow economies of scale, although here other costs are considered to be constant with respect to demand/production, including costs for batteries, integrated circuits, and ‘miscellaneous,’ which are assumed to be $115 in total (as per Wang et al. Reference Wang, Kannan and Azarm2011). EBook prices can themselves be broken down into margins, royalty fees, taxes, and delivery costs. Since royalty fees make up the majority of an eBook’s price (Amazon 2012b ), only the royalty fee is considered as the cost of eBook service provision, and the iBooks’ royalty rate, 70% is used (Mill City Press 2012).

4.3.1 Decision variables and optimization

Figure 2 is referred to again for an overview of the nature of the decision space and overall optimization strategy. Optimization can be achieved in various ways, and the general procedure is agnostic, to what is used. However, the procedure described below has the virtue of scaling well in the number of PS-producing firms. At its center, is an iterative process that checks whether equilibrium conditions are met at every pass. In broad schematic, at every pass, each of the four producers must enact two types of Yes/No decisions: (1) on each of the services for the other three producers (they must always offer their own service); and (2) on whether to offer its service on the other three platforms. This entails eight options which enable other services to be allowed on its product, and eight options which enable products to carry the producer’s own services. These total 64, in all. To choose among these 64 options – each of which requires that all other design elements are optimized – each of the four producers optimizes (as detailed subsequently). After all the four producers have done this, equilibrium conditions are checked; if they are not met, iteration continues. [As mentioned above, it is also possible to perform a one-shot optimization for all $(64)^{4}=16777216$ ensuing possibilities, but this number grows exponentially in the number of producers – with $k$ producers, there $2^{2k(k-1)}$ possibilities – and is prone to local maxima.]

The decision variables are the PS channels ( $z_{1},\ldots ,z_{16}=0$ or 1), tablet price ($129⩽z ₁₇⩽$499), display size ( $7\leqslant z_{18}\leqslant 10$ ), memory storage size $(8\leqslant z_{19}\leqslant 128)$ , and eBook price change (-$2⩽z ₂₀⩽ +$ 2). The PS channel decisions are binary decision variables. Because there are four products and four services, the PS channel matrix, as mentioned previously, is 4 by 4, so the space of possible channel combinations has the size $2^{(4\times 4)}=65,536$ . However, some of these are impermissible: the PS channels between the same producers (i.e., on the diagonal) must be set to 1, and a producer can control only its channels so that each producer has possible PS channel options of $2^{6}=64$ . Procedurally, as depicted in Figure 2, each producer optimizes its decision sequentially so that the tablet brand and the eBook market brand are optimized in order. As discussed earlier, in terms of PS channel acceptance between competitors, removing a PS channel does not require the other party’s agreement, while adding a PS channel is possible only when neither player’s profits are harmed. Profit optimization is achieved subject to this PS channel constraint in addition to the tablet and eBook design boundary constraints.

For the equilibrium calculation, optimization is carried out sequentially; this is repeated until the optimal design decisions of all producers have converged, and profit cannot be enhanced by further changes. Previous producers’ (optimal) decisions are used for the next producer’s optimization, as parameters of the demand model. Because product features cannot be changed frequently, it is assumed that producers first decide on all decision variables, including product attributes, and secondarily decide on only product/service prices and channels.

The study compares six different scenarios varying in the type of channel and optimization orders as shown in Table 4. The first and last scenarios are used as the baseline to compare with optimal channel scenario. Since there could be a first mover advantage in the game, four optimal channel scenarios are set (S1, S2, S3, and S4) with different sequential optimization orders.

Table 4. Sequential optimization scenarios

An exclusive channel scenario is the case where there is no channel among competitors, and a non-exclusive symmetric channel scenario is the case where all competitors are fully connected through channels, as explained in Section 3.2. These two scenarios fix channels, and then optimize other decision variables in order to compare them with the scenarios that find optimal channels. In the pilot test, when channels are not decision variables, the sequential optimization order does not affect the results significantly. Therefore, the exclusive channel and non-exclusive symmetric channel scenarios use the same optimization order as S1. Optimal channel scenarios are the cases that optimize all decision variables including channels at the same time. There are 24 cases when four producers make decisions sequentially, but four cases were selected where each producer can experience all orders in balance.

Since the design problem is a mixed-integer optimization one due to discrete channel decisions, all possible channel configurations are examined and the continuous decision variables are optimized for each channel configuration on every optimization pass. The profit optimization problem was solved via SQP (sequential quadratic programming), implemented in MATLAB (MathWorks 2017). Since there are 64 possible PS channel configurations for four producers, enumeration with deterministic algorithms was possible. However, if there are many producers in the market, heuristic optimization algorithms will likely be necessary.

Owing to high computational costs for performing optimization and validation at the individual level, mean part-worths were calculated and used as inputs to optimization; for validation, the demand was computed at the individual level and then averaged as in Eq. (3). Thus, heterogeneity measured via the HB conjoint model formulation was accounted for at the validation stage, and all reported metrics thereby accommodate it.