Keywords

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1 Introduction

High-technology companies invest extensively in research and development (R&D) to enhance their competitiveness through technological advances. In practice, much of R&D is carried out in projects that differ in scope, relevance, novelty, phase, risk, and return (Henriksen and Traynor 1999; Brummer et al. 2011). Large firms, in particular, launch, continue, and discontinue projects with the aim of building and maintaining a project portfolio that satisfies resource constraints and responds to relevant business objectives. Often, the resulting R&D portfolio selection problem is complex enough to benefit from the use of formal decision modeling. This is one of the reasons why numerous resource allocation models have been proposed for R&D portfolio selection (see, e.g., Kleinmuntz 2007; Henriksen and Traynor 1999).

In this chapter, we present a decision model for allocating resources to standardization activities in a large telecommunication company. By definition, standardization activities contribute to the establishment of standards which provide benefits such as compatibility and interoperability. These activities resemble traditional R&D investments, and thus resource allocation models for R&D portfolios are, in principle, applicable. Yet there are important differences as well. First, standardization activities may take longer to execute than most R&D projects and, as a result, the resource allocation problem becomes effectively that of adjusting the overall portfolio rather than that of selecting new projects. Second, completed standardization activities may generate business impacts only after a considerable delay so that these impacts can be quite uncertain. Third, these impacts may crucially be dependent on what other standardization activities have been successful. Motivated by these observations, our decision model differs from traditional R&D portfolio selection models in that it responds to the need (1) to adjust the activity portfolio over extended periods of time, (2) to capture uncertainties concerning later developments after the completion of standardization activities, and (3) to account for interactions among the activities.

In the methodologically oriented literature on resource allocation, decision models for the selection of R&D portfolios are often deployed as one-shot interventions (e.g., Lindstedt et al. 2008; Santiago and Vakili 2005; Henriksen and Traynor 1999). But when the projects are of different duration so that new project proposals arise before earlier projects are completed, these models can also be used for adjusting portfolios by evaluating ongoing and prospective projects together before taking decisions about which projects are launched, continued, or killed. In many cases, such selection models can be redeployed with little extra effort by updating the relevant model parameters (Salo and Liesiö 2006). Yet, when applying such models with updated parameters, it is necessary to estimate nonlinear changes in the rates of resource consumption and technological progress, to ensure that the marginal costs of further technological progress are correctly assessed and that the resources can be deployed where they are likely to have the greatest positive impact.

R&D project selection models typically involve parameters about the projects’ expected resource consumption levels, future cash flows, and success probabilities. These parameters are usually elicited from experts, because the uniqueness of different projects offers only limited possibilities for making use of other sources of information. However, a challenge in R&D management is that it may be difficult or impossible for the experts to provide point estimates that they would feel confident about, given the large uncertainties that characterize R&D activities and their impacts. In principle, uncertainties about these parameters could be described with probability distributions that are assessed with standard elicitation techniques (see, e.g., Hora 2007). Yet a complication of such an approach is that the experts may not be able to provide reliable estimates of such distributions, particularly if the R&D projects generate impacts after a long delay or if these impacts are complicated (e.g., Salo and Hämäläinen 1992, 2010). In consequence, it may be useful to characterize uncertainties with the help of confidence intervals and to apply Preference Programming methods which have been deployed successfully to address uncertainties without making specific assumptions about probability distributions (e.g., Salo and Hämäläinen 1992; Arbel 1989; Liesiö et al. 2007; Könnölä et al. 2007; Brummer et al. 2011).

A further challenge in the management of R&D portfolios is that there may exist interactions such as synergy or cannibalization effects among the projects (Kleinmuntz 2007; Stummer and Heidenberger 2003; Liesiö et al. 2008; Fox et al. 1984). For instance, two projects may be related to substitute technologies, in which case the successful completion of both projects would offer less value than what would be achieved by summing their values subject to the constraint that only one of the project will be undertaken. Often, it is sufficient to account for interactions by judgmental tradeoffs based on expert opinion (Phillips and Bana e Costa 2007). However, when the number of project dependencies or interactions grows, such judgments become increasingly difficult to assess (Fox et al. 1984). It may therefore be relevant to build an approximative model of these interactions to better understand their impacts at the portfolio level.

In relation to these challenges, our decision model for allocating resources to standardization activities is novel in that it combines three methodological features, most notably (1) the recurrent use of the model where impacts of alternative resource levels are systematically assessed, (2) the modeling of uncertainties through confidence intervals and Preference Programming methods, and (3) the approximative modeling of interactions among the activities. These features are discussed in the context of a case study. The methodological results of the case study are now in full operational use.

The rest of this chapter is structured as follows. Section 11.2 reviews resource allocation models. Section 11.3 describes the context of our case study, i.e., telecommunication standardization, and presents the resource allocation model. Section 11.4 concludes.

2 Resource Allocation Models in R&D Management

There exist a wide range of resource allocation models for R&D project selection (for overview and references see, e.g., Henriksen and Traynor 1999; Kleinmuntz 2007). Many of these models are variants of the capital budgeting model in that they (1) consider R&D projects that are either funded at the proposed funding level or alternatively discarded, (2) impose a budget constraint that limit the selection of projects, and (3) provide recommendations as to what the “best” projects to be funded are (for details, see Kleinmuntz 2007). Some of these assumptions have been relaxed. For instance, in their resource allocation model for SmithKline Beecham, a large pharmaceutical company, Sharpe and Keelin (1998) relax the assumption that projects can either be fully funded or discarded; instead, they consider four alternative variants of each project, namely (1) the current plan, (2) a buy-up option, (3) a buy-down option, and (4) a liquidation plan. They then identify projects that yield only relatively small benefits compared to their cost and derive recommendations as to how resources should be reallocated to other projects. They report that evaluation of these alternatives encouraged creative decisions and improved the understanding of which parts of each project offered most value to the company.

Santiago and Vakili (2005) present a model where the R&D process is divided into a development phase and a commercialization phase. They argue that because of asymmetrical information, the development phase cannot easily attract funds outside the company, while funds can be raised from the market during the commercialization phase. They model this information asymmetry as a staged development process where the commercialization of each R&D project is contingent on the success of the development phase. Thus, they have effectively two budget constraints, of which the first is a hard constraint on the consumption of development resources, followed by the second which is induced by the market on commercialization resources. These budget constraints are related to each other through contingency constraints.

The elicitation of model parameters by experts may be prone to errors also because vested interests may cause some projects to be unfairly evaluated (e.g., Salo and Liesiö 2006; Sharpe and Keelin 1998). Such tendencies can, in part, be partly mitigated by eliciting incomplete information about numerical assessments, because it may be easier to agree on reasonable bounds of interval-valued statements or to obtain ordinal information instead of seeking to elicit point estimates for probabilities or other numerical parameters. That is, even if it is not possible to reach a consensus on what the probability of a given scenario is, it may be possible to accept statements such as “the probability of scenario 1 is less than 0.1” or “the probability of scenario 1 is greater than that of scenario 2.”

Robust Portfolio Modeling (RPM; Liesiö et al. 2007, 2008) is a framework for portfolio selection under incomplete information. In RPM, uncertainties about parameters are modeled by forming feasible sets that contain all the plausible parameter values (e.g., defined as confidence intervals about the uncertain parameters). The novelty of the RPM approach is that it determines all the nondominated portfolios, i.e., those portfolios which are not dominated by any other portfolio that would yield higher or equal value for all the parameters contained in the feasible sets. The RPM approach then examines these nondominated portfolios and determines which projects are contained in all, some, or no nondominated portfolios, which results in a classification of projects into core, borderline and exterior projects, respectively. This approach has been employed successfully in several case studies such as Könnölä et al. (2007), Lindstedt et al. (2008), and Brummer et al. (2011) where there have been considerable uncertainties. For example, Könnölä et al. (2007) report a case study on the screening of innovation ideas where the ratings by several respondents were analyzed by identifying those ideas that were among the best ones (core) based on the use of mean ratings (consensus-oriented approach) and those which were more controversial in that they were brought to the fore when using the variances of respondents’ ratings (dissensus-oriented approach).

R&D projects often have interactions or interdependencies (Phillips and Bana e Costa 2007; Stummer and Heidenberger 2003; Liesiö et al. 2008; Fox et al. 1984). These interactions can be categorized into (1) cost or resource utilization interaction; (2) outcome, probability, or technical interaction; and (3) benefit, payoff, or effect interaction (Fox et al. 1984). The easiest interactions to model are often those that relate to costs or to the utilization of resources, because costs are usually known in advance and the cause of the interaction is therefore known. For instance, if two projects make use of the same piece of equipment, this could be modeled as a cost saving interaction. In contrast, interactions that pertain to the outcomes, success probabilities, or technical interactions can be more difficult to model. In principle, such interactions can be captured through joint distributions that are determined with the help of copulas, for instance (Clemen and Reilly 1999).

In the presence of benefit, payoff, or impact interactions, the value of a project will depend on what other projects are selected. For instance, if two projects are related to the same technology, they may compete for the same customers. These interactions have not received much attention in literature (Stummer and Heidenberger 2003; Fox et al. 1984), possibly because it is often difficult to specify these interactions in detail or to separate their impacts from those of actual projects, meaning that the exact specification and assessment of all significant interactions would be tedious (see Fox et al. 1984). Moreover, authors such as Phillips and Bana e Costa (2007) argue that interactions do not affect decision recommendations very often and hence only the strongest interactions need to be accounted for, at least in the first approximation. But when the number of interactions grows, it becomes harder to determine which interactions are significant, especially if the impact of one interaction is enhanced by the presence of another interaction. Thus, in the presence of multiple interactions, it may be helpful to build an approximate model for interactions to better understand the overall impact of interactions on the resource allocation decision.

3 Resource Allocation Model for Standardization in Telecommunications

Participation in technical standardization provides many benefits to companies, such as technical compatibility and interoperability for meeting consumer expectations (see, e.g., Glimstedt 2001). The outcome of technical standardization is a (technical) standard, defined as “…a recording of one or more solutions to one or more problems of matching persons, objects, processes or any combination thereof, and which is intended for common and repeated use in any technical field” (Lea and Hall 2004).

In telecommunication, there are hundreds of standardization activities that companies can participate in. The benefits and costs of standardization activities may differ, and it is not viable to participate in all such activities to secure benefits from standardization. The selection of which standards a company should participate in is essentially an R&D portfolio selection problem.

Compared to traditional R&D portfolio selection, there are additional modeling challenges:

  1. 1.

    Standards are often interrelated to each other. For instance, standards may relate to substitute technologies, which means that two competing standards may not coexist very long.

  2. 2.

    The benefits of standardization do not accrue immediately and may impact sales after several years. The benefits are contingent on the success of the standard and also on how well the company can exploit the opportunities of standardization.

This section describes the development of a standardization resource allocation model for a large telecommunication company. The company is involved in hundreds of standardization activities and has a dedicated standardization unit. Apart from modeling challenges, the design and development of the decision model involved organizational issues. Specifically, because standards are related to different technologies, the required expertise for elicitation was distributed across different parts of the company: technical standardization experts had best technical know-how of standards, whereas managers and road-mappers were best aware of market conditions and strategic considerations. For this reason, model parameter assessment needed input from numerous experts, including managers with limited possibilities to take part in lengthy face-to-face meetings. The experts were also geographically distributed, which constrained opportunities for gathering expertise through decision conferencing in face-to-face meetings. These challenges implied that a requisite model should be simple in the sense that the parameters would need to be correctly and coherently elicited with minimal training and limited possibilities to get support in understanding the decision model.

3.1 Rationales for Standardization

As a part of out case study, the company standardization experts identified three value adding objectives: (1) maximization of revenues, (2) alignment of the standardization portfolio with company strategy, and (3) diversification of risks. These objectives and means to achieve them are summarized in Table 11.1.

Table 11.1 Value adding objectives in standardization and means for achieving them
Full size table

In revenue maximization, standardization can be seen as a support activity for product sales. The consensus was that the impacts of standardization on expected sales were mainly driven by widely adopted technologies, that is, architectures (product and/or process) that become widely accepted as industry standards (also known as dominant designs; see, e.g., Anderson and Tushman 1990). In this setting, standardization contributes to the development of widely adopted technologies (Koski and Kretschmer 2007). Because the emergence of widely adopted technologies has an impact on the survival of the firm (Suarez and Utterback 1995) and yields revenues to the holder of proprietary rights to the technology in terms of establishing a natural monopoly (Schilling 2008), the value of standardization can be approximated using this link to future sales.

For creating a balanced portfolio, a company must also consider objectives that cannot be expressed in terms of future sales. Proprietary technologies are often made available to other parties to introduce products that comply with a standard, which can lead to a bandwagon effect where one technology quickly becomes adopted by the industry (Farrell and Saloner 1985). As a consequence, early standardization is critical to competitiveness in network markets (Edquist and Hommen 1998). Thus, the company needs to consider standardization from the viewpoint of promoting technologies. Wider diffusion of company technologies also improves the utilization of internal know-how.

Standardization can also be used in risk management: by participating in the development of key technologies, the company increases the chances of acquiring having rights to technologies or products that benefit from bandwagon effects. However, there are alternative costs of allowing other participating parties to enter the same markets.

3.2 Mathematical Development of a Resource Allocation Model

We assume that there are standardization activities j = 1, …, m, which are associated with a specific set of features or technical properties that can be implemented in a product. If the implementation of the standardization activity is successful, a widely adopted technology emerges. This technology, in turn, will eventually create (an increase in) sales S j through the products that are based on that technology.

Each activity j can be funded by committing r j s ≥ 0 resources to standardization and r j d ≥ 0 resources for development. For this resource allocation, the probability of succeeding in standardization is p j s(r j s), while the probability of successfully developing a widely adopted technology is p j d + (r j d) if standardization is successful and p j d − (r j d) if standardization is unsuccessful. The probability of creating a widely adopted technology can be positive even if standardization fails, because widely adopted technologies can emerge through de facto standards, for instance. Standardization activity j generates sales if and only if the corresponding widely adopted technology is established, which occurs with total probability P(r j s, r j d) = p j s(r j s)p j d + (r j d) + (1 − p j s(r j s))p j d − (r j d). The corresponding decision tree is shown in Fig. 11.1.

Fig. 11.1
figure 1_11

Decision tree for a standardization activity

Full size image

We discretize choices concerning the amount of resources that are allocated to standardization activities to limit the amount of elicitation and computational effort when dealing with tens or hundreds of activities. For each activity j, we define 16 different variants by restricting our choice of activity standardization and development funding levels r j s and r j d to L = { − 100%, − 50%, + 0%, + 100%} of the current plan, respectively. Thus, standardization funding level i ∈ L and development funding level k ∈ L imply that the amount of resources committed to standardization is r ji s and resource committed to development is r jk d. As a result of this discretization, we can analyze the impact of significant increases or decreases in funding with only 12 probability assessments per activity, that is, 4 assessments of standardization success probability with different funding levels and 8 assessments the probabilities of developing a widely adopted technology conditioned on the success/failure of standardization of the activity. The use of the relative scale in discretization is motivated by the wish to emphasize that the assessments are changes to the current plan.

The expected sales resulting from the portfolio, that is

$$\mathit{ES} =\sum\limits_{j=1}^{m}P({\mathit{r}}_{\mathit{ j}}^{\mathit{s}},{\mathit{r}}_{\mathit{ j}}^{\mathit{d}}){S}_{ j},$$
(11.1)

is maximized with respect to standardization and development budget constraints ∑ j = 1 m r j s ≤ B s and ∑ j = 1 m r j d ≤ B d , where B s and B d are the respective budgets. For the time being, we assume that budgets are not interchangeable (meaning that standardization resources cannot be allocated to development and vice versa). This reflects the practical limitation that short-term resources in standardization (e.g., employees) cannot be easily transferred to development and vice versa.

We formulate the optimization model for solving the optimal resource allocation by introducing binary variables x ik j, which indicate that the activity j has standardization level i ∈ L and development level k ∈ L. Using these variables, the resource allocation for each standardization activity can be expressed with r j s =  ∑ i ∈ L ∑ k ∈ L r ji s x ik j and r j d =  ∑ i ∈ L ∑ k ∈ L r jk d x ik j, along with the constraints

$$\sum\limits_{i\in L}\sum\limits_{k\in L}{x}_{ik}^{j} = 1\quad \textrm{ for all $j = 1,\ldots,m$},$$
(11.2)

which enforce that only one resource level is indicated for each activity. The success probabilities are given by

$$ P({r}_{\mathit{ ji}}^{s},{ r}_{\mathit{ jk}}^{d}) = {p}_{j}^{s}({ r}_{\mathit{ ji}}^{s}){p}_{ j}^{d+}({ r}_{\mathit{ jk}}^{d}) + \Big{(}1 - {p}_{ j}^{s}({ r}_{\mathit{ ji}}^{s})\Big{)}{p}_{j}^{ d-}({ r}_{\mathit{ jk}}^{ d}).$$

The resource allocation that maximizes expected sales is the solution to the Mixed Integer Linear Program (MILP)

$$\begin{array}{rcl} \max\limits_{x}\qquad & & \sum\limits_{j=1}^{m}\sum\limits_{i\in L} \sum\limits_{k\in L}P({r}_{\mathit{ji}}^{s},{r}_{\mathit{ jk}}^{d}){S}_{ j}{x}_{ik}^{j} \\ \mathrm{subject\ to}\qquad & & \sum\limits_{j=1}^{m}\sum\limits_{i\in L}\sum\limits_{k\in L}{r}_{\mathit{ji}}^{s}{x}_{\mathit{ ik}}^{j} \leq {\mathit{B}}_{ s} \\ & & \sum\limits_{j=1}^{m}\sum\limits_{i\in L}\sum\limits_{k\in L}{r}_{\mathit{jk}}^{d}{x}_{\mathit{ ik}}^{j} \leq {\mathit{B}}_{\mathit{ d}} \\ & & \sum\limits_{i\in L}\sum\limits_{k\in L}{x}_{\mathit{ik}}^{j} = 1,\ j = 1,\ldots,m \\ & & \qquad {x}_{\mathit{ik}}^{j} \in \{ 0,1\},i \in L,\,k \in L,\,j = 1,\ldots,m. \end{array}$$
(11.3)

Although the model has only budget constraints, it is possible to introduce additional linear constraints to account for other constraints such as mutual exclusivity of activities. These additional constraints can be included in the above MILP using standard modeling techniques. The portfolios that satisfy constraints in (11.3) and the possible additional constraints form the set of feasible portfolios, which is denoted by Π f .

3.3 Modeling Sales Uncertainty

The sales S j for each widely adopted technology was relatively difficult for experts to assess. Although the decision tree defined scenarios on which the assessment could be conditioned, the standardization experts felt they were unable to specify a full probability distribution. However, they were able to provide plausible upper and lower bounds for sales. This approach was also believed to be transparent in the sense that these assessments could be more easily debated than probability distributions. Thus, let the sales interval be \({\underline{S}}_{j} \leq {S}_{j} \leq {\overline{S}}_{j}\), where \underline{S} j and \({\overline{S}}_{j}\) are the assessed lower and upper bounds of sales, respectively. The set of sales vectors is \(\mathbb{S} = [{\underline{S}}_{1},{\overline{S}}_{1}] \times \cdots \times [{\underline{S}}_{m},{\overline{S}}_{m}]\).

The optimum of problem (11.3) depends on what point estimates S j are chosen from the set of sales vectors \(\mathbb{S}\). In this setting, some portfolios are not interesting choices in the sense they are not optimal regardless of which sales estimates from \(\mathbb{S}\) are chosen. We therefore focus on potentially optimal portfolios (portfolios that maximize expected sales for some feasible sales) Π PO , i.e.,

$${\Pi }_{PO} = \Big\{\pi \in {\Pi }_{f}\Big\vert \exists S \in \mathbb{S} : \pi \in \arg \max\limits_{\pi '}{\textrm{ES}}_{S}(\pi ')\Big\},$$

where { ES} S (π′) is the expected sales for vector S.

The set of potentially optimal portfolios can be used to provide guidance for resource allocation decisions. Following RPM (Liesiö et al. 2007), we define the core indexCI of a resource allocation (r j s, r j d) for activity j as the share of potentially optimal portfolios that contain that allocation for the activity, that is

$$CI({r}_{j}^{s'},{r}_{ j}^{d'}) = \frac{\Bigg\vert \Bigg\{\pi = \Big(({r}_{1}^{s},{r}_{ 1}^{d}),\ldots,({r}_{ m}^{s},{r}_{ m}^{d})\Big) \in {\Pi }_{ PO}\vert ({r}_{j}^{s},{r}_{ j}^{d}) = ({r}_{ j}^{s'},{r}_{ j}^{d'}) \Bigg\}\Bigg\vert } {\Big\vert {\Pi }_{PO}\Big\vert }$$

where | . | denotes the number of elements in a set.

If a resource allocation has a core index of 1 (core allocation), it is included in all potentially optimal portfolios and can therefore be recommended. Conversely, if a feasible allocation with a core index 1 would not be in a funding portfolio, then for all sales estimates there exist some other portfolios which yield higher expected sales. The parallel argument applies for allocations with core index 0 (exterior allocation) and these allocations should not be included in the final portfolio. Decision recommendations for allocations with core indices between 0 and 1 (borderline allocation) are dependent on the sales estimate within the set of possible sales, wherefore a decisive recommendation cannot be given.

In large problems it may not be possible to compute all potentially optimal portfolios with a brute force algorithm, because checking all 16m possible portfolios would soon become computationally intractable. A subset of potentially optimal portfolios can be found with Monte Carlo simulation by generating uniformly distributed sales vectors from \(\mathbb{S}\) and solving the optimization problem (11.3) for each generated vector. Although the subset found by Monte Carlo simulation does not necessarily contain all potentially optimal portfolios, we use this set for approximating the core indices.

3.4 Visualization of Results

The resource allocation recommendations were visualized as a matrix, as shown in Fig. 11.2, where each cell in the matrix represents the core index of the corresponding resource allocation decision. For instance, the upper right corner of the matrix represents the decision of increasing both standardization and development resources by 100%. The core index of this decision is 0.19, meaning that this action is included in 19% of the potentially optimal portfolios. The shading is based on a linear gray scale, where white corresponds to a core index of 0 and black a core index of 1. If the sales parameters were to be specified as point estimates, there would be only one optimal portfolio and thus only one cell would have a core index of 1 (thus shaded black), and the other cells would have a core index of 0 (thus shaded white).

Fig. 11.2
figure 2_11

Example of a decision recommendation, which illustrates the core indices in a matrix

Full size image

The decision recommendations can be further visualized by representing the ranges within which the expected sales vary when resources are either decreased or increased. Figure 11.3 shows these ranges for six activities and the expected sales’ midpoint with the current funding plan. This gives an overview of the up or down potential of the activities. For instance activity 1 is almost at the top of its range with current funding, thus it is unlikely to benefit from additional resources. Activity 3 in contrast has plenty of potential with additional resources.

Fig. 11.3
figure 3_11

Example ranges for the activities expected sales when funding is varied from − 100% to + 100% compared to the current plan. Current funding level is denoted with a dot

Full size image

3.5 A Model for Binary Activity Interactions

The success or failure of a standardization activity or a group of activities may have a positive or negative effect on other standardization activities. These effects are called interactions. Although an interaction can pertain to several standards, a first approximation is to consider pairwise interactions. We capture these pairwise interactions by describing the magnitude of influence caused by the success or failure of a dependent activity with a reward or penalty.

Continuing with problem (11.3), let activities j 1 and j 2 have an allocation of standardization and development resources defined by the binary selection variables x j and indices \((i,k,\hat{i},\hat{k})\) such that activity j 1 uses \({r}_{{j}_{1}i}^{s}{x}_{ik}^{{j}_{1}}\) for standardization and \({r}_{{j}_{1}k}^{d}{x}_{ik}^{{j}_{1}}\) for development and activity j 2 uses \({r}_{{j}_{2}\hat{i}}^{s}{x}_{\hat{i}\hat{k}}^{{j}_{2}}\) for standardization and \({r}_{{j}_{2}\hat{k}}^{d}{x}_{\hat{i}\hat{k}}^{{j}_{2}}\) for development. We define interaction variables

$${I}_{\mathit{ik\hat{i}\hat{k}}}^{{j}_{1}{j}_{2} } = \left \{\begin{array}{@{}l@{\quad }l@{}} 1,\quad \textrm{ if}\ {x}_{\mathit{ik}}^{{j}_{1}} = {x}_{\mathit{\hat{i}\hat{k}}}^{{j}_{2}} = 1\quad \\ 0,\quad \textrm{ otherwise} \quad \end{array} \right.$$

to indicate that a combination of standardization resource allocations is active. Constraint (11.2) ensures that a unique interaction is indicated for every resource allocation.

We model the impact of an interaction as follows: The expected sales of activity j 1 without interactions is \(P({r}_{{j}_{1}}^{s},{r}_{{j}_{1}}^{d}){S}_{{j}_{1}}\). Let P I be the probability of the interaction occurring and a≠0 be the relative change in expected value of activity j 1 if the interaction occurs. Then, the expected impact of the interaction on portfolio expected sales is \(aP({r}_{{j}_{1}}^{s},{r}_{{j}_{1}}^{d}){S}_{{j}_{1}}{P}_{I}\). We modeled only pairwise interactions, that is, activity j 2 impacts activity j 1, and the occurrence of the interaction depends only on either the success or failure of the impacting activity. Thus, we modeled interactions as follows:

  • If the success of activity j 2 has an impact on the probability of success of activity j 1, we add \({I}_{ik\hat{i}\hat{k}}^{{j}_{1}{j}_{2}}\) in the objective function of problem (11.3) with the coefficient

    $${a}_{{j}_{1}{j}_{2}}P({r}_{{j}_{1}i}^{s},{r}_{{ j}_{1}k}^{d}){S}_{{ j}_{1}}P({r}_{{j}_{2}\hat{i}}^{s},{r}_{{ j}_{2}\hat{k}}^{d}),$$

    where \({a}_{{j}_{1}{j}_{2}}\) is the constant describing the strength and direction of the interaction (\({a}_{{j}_{1}{j}_{2}} > 0\) positive impact, \({a}_{{j}_{1}{j}_{2}} < 0\) negative impact).

  • If the failure of activity j 2 has an impact on the probability of success of activity j 1, we add \({I}_{ik\hat{i}\hat{k}}^{{j}_{1}{j}_{2}}\) in the objective function with the coefficient

    $${a}_{{j}_{1}{j}_{2}}P({r}_{{j}_{1}i}^{s},{r}_{{ j}_{1}k}^{d}){S}_{{ j}_{1}}\Big{(}1 - P({r}_{{j}_{2}\hat{i}}^{s},{r}_{{ j}_{2}\hat{k}}^{d})\Big{)}.$$

Because the sales gain or loss is proportional to the expected sales of activity j 1 (i.e., \(P({r}_{{j}_{1}i}^{s},{r}_{{j}_{1}k}^{d}){S}_{j}\)) in cases where the invoking activity will always succeed or fail, the interactions are always full or none, respectively. Thus an expert assessing the constant \({a}_{{j}_{1}{j}_{2}}\) can interpret it as the relative increase or decrease in sales that occurs if the interaction is present. In our case, the strength of interactions were assessed on a qualitative scale “critical”–“very critical”–“extremely critical,” which was converted to numerical values such that \({a}_{{j}_{1}{j}_{2}} \in \{\pm 0.3,\,\pm 0.6,\,\pm 0.9\}\). However, these penalties/rewards are nonprobabilistic because they cannot be interpreted as the absolute increase in expected value that the success of a beneficial activity would give.

To guarantee that an interaction variable I is positive only when the associated funding levels are selected, we introduce the following constraints:

  • A positive interaction term (a > 0) should be allowed a nonzero value only if

    $$2{I}_{ik\hat{i}\hat{k}}^{{j}_{1}{j}_{2} } \leq {x}_{ik}^{{j}_{1} } + {x}_{\hat{i}\hat{k}}^{{j}_{2} }.$$

  • A negative interaction term (a < 0) is allowed to be zero only if

    $$2{I}_{ik\hat{i}\hat{k}}^{{j}_{1}{j}_{2} } \geq {x}_{ik}^{{j}_{1} } + {x}_{\hat{i}\hat{k}}^{{j}_{2} } - 1.$$

At optimum these constraints are equalities, because in the first case the interaction term has a positive coefficient in the objective function (to be maximized) and a negative in the latter case. Suppose that there are four sets of interactions defined by triplets \(({j}_{1},{j}_{2},{a}_{{j}_{1}{j}_{2}})\) meaning that the interaction prescribes the magnitude of interaction \({a}_{{j}_{1}{j}_{2}}\) on activity j 1 by activity j 2:

  • A( + , + ) is the set of interactions which enhances j 1 when j 2 succeeds.

  • A( + , − ) is the set of interactions which enhances j 1 when j 2 fails.

  • A( − , + ) is the set of interactions which weakens j 1 when j 2 succeeds.

  • A( − , − ) is the set of interactions which weakens j 1 when j 2 fails.

Then the complete heuristic model extended from (11.3) is

$$\begin{array}{rcl}& & \max\limits_{x,I}\quad \sum\limits_{j=1}^{m}\sum\limits_{i\in L} \sum\limits_{k\in L}P({r}_{\mathit{ji}}^{s},{r}_{\mathit{ jk}}^{d}){S}_{ j}{x}_{\mathit{ik}}^{j} \\ & & \quad +\sum\limits_{\begin{array}{c}({j}_{1},{j}_{2},{a}_{{j}_{ 1}{j}_{2}}) \\ \in A(+,+)\cup A(-,+)\end{array}}\sum\limits_{i\in L}\sum\limits_{k\in L}\sum\limits_{\hat{i}\in L}\sum\limits_{\hat{k}\in L}{a}_{{j}_{1}{j}_{2}}P({r}_{{j}_{\mathit{1i}}}^{s},{r}_{{ j}_{\mathit{1k}}}^{d}){S}_{{ j}_{1}}{I}_{\mathit{ik\hat{i}\hat{k}}}^{{j}_{1}{j}_{2} }P({r}_{{j}_{2}\hat{i}}^{s},{r}_{{ j}_{2}\hat{k}}^{d}) \\ & & \quad +\sum\limits_{\begin{array}{c}({j}_{1},{j}_{2},{a}_{{j}_{ 1}{j}_{2}}) \\ \in A(+,-)\cup A(-,-)\end{array}}\sum\limits_{\mathit{i\in L}}\sum\limits_{\mathit{k\in L}}\sum\limits_{\mathit{\hat{i}\in L}}\sum\limits_{\mathit{\hat{k}\in L}}{a}_{{j}_{1}{j}_{2}}P({r}_{{j}_{\mathit{1i}}}^{s},{r}_{{ j}_{\mathit{1k}}}^{d}){S}_{{ j}_{1}}{I}_{\mathit{ik\hat{i}\hat{k}}}^{{j}_{1}{j}_{2} }\left (1 - P({r}_{{j}_{2}\hat{i}}^{s},{r}_{{ j}_{2}\hat{k}}^{d})\right)\end{array}$$
(11.4)
$$\begin{array}{rcl} \mathrm{subject\ to}\quad & & 2{I}_{ik\hat{i}\hat{k}}^{{j}_{1}{j}_{2} } \leq {x}_{ik}^{{j}_{1} } + {x}_{\hat{i}\hat{k}}^{{j}_{2} },\quad i,k,\hat{i},\hat{k} \in L\,,({j}_{1},{j}_{2},\ldots ) \in A(+,+) \\ & & \qquad \cup A(+,-) \\ & & 2{I}_{ik\hat{i}\hat{k}}^{{j}_{1}{j}_{2} } \geq {x}_{ik}^{{j}_{1} } + {x}_{\hat{i}\hat{k}}^{{j}_{2} } - 1,\quad i,k,\hat{i},\hat{k} \in L\,,({j}_{1},{j}_{2},\ldots ) \in A(-,+) \\ & & \qquad \cup A(-,-) \\ & & \sum\limits_{j=1}^{m}\sum\limits_{i\in L}\sum\limits_{k\in L}{r}_{ji}^{s}{x}_{ ik}^{j} \leq {B}_{ s} \\ & & \sum\limits_{j=1}^{m}\sum\limits_{i\in L}\sum\limits_{k\in L}{r}_{jk}^{d}{x}_{ ik}^{j} \leq {B}_{ d} \\ & & \sum\limits_{i\in L}\sum\limits_{k\in L}{x}_{ik}^{j} = 1,\quad j = 1,\ldots,m \\ & & {x}_{ik}^{{j}_{1} },{I}_{ik\hat{i}\hat{k}}^{{j}_{1}{j}_{2} } \in \{ 0,1\},\quad i,k,\hat{i},\hat{k} \in L\,,{j}_{1},{j}_{2} = 1,\ldots,m\end{array}$$
(11.5)

There are | L | 4 binary variables for each interaction, where | L | denotes the number of resource allocation levels. Because | L | was 4 in our case, each interaction can be captured with 256 binary variables. Because the optimum of the problem (11.4) needs to be solved a large number of times in the Monte Carlo simulation and because the growing number of binary variables increases the computation time, we reduced the amount of variables as follows: We assume that the interaction depends only on the standardization funding and that standardization of activities j 1 and j 2 is done with current/planned development budgets. Then, the interaction variables \({I}_{ik\hat{i}\hat{k}}^{{j}_{1}{j}_{2}}\) and \({I}_{i,\mathcal{l},\hat{i},\mathcal{l}}^{{j}_{1}{j}_{2}}\) (also their coefficients in the objective function) are equal, where ℓ =  + 0% denotes the index of the current/planned standardization and development budgets, and they can be collapsed to a single variable. This reduces the number of interaction variables to | L | 2 = 16.

With the reduced number of interaction variables, the impact of interactions can be visualized with a core index matrix as in Fig. 11.2. For interactions, the columns of the matrix represent core indices of standardization levels of the impacted standard and the rows core indices of standardization levels of the impacting standard (or vice versa). Then the impact of the interaction can be visualized by comparing this matrix computed with and without interactions.

3.6 Experiences of Using the Model

The model was first used with 100 activities from several different areas of technical standardization. Data were gathered with a spreadsheet questionnaire that was supplemented with background material including a general description of the model. The respondents were asked to provide assessments of the model parameters, namely sales intervals, standardization and development costs, and standardization and development success probabilities.

There were numerous interactions. Thus, computational tractability was ensured by accounting only for strong interactions. This resulted in nine interactions on a scale of “critical”–“very critical”–“extremely critical,” which were converted to numerical values.

The results were visualized to the experts by showing a matrix of core indices for each activity. The results were computed with and without interactions and corresponding core index matrices were presented together with a visualization of the alternative data. The recommendations were either strong in the sense that only few allocations had positive core indices or weak in the sense that many allocations had a positive core index. If all the positive core indices for an activity suggested increased standardization funding, the corresponding standardization activity was considered as a candidate for receiving more funding. Suggestions for decreased funding were interpreted analogously.

Interactions did not have a significant impact on the decision recommendations, because increased funding was typically recommended to the same activities regardless of whether interactions were accounted for or not. This was, in part, because positive interactions tended to impact those activities for which the model recommended additional resources in the absence of interactions whereas negative interactions impacted those activities for which the model recommended reduced resources in the absence of interactions. Thus, the modeling of interactions was not as important as their potential impact would have suggested.

The elicitation of information about future sales was challenging and often resulted in wide and overlapping intervals. This was because the additional sales will not materialize in the near future and that they are also affected by external uncertainties such as market size and intensity of competition. As a result, most activities had positive core indices for several allocations. However, this was in fact a strength of the model because the recommendations still gave direction to overall resource reallocation. In this setting, the fact that there was no unique optimal decision recommendation resulted in increased confidence in the model, because several different allocations could indeed be justified.

Structuring of the model as a decision tree helped explain the results. In comparison with more general resource allocation models (such as capital budgeting models), a closer inspection of standardization as means for developing widely adopted technologies gave insights, especially when seeking to build a consensus based on the estimates of several experts with different fields of expertise. In particular, without explicating how an activity brings value to the company, it would have been difficult to explain to a standardization engineer why the value of a technically superior standard may be low for the company.

As a summary, the modeling approach was sound and transparent enough to guide the resource allocation decisions. Furthermore, the model was considered general enough to also support resource allocation decisions of other areas of technological standardization. The company currently has the model in extensive operational use for allocating resources to activities in all essential areas of telecommunication standardization.

4 Conclusions

In this chapter, we have presented a resource allocation model for standardization activities in a major telecommunication company. The resource allocation problem was structured with decision trees, and Preference Programming methods were applied to model the uncertain future sales associated with standardization activities. The model was first piloted with 100 standardization activities and, based on initial favorable experiences, it was subsequently adopted into operational use. Currently, it is employed in support of resource allocation decisions in all areas of telecommunication standardization that the company is active in. The strengths of the model – which have partly facilitated its uptake – include features such as parsimony with relatively few parameters, computational tractability, and ease of extending the model to the analysis of new activities. Although the model has been developed in the context of standardization, it holds promise when allocating resources to other R&D activities as well.