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Top1. Introduction
Decision analysis has for a long time dealt with problems that consider individual, mutually exclusive decision alternatives and has formulated problems such as choice problems, in which a single alternative has to be chosen, or ranking and sorting problems, in which individual alternatives are ranked or assigned to predefined categories (Roy, 1971). More recently, researchers have begun to study problems of portfolio decision analysis (Salo et al., 2011), in which several alternatives can be implemented simultaneously. Portfolio decision problems are relevant in many applications, such as research and development projects (Heidenberger and Stummer, 1999), planning of human resources in projects (Gutjahr et al., 2010), environmental decisions (Huang et al., 2011) or decision about information technology infrastructure (Angelou and Economides, 2008).
As long as only one alternative can be selected in a decision problem, inter- dependencies between alternatives are not relevant. However, this is no longer true in portfolio problems, where several projects can be realized together. Early models of portfolio decisions and project selection (Stummer and Heidenberger, 2003) were mainly concerned with interdependencies in the implementation of projects, e.g., that one project can only be carried out if another project is also carried out, or that two projects are mutually exclusive. In the present paper, we deal with interactions in the form of positive or negative synergies of projects. For example, execution of one project might have a positive or negative impact on the payoff of another project, or two projects might be able to share some resources, leading to synergies in their resource consumption.
Considering the presence of interactions among projects is not so new in the literature, the first studies on the subject date back to 1963 (Reiter, 1963). However, most studies do not consider interactions in the project portfolio selection process or consider only those that affect the viability of a specific project (Abbassi et al., 2014, Rungi, 2010).
Interactions between projects can affect more than just a project’s viability. Aaker (Aaker and Tvebjee, 1978) cites three types of interactions: (1) Overlap in resource utilization (reduction of project resource consumption based on shared results, effort, equipment among others); (2) Effect interdependencies (the result of a project is affected by the result of one or more other projects); (3) Technical interdependencies (the success of one project affects the chance of success of one or more other projects). The first type of interaction has an impact on resource consumption, which is generally a coefficient on the left side of the inequality of at least one of the constraints of the knapsack problem. Typically, such interactions lead to resource savings. Consequently, this increases the number of projects in the set that can be implemented, with the potential to indirectly increase the value of the final solution. The second type of interaction directly affects the value of the projects, being able to increase or decrease it. This does not affect feasibility, but has a direct impact on the objective function of the decision problem. The third type of interaction affects the chance of success for projects, which may affect criteria associated with project and portfolio risks or the value of utility, depending on the approach used in calculating the value of projects and the portfolio. None of these interactions defines that a specific project becomes feasible or unfeasible for a given portfolio, but it affects (directly or indirectly) how much the project can contribute to the objectives of the decision.
Some studies show the importance of interactions in different real application contexts, such as R&D (Abbassi et al., 2014, de Almeida and Duarte, 2011, Aaker and Tvebjee, 1978, Stummer and Heidenberger, 2003), telecommunication (Jafarzadeh et al., 2018), information technology (Ghapanchi et al., 2012) and infrastructure (Iniestra and Gutierrez, 2006). There are also studies related to the sources of interactions among projects, such as aspects related to human resources involved in the projects (Rungi, 2018), compatibility of technologies involved in the implemented projects (Ghapanchi et al., 2012) and partnerships between organizations that execute the projects (Wassmer and Dussauge, 2011).