Interdependencies among projects in project portfolio management

a content analysis of techniques


Lappeenranta University of Technology, Lappeenranta, Finland


Humankind has been investigating interdependencies among alliances and companies for decades. This work investigates resource, technological, and market interdependencies among projects. Interdependencies are an important factor in selecting better projects into a project portfolio. They also help to increase the success rate in the field of project management, where high failure rates prevail. Empirics have shown that interdependency techniques influence the success rate and other aspects of productivity to different extents. Interdependencies are also deeply involved with research and development (R&D) and innovation. This paper presents a literature review of techniques addressing interdependencies. Although research exists on interdependency, prior publications have not given a thorough review of most available techniques in one paper. Also, the plurality of techniques indicates that there is no strong standpoint, and therefore researchers tend to go in different directions. This paper gives a compact overview of the techniques, with a short description of the techniques, and their advantages and disadvantages, to make the decision maker's choice easier in finding an appropriate method for the situation. This literature review is based on widely used electronic academic business databases. The titles and abstracts of articles have been examined, and relevant articles have been studied closely. The final review consists of some 200 articles.

Keywords: project portfolio management, interdependency techniques


Inter-unit interdependencies have been a widely used and important aspect of foundational organization and management studies, including works such as Thompson (2003) and Mintzberg (1983) (Sanchez & Worren, 2005, p. 5). This work investigates interdependencies among projects as modern subunits in companies today. Projects often have interdependencies with each other, and it has been found that managing these interdependencies systematically helps to increase the success rate of the projects (Rungi, 2010). Interdependencies are also deeply involved with research and development (R&D) and innovation (Rungi, 2009a). This is due to the fact that considering the interdependencies among projects helps in selecting better projects into the project portfolio (Archer & Ghasemzadeh, 1999a, p. 221). The interdependencies issue grows when the size of the project portfolio becomes larger. “Most project companies are seeking means to control and manage” multiproject management with interdependencies among projects (Arenius, Artto, Lahti, & Meklin, 2002, p. 291). Interdependencies are one of the major difficulties regarding a project's selection into a portfolio (Ghasemzadeh, Archer, & Iyogun, 1999, p. 745). Unfortunately, the academic literature has only rarely focused on the interdependency issue. Review articles are available that introduce the topic of interdependency and its techniques (e.g., Santhanam & Kyparisis, 1996; Staudenmayer, 1997; Archer & Ghasemzadeh, 1999a; Heidenberg & Stummer, 1999; Verma & Sinha, 2002; Cooper, Edgett, & Kleinschmidt, 2006), but they don't cover a full list of techniques and/or don't always reveal how the method(s) discussed deal with the interdependency issue. More importantly, most popular techniques for project selection neglect the interdependency issue totally (Santhanam & Kyparisis, 1996, p. 380), primarily due to the complexity and because their main research target has been project portfolio management (PPM) or anything else in general, not interdependencies per se. There is a gap in the literature (Schmidt, 1993). Also, the plurality of techniques indicates that there is no single strong standpoint and that researchers tend to go in different directions, and therefore a comprehensive review is usable. Some authors argue that knowledgeable techniques and other hard skills constitute 20% of project success (McKinlay, 2008); however, it is worthwhile investigating this percentage, considering the high failure rates of projects. It can be argued that if there were a full list of techniques, with a description of how the interdependency techniques can be applied, including the possible pros and cons of the techniques, it would help the decision maker to choose the one that fits the current situation of the company best. Empirics have shown that interdependency techniques influence success rates and other productivity aspects to different extents (Rungi & Kässi, 2009).

In general, empirics from companies about the use of techniques in practice are rare (Killen, Hunt, & Kleinschmidt, 2007, p. 25); this literature review serves also as a base for empirical research (Rungi, 2009b; Rungi & Kässi, 2009).

This paper is organized as follows. First, interdependency-related ontological issues are described. Then, an overview of the data gathering is given (i.e., how the literature review was performed). Thereafter, a short overview of project portfolio techniques is presented, which serves as a working context for interdependency techniques. Fourth, considerable prior work on different techniques of interdependency, including their pros and cons, are covered in next, two main sections, and final section concludes the paper.

Short Overview of Interdependency

Interdependency is defined as a contingent relationship between projects (modified from Thompson, 2003), therefore “interdependency” and “relationships” are used interchangeably in this article. According to Santhanam and Kyparisis (1996, p. 383), “the first ideas on project interdependencies were discussed by Weingartner and Reiter [in 1963], in the area of capital budgeting.”

The interdependency issue can be explained by many theories, among them PPM theory (e.g. Cooper, Edgett, & Kleinschmidt, 2006), PPM methods (e.g., Santhanam & Kyparisis, 1996), interdependency theory (e.g. Verma & Sinha, 2002; Staudenmayer, 1997), and interdependency methods and techniques (e.g. Heidenberger & Stummer, 1999).

The PPM process consists of two different parts: project selection and portfolio review. “The portfolio selection process is characterized by uncertain and changing information, dynamic opportunities, multiple goals and strategic considerations, interdependence among projects, and multiple decision makers and locations” (Cooper et al., 2006, p. 3). The critical factor is identifying the right projects for the portfolio. In detail, PPM has three main goals: 1) “maximizing the value of the portfolio,” 2) “balancing in the portfolio,” and 3) strategic alignment (Cooper, Edgett, & Kleinschmidt, 1999b, p. 29).

Cooper et al. (1999b, p. 28) emphasize that PPM and project selection are the most important strategic issues, especially, improvements in project selection (Scott, 2000). One survey (Archer & Ghasemzadeh, 2004, p. 239), indicates that 50% to 60% of new product development (NPD) projects fail. If the project selection is done with care, the success rate of the project portfolio is higher (Archer & Ghasemzadeh, 2004, p. 238). The project selection process consists of (1) idea gathering, (2) portfolio screening, (3) portfolio evaluation, and (4) portfolio prioritization (Koivuniemi, Piippo, Kärkkäinen, & Tuominen, 1999).

“Projects may be mutually exclusive” if companies explore competing technologies and products (Childs, Ott, & Triantis, 1998, p. 306). At the opposite end of the continuum, when projects are contingent, a “project can be chosen only when a second project is also selected” (Kleinmuntz, 2006, p. 7); for example, the development of an executive support system (ESS) is dependent on the development or existence of a basic accountant system. The modular structure of technical products, where modules serve as building blocks for several different systems, is another example of interdependencies between projects. “Other examples include situations where the success of one project may change the likelihood of success of another project” (Archer & Ghasemzadeh, 1999a, p. 221) or resource overlap (Ghasemzadeh et al., 1999, p. 749).

A more comprehensive review of interdependencies can be found in the following sources Staudenmayer (1997), and Sanchez and Worren (2005).

Procedure and Data of Bibliographic Study

There are many articles available, which deal with interdependency techniques among projects (Santhanam & Kyparisis, 1996; Archer & Ghasemzadeh, 1999a; Heidenberger & Stummer, 1999; Cooper et al., 2006), but they don't cover a full list of techniques and/or don't always reveal fully how the interdependency issue is dealt with by the techniques and in companies. There is a gap in the literature, mostly because interdependency has not been their main research target. For example, usually visual techniques are missing and/or a list of mathematical techniques is presented partially. Because interdependency, as such, has been found to be an important issue, a review article was considered to be relevant.

To fill the gap presented above, a search in the electronic online databases EBSCO, Emerald, IEEE Xplore, ProQuest, ScienceDirect/Elsevier, and JSTOR was performed in 2007/2008. These databases include articles from most well-known management journals distributed worldwide.

The bibliographic study was decided not to be limited by top journals, because according to Thiry and Deguire (2007, p. 650), project phenomenon is very rarely published in management literature. Only a few exceptions are available in top journals (e.g., Schwab & Miner, 2008).

The bibliographic research in the electronic databases was done by combining the search terms/keywords portfolio, multiproject, project, interdependency, interaction, interface, complexity, relationship, coordination1 and program/programme2, which in turn were used together with the name of the method, when a new interdependency method was found. The search terms were chosen on the basis of the linguistic similarity between the keywords, for example synonyms (e.g., portfolio and multiproject; and interaction, interdependency, and relationship), and on the basis of keywords found as a result of the first round of database searches (e.g. coordination). Following the bibliometric study of Artto, Martinsuo, Gemünden, and Murtoaro (2008, p. 3) “different keywords were combined to form one single keyword, for example: singular and plural forms of the same word” (e.g., interdependency and interdependencies), “two language versions of the same keyword” (e.g., integer optimization and integer optimisation), and “two ways to express the same issue” (e.g., design structure matrix and DSM, and multi-project and multiproject). The titles, abstracts, and keywords of the found articles were worked through and the most relevant ones were investigated deeply. As another data source for the review, the references were checked in the found articles. There were certain overlaps between the result sets received with different search terms, and these sources were investigated more deeply. Finally, some 200 sources were worked through.

Many kinds of research work have been conducted dedicated to interdependencies, such as interdependencies between companies/virtual organizations (Jarimo & Salo, 2006; Dabholkar & Neeley, 1998), between alliances and networks (Hoffmann, 2005), between the objectives of projects (Medaglia, Graves, & Ringuest, 2007), between project teams (Dietrich, 2007), or symbiotic interdependence (Pfeffer & Salancik, 1978), but these areas are not the subject of this article. This article deals only with interdependencies among projects.

Short Overview of Project Portfolio Techniques

“Over two hundred qualitative and quantitative [techniques]…exist in the literature for R&D project selection” (Coffin & Taylor, 1996, p. 208). A rather broad source of project portfolio selection techniques is available in Martino (1995). Hereby, the typology of the main portfolio selection techniques is drawn (Figure 1), categorized by goals of PPM (modified from Cooper et al. 1999b, p. 29; Archer & Ghasemzadeh, 1999a, pp. 211–220).

Portfolio selection techniques on the basis of PPM goals

Figure 1: Portfolio selection techniques on the basis of PPM goals.

The effective use of each method is limited. Also, there is no consensus among academicians and practitioners regarding which method is the best (Koivuniemi & Edelman, 2003, p. 7). Most of the proposed techniques, including financial techniques, scoring models, the analytic hierarchy process, and ranking are claimed to neglect relationships among projects clearly (Santhanam & Kyparisis, 1996, p. 384; Archer & Ghasemzadeh, 1999b, p. 212; Lee & Kim, 2000, p. 369), but according to Cooper et al. (2006), these models are most popular among decision makers.

Overview of Techniques Addressing Interdependencies

A list of techniques addressing interdependencies among projects is given in Figure 2. More detailed descriptions of the techniques are presented below. The literature is full of descriptions of different techniques; however, there is a lack of discussion of the empirics (Killen et al., 2007, p. 1865) and examples in the literature.

Informal Techniques

There are some informal techniques for how interdependencies can be dealt with (e.g., “gut feeling,” “sacred cow,” formal/informal meetings, and (half-informal) group decision support systems (GDSS)). Informal techniques are rarely mentioned in the literature compared with the more formal techniques, although, there are indications that informal techniques are widely used (e.g., a survey by Rungi [2009b] found this to be the case). For meetings and their role to closely related strategy field, see Jarzabkowski and Seidl (2008). These techniques are easily understandable by common sense. Unfortunately, these techniques produce only roughly correct decisions. However, there is scientific evidence (experiments) that decisions based on gut feelings have produced better results than ones based on formal thinking (Aru & Bachmann, 2009).

Overview of techniques taking into account interdependencies among projects in a

Figure 2: Overview of techniques taking into account interdependencies among projects in a portfolio.

The “sacred cow” is defined as a method where “the project is suggested by a senior and powerful official in the organization” (Meredith & Mantel, 1999, p. 141). “Gut feeling” refers to decisions made on the basis of intuition. Informal conversations and meetings (e.g., lobbying work, corridor discussions, and lunch table) are considered as very powerful and effective ways to influence and push one's will through.

GDSS are computerized techniques to support groups in their decision making (Kengpol & Tuominen, 2006). These interactive software techniques permit decision makers to work anonymously in parallel to find solutions for unstructured problems (ibid.; Kengpol, 2007, pp. 27–28).

How is Interdependency Handled?

Interdependencies are managed mostly in the mind. Project selection is based on intuition, projects are “driven more by personality and initiative, than by any explicit weighting of trade-offs among projects,” and the company perceives this personal involvement as a “strength” (Loch, Pich, Terwiesch, & Urbschat, 2001, p. 72). In the case of small portfolios, the responsible people are capable of considering most relationships among projects.

Mathematical Optimization Techniques

There are many models based on mathematical techniques (Coffin & Taylor, 1996, p. 208). The mathematical models usually optimize the objective function, with such constraints as resources, technology, strategy (Wang & Hwang, 2007, p. 248), and interdependencies. There are a number of modifications of integer optimization techniques, the division consists of “linear, nonlinear, integer, dynamic, goal, and stochastic mathematical programming” (ibid.). Among them, the “linear programming models assume that…no interdependencies exist” among the projects (Heidenberger & Stummer, 1999, p. 205); however, some nonlinear programming models can be equivalently formulated as linear programming models (see e.g. Anglani, Grieco, Guerriero, & Musmanno, 2005, p. 706). The method is called 0–1, “because of [its] discrete ‘select or not select' nature” (Ghasemzadeh et al., 1999, p. 746).

Integer Programming Models

In real life, there are many situations dealing with yes/no (i.e. go/no-go) decisions (Heidenberger & Stummer, 1999, p. 207). Real life offers “decision problems which are non-linear by nature” (ibid., p. 206).

How is interdependency handled?

Interdependencies among projects can be dealt with by solving the objective function (equation 1) (Ghasemzadeh et al., 1999, pp. 748–749): “



Z is a value function to be maximized, and

ai is the score of project i (for example, the AHP score)” (ibid., p. 748). “The decision variables are defined by:


for i = 1, …, N, where N is the total number of projects being considered, and

j = 1, …, T” (ibid., p. 748) where T is the total number of time periods in planning horizon with the following set of constraints for interdependency: “


“for iPl, where Pl is the set of predeccor projects for a particular project l; l = 1, …, L” (ibid., p. 749). “Di is the duration of project i” (ibid., p. 749). These constraints guarantee that “the selection of precursor projects, once a project is selected” (equation 2), and “that all the precursor projects will be finished before the successor project starts” (ibid., p. 749) (equation 3).

It is difficult to do mathematic programming manually; there are software tools to carry out these techniques (see ibid., p. 751; Loch et al., 2001, p. 76).

Goal Programming Models

According to Heidenberger and Stummer (1999, p. 208), “goal setting is a common phenomenon” in real life. Therefore, techniques supporting it are preferred as well, and goal programming (GP) approaches are used quite often (ibid.). GP “can be used when more than one objective is explicitly identified and a clear priority exists among these goals. In goal programming, multidimensional goals are met in a sequential manner, where the decision maker's preferences are used to specify goals and priorities for each objective. The goal with highest priority is given the highest weight, followed by the second highest priority and so on” (Ghasemzadeh et al., 1999, pp. 745–746).

How is interdependency handled?

Lee and Kim (2000) have developed an analytic network process within a 0–1 goal programming model for project selection. The mathematical model of GP is similar to the non-linear programming model (see the section on integer programming, earlier in this paper, for further details). Mostly the goals are traditional PPM goals.

Fuzzy Mathematical Programming Models

In mathematics, values are usually taken as exact measurements (Coffin & Taylor, 1996, p. 210), but the surrounding environment doesn't usually provide precise data. In decision making, humans are reluctant “to make unqualified predictions” (Heidenberger & Stummer, 1999, p. 211), and here fuzzy logic can help. Fuzzy logic includes the “uncertainty [factor] into decision variables,” the objectives of the selection problem can be defined as a fuzzy set (Coffin & Taylor, 1996, pp. 210–211).

There are different interpretations of the fuzzy number. In project management literature, the trapezoidal fuzzy number is mostly used (Kuchta, 2001; Carlsson, Fuller, Heikkilä, & Majlender, 2007; Wang & Hwang, 2007). “The trapezoidal fuzzy number img = (m1 m2, α, β) is defined as [equation 4]:


“where m1 and m2 are the left and right modal values and α and β are the left and right spreads” (Wang & Hwang, 2007, p. 249), where A represents the unknown quantity. The value of the function μA(x) is “the possibility distribution,” where x is a pregiven real number (Kuchta, 2001, p. 165).

Technological relationships, such as modularity, don't have such clear meaning in fuzzy mathematical programming, as in case of resource relationships. However, framework availability on time (technical relationship), has a meaning.

How is interdependency handled?

Kuchta (2001, p. 168) explains resource utilization through the fuzzy number approach: if there are S resources, then a fuzzy number represents “the [resource] utilization of the p-th resource by the i-th project.” This representation is a possibility distribution, which defines to what extent value x of the given resource “will be the actual utilization by the given project” (ibid.). Fuzzy numbers can then be used to model integer programming (see the integer programming chapter).

For an example of how fuzzy numbers are turned to integer programming, see Anglani et al. (2005).

Stochastic Programming

In stochastic programming, “at least one input is uncertain” and can vary (Heidenberger & Stummer, 1999, p. 210). The works of Medaglia et al. (2007, p. 870) discuss stochastic parameter space investigation (PSI). Through stochastic PSI, it is possible to solve the selection problem with the constraint of the relationships.

How is interdependency handled?

The method proceeds in the following way (Medaglia et al., 2007, p. 870): (1) “project [resource] allocations are generated” on the basis of constraints: lower and upper bounds; (2) “if a project allocation does not satisfy the constraints on the resources, that configuration is discarded”; (3) if the allocation satisfies the constraints, then project objectives are evaluated through simulation; (4) from the simulation results, the statistics and deviation are found; and (5) if the project allocation is not a dominant one, then “it is preserved for…the decision maker at the end of the procedure (otherwise…discarded).” The model allows project relationships to be modeled by the objective functions (Medaglia et al., 2007, p. 870) (see the integer programming chapter for further details).

Dynamic programming models

Dynamic programming (DP) is a recursive technique (Heidenberger & Stummer, 1999, p. 209). If there is “a set of sequential decisions” and the optimal path needs to be found, then this technique is worth using (ibid.).

Real options

In portfolio selection literature, there are two different techniques with the same name: one is based on the idea of a decision tree and described here; the other one is based on the scoring model and is described below.

Real options (based on the decision tree approach) are similar to financial options in that they are based on the possibility “to choose for or against something” (Carlsson et al., 2007, p. 99), and “to take stepwise decisions” based on most up-to-date information (Gustafsson & Salo, 2005, p. 946).

This approach can be used in a situation in which the project has great potential to be successful in general, but is currently having problems, and the “decision maker has the opportunity to react…in different ways” (Perlitz, Peske, & Schrank, 1999, p. 256). The decision tree consists of decision-making points, and at each decision point the decision maker has to choose between possible actions (Gustafsson & Salo, 2005, p. 950). For making that decision, the decision maker has information on what state “prevails at this point” and what actions have been taken before (ibid.).

Simulation methods are also considered to be subpart of the real options methods (see also the section on the scoring model, later in this paper). One of the most known simulation methods is the Monte Carlo method. According to Martino (1995) simulation is appropriate to be used for resource dependencies.

How is interdependency handled?

The decision tree, together with the constraints of the relationships, can be modeled through an objective function, defined by a state tree (Gustafsson & Salo, 2005). After this has been created, the objective function of the decision tree can be cast in the form of integer programming (see the section on integer programming, earlier in this paper, for further details).

Scoring Model

Scoring models use a list of criteria to rate projects. Usually there are not many decision criteria in use per one problem/situation (Archer & Ghasemzadeh, 1999a, p. 213). Each criterion is rated by evaluators (Cooper et al., 1999a, p. 107), most “typically on 1–5 or 0–10 [score] scales”. After the evaluating, the “scores are multiplied by the weightings [of the criteria], and summed across all criteria to yield a project score for each project” (op. cit., p. 107). Then the final scores are compared and projects with higher scores are selected.

How is interdependency handled?

There is some criticism about the suitability of scoring models—that is, from the mathematical point of view, the scoring model doesn't consider interdependency very well (Archer & Ghasemzadeh, 1999a, p. 214).

In the beginning, the model is similar to the traditional scoring model, but then the project selection decision is cast to the linear integer programming model (Meredith and Mantel, 1999, p. 151) (see the section on integer programming, earlier in this paper).

The unsuitability of the scoring model can be argued against. This could be the case from the mathematical point of view, and in any event it is more formal than informal techniques. The scoring model can lead to the same result as the widely used informal techniques, although Rungi and Kässi's (2009) results showed otherwise.

Real Options Reasoning (Based On The Scoring Model)

Real options are a “method for assessing uncertain projects that approximates option value through scoring a series of statements” (McGrath & MacMillian, 2000, p. 35). Method uses rated statements, which allow comparing different projects by comparing the scores. The Strategic Technology Assessment Review (STAR) statements have been developed to evaluate projects (ibid.).

How is interdependency handled?

The model contains statements, which are divided into several groups. For instance, the group “spillover” consists of statements for market and other interdependencies. The spillover group has statements whose target is to achieve cost advantages (McGrath & MacMillian, 2000, p. 43): “We may be able to use the evolving technology to reduce the cost of existing products;” “this project will create know-how and build skills that will be useful even after the project is over;” and “there is a significant danger that the product will cannibalize existing products.” These statements are rated to get the overall score for the project, under assessment.

Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP)

The analytic hierarchy process (AHP) was first introduced by Saaty in the 1970s. AHP “is a theory of measurement through pairwise comparisons and relies on the judgments of experts to derive priority scales” (Saaty, 2008, p. 83). It combines mathematics and human psychology, it cleverly uses the idea that psychologically it is easier to compare pairs than all choices at a time. It divides a problem hierarchically into smaller parts/criteria, then for each criteria, a weight is assigned according to its importance. After that, possible alternatives (e.g., projects) are evaluated against each other in pairs in the light of the criteria, to see which one is more preferred (these evaluations are later on converted to numerical values). On the basis of the given evaluations and weights, the model calculates rankings for alternatives.

AHP assumes that the criteria are uncorrelated and unidirectional (Kengpol, 2007, pp. 28–29), and therefore Saaty introduced the analytic network process (ANP), which doesn't require hierarchical dividing from general to detailed, but is based on a network with feedback loops instead (ibid.; Kengpol & Tuominen, 2006, pp. 160–161).

How is interdependency handled?

In the project selection problem, one of the criteria can be the interdependency issue. Then the projects are compared with each other to see which one is more interrelated—for example, how much other projects depend on the project or how much the project can benefit from other projects. This can be based on a subjective judgment or predicted calculated figures. Later, the given estimations for this and other criteria are used to calculate the rankings for the projects. See the section on the scoring model, earlier in this paper, as well.

Dependency Matrix

Dickinson, Thornton, and Graves (2001, p. 523) have created a dependency matrix.

How is interdependency handled?

The “dependency matrix is a square matrix” (Dickinson et al., 2001, p. 523), where each project represents one column and one row. Each element of the matrix dij represents the dependency that project i has on project j. The value must be between 0 and 1. A value 0 means that the “project i is entirely independent of project j” (ibid.). A value of 1 means the opposite—that is, “that project i is entirely dependent on project j” (ibid.). In the latter case, it is good to combine these two projects for the next portfolio selection meeting. The matrix makes it possible to calculate how much of a project's revenue comes from its interdependencies, as well as the percentage of the dependency of project i on project j.

For this purpose, input variable “minimum benefit level” (Mi) is used: “Mi is the percent of revenue expected if project is funded without funding the projects it depends on” (Dickinson et al., 2001, p. 523). “The remaining benefit of project i (1- Mi) is allocated to its dependent projects,” and the value of “W ij is the percentage dependency of project i on project j” (equation 5): “


where np is number of projects (ibid.).

Visual Techniques

Visual methods visualize relationships between projects, and there are different approaches with different notification systems (i.e., elements of how the project is presented on a diagram). According to Cooper et al. (1999a: p. 33), “many portfolio models yield information overload.” Decision makers want easily understandable solutions, and visual techniques have been popular for years. There are few visual techniques concerning interdependencies. Few of them are described here.

Design Structure Matrix

The design structure matrix (DSM) is similar to the dependency matrix discussed earlier. DSM is a square matrix, where each element (e.g., project, module) is represented by one column and one row. DSM was originally constructed by Warfield in the 1970s and Steward in the 1980s (MIT DSM Research Group).

How is interdependency handled?

The relationship between projects is marked (MIT DSM Research Group). For example, if project i gets input from projects j and k, then the corresponding matrix element (row i, column j and row i, column k) are marked. If the same project i gives output to project s, then the matrix element (column i, row s) are marked. If there is no relationship between two projects, then the corresponding place is left empty.

DSM can be used to represent static (clustering algorithm) and time-based (sequencing algorithm) relationships (Danilovic & Browning, 2007, pp. 302–304). The clustering algorithm is useful for “grouping highly related” modules as technological components of projects (Danilovic & Browning, 2007, p. 302) “into larger ‘modules'” (Hellström, 2005, p. 38), the sequencing algorithm can be used to “maximize the feed-forward flow of provided information and materials” (Danilovic & Browning, 2007, p. 302). As a result of the sequencing algorithm, it becomes clear which activities can be run simultaneously, plus it allows feedback loops to be removed (ibid., p. 302).

See also the section on the dependency matrix, earlier in this paper.

Program-Level Network

Thiry (2004, p. 275) proposes the trivial arrow diagramming method (ADM).

How is interdependency handled?

In this visual method the interdependencies are dealt with by “activities-on-arrow or a milestone chart” (Thiry, 2004, p. 273). The relationships are visualized by one-headed arrows. The arrow points to the direction of relationship.

Nested Options Model

Bardhan, Bagchi, and Sougstad (2004, pp. 33–34) have developed a model to value and prioritize projects.

How is interdependency handled?

The model of Bardhan et al. (2004) consists of visual and mathematical parts, so it is not a pure visual method. The mathematical part is a binomial model, which can be cast by the integer programming model (Bardhan et al., 2004) (see the section on the integer programming model, earlier in this paper). In the visual part, the relationships are again visualized by one-headed arrows, and projects are visualized as boxes.


Groenveld (1997) has developed a trivial method, which is based on “precedence relationships between projects” (Bardhan, 2004, p. 35). In addition, it links projects with objectives and technologies (ibid.).

How is interdependency handled?

Groenveld's approach is not a pure interdependency approach. Roadmapping integrates business objectives and technology (Groenveld, 1997, p. 48), and relationships between them are presented by arrows across time.

Intra-dependency Index

Vaidya and Kumar (2003, pp. 1099–1100) introduce a classification of interdependency as: (1) “extrovert dependency” (how many components depend on any specific component); (2) “introvert dependency” (how much one component depends on other components); and (3) “self dependency” (how much one component depends on itself).

How is interdependency handled?

The model of Vaidya and Kumar allows computing the introduced dependencies, and finding most critical and least important components within the system. They mention that the “higher the value of the intra-dependency index, [the] more sensitive will be the system to failure/partial-failure of the constituents; and hence, there is a greater need to design the system with great concern for better reliability” (Vaidya & Kumar 2003, pp. 1099–1100).

Main Pros and Cons of the Techniques

No model is perfect, and even the best one has its limits. The appendix presents the pros and cons of the techniques from the literature.

In addition, empirical evidence was collected from northern Europe to find out main problems (Rungi, 2009b) and the extent of advantages from techniques (Rungi & Kässi, 2009). With regard to the techniques, the following general problems were reported: not enough time to implement corresponding procedures, lack of knowledge, and that techniques can consider only limited number of relationships (Rungi, 2009b). Also, the influence from the use of techniques to the success rate and resource reduction was analyzed. Best success rate values were “achieved by mathematical methods, dependency matrix, and some visual methods …. [T]he usage of informal methods ends with worse results. Very surprisingly, the same can be claimed for popular scoring model.…Predictably, the usage of mathematical methods resulted in shortest length of projects among the users of interdependency…[S]urprisingly, the usage of scoring model increases the length of project for users of interdependency” (Rungi & Kässi, 2009).


This literature review has focused on giving a comprehensive overview of portfolio selection techniques concerning interdependencies among projects.

There are a great many interdependency techniques available, most of which are theoretically strong and complex, but there are considerably fewer visual techniques, which have shown to be very usable and popular among decision makers. In addition, descriptions of these techniques are dispersed over many different sources, and not in one place, making it difficult for the decision maker to choose the right one. Although there is much research on interdependency, prior publications have not given a full review of all available techniques in one paper. The main contribution of this paper is a compact overview of the main relationship techniques, including their advantages and disadvantages, and descriptions of how interdependency is handled. In addition, the classification of techniques has been developed further and some criticism given in addressing the techniques.

This bibliometric study also has limitations. First, no research can be absolute, and as this research is based only on articles searched from online databases, with a given set of search keywords and within certain time period, there is a chance that not all techniques are covered. However, on the basis of performed study, it can be claimed that the most influential solutions are covered. Secondly, during the study, greater emphasis was placed on describing the techniques in general, not introducing certain software packages where relationship techniques are implemented (e.g., enterprise resource planning [ERP]).

Future research will pursue empirical work to test the existing theories in practice and find out what concerns companies most when dealing with the interdependency issue today.


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Appendix: Main Pros and Cons of Relationship Techniques

Technique Pros Cons
General techniques
  • Easy to understand and use.
  • “Individual persons' opinions or single criteria have too much influence on selection” (Piippo, Kärkkäinen, Ojanen, & Tuominen, 1999).
Informal methods (IM)
  • IM are widely usable, very common to people's behavior in real life.
  • A very powerful and quick way to make a decision.
  • IM are roughly right.
Group Decision Support System (GDSS)
  • GDSS allows enhancement of ideas, thanks to provided anonymity (Kengpol, 2007, p. 28) and “controlled feedback” (Heidenberger & Stummer, 1999, p. 204).
  • GDSS is ineffective for meetings of less than four and more than 20 participants (Kengpol, 2007, p. 28).
  • GDSS slows down communication speed in meetings, most ideas are not presented verbally, but instead through anonymous entering via software (ibid.).
Scoring model (SM)
  • - Real options reasoning (based on the scoring model)
  • SM allows “integration of quantitative and qualitative attributes” (Archer & Ghasemzadeh, 1999a, p. 213).
  • “Projects can be added or deleted [into SM] without affecting scores of other projects” (Heidenberger & Stummer, 1999, p. 200).
  • Decisions are with good quality (“85% predicative ability”) and the decision process forces evaluators to discuss (Cooper, Edgett, & Kleinschmidt, 1998, pp. 50–51).
  • From mathematical point of view, SM doesn't consider interdependency very well (Archer & Ghasemzadeh, 1999a, p. 214), with the exception of Dean's method (Meredith & Mantel, 1999, pp. 153–156).
  • SM doesn't “concern about the right balance of projects in the portfolio” (Cooper et al., 1998, p. 13).
  • SM is difficult to use at a review meeting, since “much of the data” (weights etc.) have to be provided “at the meeting,” not easy for evaluators (Cooper et al., 1998, p. 44).
  • SM doesn't consider risks (Archer & Ghasemzadeh, 1999a, p. 214).
Analytic Hierarchy Process (AHP)
  • AHP allows pairwise comparison, which is easier for most people than making comparisons all at one time.
  • AHP allows integration of quantitative and qualitative attributes (Kengpol & Tuominen, 2006, p. 168).
  • “AHP is relatively simple on its procedure” (Iamratanakul, Patanakul, & Milosevic, 2008, p. 291).
  • AHP cannot be used if the decision problem cannot be hierarchically structured (Kengpol & Tuominen, 2006, pp. 160–161).
  • “AHP is subjective in nature” (Iamratanakul et al., 2008, p. 291).
Analytic Network Process (ANP)
  • Network nature of presenting criteria helps one to go more deeply into the subject than in AHP (Kengpol, 2007, p. 29).
  • In ANP “more complicated relationships can be analyzed …, e.g. inner relationship or self-influenced relationship itself” (Kengpol, 2007, p. 29).
  • ANP is more complex and time consuming than AHP (Kengpol & Tuominen, 2006, p. 161).
Dependency matrix (DM)
  • Projects can be easily added or deleted in DM (Dickinson et al., 2001, p. 523).
  • DM is a compact way to present relationships.
  • The mathematics involved with DM may make it less popular among decision makers.
Mathematical techniques (MTs)  
  • MTs are based on financial data, which is unreliable in the early phases of a project (Cooper et al., 1999a, p. 33) or cannot easily be provided by the management (Heidenberger & Stummer, 1999, p. 205), including financial data, “timing information, resource needs,” and success rates (Cooper, 1997, p. 171).
  • MTs can consider only a limited number of interdependencies, otherwise the methods get computationally very complex (Santhanam & Kyparisis, 1996, p. 384).
  • MTs are not popular among decision makers (Cooper et al., 1999a, p. 29; Meredith & Mantel, 1999, p. 164), due to the complex mathematics. Often, interpretation of the results may remain unclear among the decision makers.
  • Due to the complexity (Loch et al., 2001, p. 76) supportive tools are required, hard to be solved manually, not doable in practical situations.
  • MTs don't consider risks (Gustafsson & Salo, 2005, p. 947; Archer & Ghasemzadeh, 1999a, p. 220; Loch et al., 2001, p.71).
  • “Analytical models are often incomplete and fail to capture adequately all relevant considerations” (Loch et al, 2001, p. 75), such as strategy “alignment problems that are based on central tendency approach” (Iamratanakul et al., 2008, p. 291).
Nonlinear integer programming (NLIP)
  • NLIP can consider many “different combinations of candidate projects” in a portfolio (Archer & Ghasemzadeh, 1999a, p. 219).
  • NLIP considers simultaneous projects (ibid.).
  • NLIP “explicitly considers resource limitations throughout the entire planning period” (ibid.).
  • Improves “problem formulation: the way managers think about their problems” (Loch et al., 2001, p. 78).
  • For some, “higher transparency of decisions,…more fact based decisions” (Loch et al., 2001, p. 77) and the decision making “remains transparent to the host organization” (ibid., p. 78).
  • NLIP doesn't fit for large portfolios, they have computational problems (Kleinmuntz, 2006, p. 15).
  • Robustness (Loch et al., 2001, p. 76).
Goal programming (GP)
  • It is argued that “GP is closer to the reality…than other multi-criteria decision-making techniques” (Heidenberger & Stummer, 1999, p. 208).
  • GP is “capable of handling reasonable large 0–1 problems” (Ghasemzadeh et al., 1999, p. 746).
  • “Criteria measured in incommensurable units can be kept separate during optimisation and don't have to be combined directly” (Ghasemzadeh et al., 1999, p. 747).
  • The goals must be specified in advance (Heidenberger & Stummer, 1999, p. 205), which people are reluctant to do.
  • Only “one (the optimal) proposal is received, no additional information about alternatives” (Heidenberger & Stummer, 1999, p. 208), to choose between them.
Fuzzy mathematical programming (FMP)
  • FMP methods can consider imprecise information (Wang & Hwang, 2007, p. 248).
  • FMP methods consider interdependencies between two projects (Kuchta, 2001, p. 164).
  • Decision-maker has to define at least three values for each fuzzy variable – minimum, maximum, and most possible (Anglani et al., 2005, p. 707).
  • FMP methods make “restrictive assumptions about the uncertainty” (Gustafsson & Salo, 2005, p. 947).
Stochastic programming (SP)
  • SP is easy to implement (Medaglia et al, 2007, p. 871).
  • SP “accounts uncertainty in the objectives” (ibid.).
  • SP can consider “project selection problems of a limited size (less than ten variables)” (Medaglia et al., 2007, p. 871).
  • The efficiency of SP “is dependent on the relative size of the feasible region” given by the bounds, explicit and tight bounds are required (ibid.).
Dynamic programming (DP)
  • DP is suitable for sequential decision making and finding the optimal path (Heidenberger & Stummer, 1999, p. 211).
  • In DP, “only one resource constraint” can be taken into account throughout “a project's life” (Heidenberger & Stummer, 1999, p. 209).
  • DP has “computational problems” (ibid.).
- Real options (based on the decision tree approach)
  • Real options “helps translate project options into visualize effect” (Iamratanakul et al., 2008, p. 291).
  • The size of the real options state tree can become very large. Even if there are no interdependencies, the state of the tree is still “2n, where n is the number of projects” (Gustafsson & Salo, 2005, p. 953).
  • The real options model assumes that the “cash flows from the project can be replicated…for all states,” which is not realistic in some circumstances (e.g., in case of innovative products) (Gustafsson & Salo, 2005, p. 947).
  • Real options “requires extensive data and analysis” (Iamratanakul et al., 2008, p. 291).
Visual methods
  • Easily understandable.
  • Easily programmable.
  • Visual models don't stand on a strong mathematical base (Cooper et al., 1998, p. 59) – less precise, they are recommended to be used together with other methods.
  • Visual methods based on financial data are unrealistic in the early phases of a project (Cooper et al., 1999b, p. 114).
  • Unable to visualize the extent of contingency.
Design structure matrix (DSM)
  • The DSM way to present projects is very compact, the number of projects doesn't influence the readability of the matrix (MIT DSM Research Group).
  • DSM is rather meant to identify modularity, not managing relationships between projects (MIT DSM Research Group).
  • The roadmapping method “does not address the balance of the portfolio or maximize its financial return” (Dickinson et al., 2001, p. 519).
Program-Level Network (Thiry, 2004)  
  • Not enough to manage the whole complexity provided by the relationships.
Nested Options Model (Bardhan et al., 2004)
  • Allows visualizing the extent of contingency in scale of soft/hard.
  • Usable only in small portfolios.
Intra-dependency Index (Vaidya & Kumar, 2003)
  • Contains a mathematical model, more precise than the average visual method.
Overall remarks  
  • “Tools are too time-consuming.”
  • Techniques are not “easy to use” and there exists ignorance of how to apply them.
  • “Problems in selecting a suitable method for different business purposes”

(Koivuniemi & Edelmann, 2003, pp. 1–2).

  • “There is a lack of practical tools for prioritization and selection in companies.”
  • “The selection criteria are unclear and inexplicit.”
  • “Decisions are made project by project”

(Piippo et al., 1999).

  • Experts may be in different locations (Cooper et al., 2006, p. 3) and time zones (Koivuniemi et al., 1999).


1 Interdependency management is also called “coordination” (Dietrich, 2007, p. 20).

2 The bibliometric study of Artto, Martinsuo, Gemünden, and Murtoaro (2008, p. 11) did not find “program” and “multiproject” to be related in business literature, however “program” was not left out due to close lingual similarity to “multiproject.”

© 2010 Project Management Institute



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