Solving a comprehensive model for multiobjective project portfolio selection

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Abstract

Any organization is routinely faced with the need to make decisions regarding the selection and scheduling of project portfolios from a set of candidate projects. We propose a multiobjective binary programming model that facilitates both obtaining efficient portfolios in line with the set of objectives pursued by the organization, as well as their scheduling regarding the optimum time to launch each project within the portfolio without the need for a priori information on the decision-maker's preferences. Resource constraints, the possibility of transferring resources not consumed in a given a period to the following one, and project interdependence have also been taken into account. Given that the complexity of this problem increases as the number of projects and the number of objectives increase, we solve it using a metaheuristic procedure based on Scatter Search that we call SS-PPS (Scatter Search for Project Portfolio Selection). The characteristics and effectiveness of this method are compared with other heuristic approaches (SPEA and a fully random procedure) using computational experiments on randomly generated instances.

Statement of scope and purpose

This paper describes a model to aid in the selection and scheduling of project portfolios within an organization. The model was designed assuming strong interdependence between projects, which therefore have to be assessed in groups, while allowing individual projects to start at different times depending on resource availability or any other strategic or political requirements, which involves timing issues. The simultaneous combination of project portfolio selection and scheduling under general conditions involves known drawbacks that we attempt to remedy. Finally, the model takes into account multiple objectives without requiring a priori specifications regarding the decision-maker's preferences.

The resolution of the problem was approached using a metaheuristic procedure, which showed by computational experiments good performance compared with other heuristics.

Introduction

Any organization needs to continuously invest in both consecutive and simultaneous projects to guarantee healthy and profitable growth. However, organizations are often confronted with having more projects to choose from than the resources to carry them out and thus one of the main management tasks is to select from an array of projects those better adapted to the organization's objectives [1]. Wrong decisions in project selection have two negative consequences. On the one hand, resources are spent on unsuitable projects and, on the other hand, the organization loses the benefits it may have gained if these resources had been spent on more suitable projects [2].

In this context, a project is a unique and unrepeatable temporal process having a set of specific objectives. Throughout this work we regard a project as a whole, without taking into consideration that it can be broken down into a set of activities or tasks [3]. In addition, the project cannot be divided in order to execute some parts of it, although different versions of a single project can be addressed, as long as each version is treated as an indivisible proposal.

On the other hand, a project portfolio is a set of projects that share resources during a given period, among which there may be complementarity, incompatibility or synergies produced by sharing costs and benefits derived from conducting more than one project at the same time [4]. This means that it is insufficient to simply compare two projects, but rather we need to compare groups of projects [5] in order to identify the one best adapted to the needs of the organization.

A great variety of methods for project selection exist in the literature [6]. The scoring method [7], [8], the multiattribute utility theory [9] and the analytical hierarchy process [10] are among the most widely used. These models aim at ranking the project set, after which resources are distributed following the priorities established in the ranking. However, this approach assumes that candidate projects are independent, which is not always true, and the interrelationships among them [11], [12] means that the best individual projects do not necessarily make the best portfolio [5]. Neither are these methods applicable in situations with multiple constraints (e.g. resource, strategic or political constraints) [13]. These limitations have led to increasing interest in mathematical programming models as they can integrate such considerations into the project portfolio selection process. This interest is supported by advances in the technical procedures used to solve the models generated [14].

Many works emphasize the importance of taking into account the interdependence between projects (see [4], [2], [15], [16], [17], [12], [18]), for a suitable selection of project portfolios. A significant advance in this field was made by Stummer and Heidenberger [19] who designed a more flexible formalization of the interdependences between any given number of projects. To this end, they introduced an additional term into the corresponding assessment function that activated when the portfolio had at least (or at most) a given number of projects (NP) with a positive (or negative) synergy between them. In the present paper, the proposed model follows this approach in a more general way.

Many other models consider the selection process for a specific period only [15], [20], [18] or, if they include a planning horizon, it is assumed that all the projects selected start at period one [19]. This can lead to some projects not being implemented because of a lack of resources in a given period, whereas it would be possible to implement them if the model allowed flexibility concerning the moment of starting of the projects. The latter option involves simultaneous scheduling and selection, but the greater complexity involved may account for the fact that this approach has been little studied in the literature. The works of Sun and Ma [21], Ghasemzadeh et al. [1] and Medaglia et al. [22] are among the few that study the simultaneous selection and scheduling of project portfolios. Nevertheless, Sun and Ma [21] only deal with one objective, whereas the other two works do not take into account possible synergies between projects, and so the value of the portfolio is obtained by simply summing the value of each individual project.

Within the wide field of multiobjective programming applied to project portfolio selection, some works use goal programming ([20], [17], [23] among others), where it is assumed that decision-makers are able to set up target values for their objectives, and where information is available regarding their preferences. Other authors, such as Ghasemzadeh et al. [1] and Medaglia et al. [22], integrate the different objectives into a single function by assigning different weighting scores to each objective according to their importance to the decision-maker. Klapka and Piños [18] minimize the distance to the ideal point. Finally, some works do not use a priori information about the decision-maker's preferences to obtain the set of efficient solutions, but include such preferences at a later stage using interactive techniques [24], [19]. Although there are many techniques available to carry out this interactive process, identifying the set of efficient solutions remains a challenge [25].

The way these models have evolved ultimately reflects the attempt to deal with the different aspects involved in project portfolio selection in such a way that the decision-making process gains in rigor and transparency. Such models also need to be flexible enough to be accepted by managers [26]. Our work proposes a nonlinear combinatorial multiobjective model which simultaneously combines the selection and scheduling of project portfolios under general conditions making it applicable to public and private settings. To this end, we have taken into account different types of interactions between candidate projects and the possibility of transferring nonconsumed money resources from a given period to the following one, as well as the availability of resources or other strategic or political requirements in different periods. Furthermore, we introduce multiple objectives without the need for a priori information on the decision-maker's preferences.

From the mathematical standpoint, the proposed model is an NP-hard problem [27]. Solving such a problem with an exact algorithm is computationally very expensive or even impossible in some cases, which has led to increasing interest in the use of heuristic procedures [28], [18], [29], [25], [30]. These procedures offer a good compromise between the quality of the solution obtained and run-time. There are several multiobjective versions of Genetic (GA), Simulated Annealing (SA) and Tabu Search (TS) algorithms [31]. In this work, we develop a metaheuristic algorithm that we call SS-PPS (Scatter Search for Project Portfolio Selection), which is an adaptation of the SSPMO evolutionary method (Scatter Search Procedure for Multiobjective Optimization, Molina et al. [32]) used to determine the set of efficient portfolios for the selection and scheduling of project portfolios.

This paper is structured as follows: we formalize the model proposed in Section 2; in Section 3 we analyze the metaheuristic procedure used to solve it; Section 4 presents the instances and discusses the results; the final section offers the conclusions.

Section snippets

Selection and scheduling of project portfolios model

Let us assume an organization with I project proposals from which we have to select the best portfolios according to a set of objectives and some constraints. We also want to specify when each project will start within a given planning horizon (PH) divided into T periods.

Thus, the decision-making variable is denoted by xit (i=1,…,I; t=1,…,T) and is defined byxit={1ifprojectistartsatt0otherwiseand thus x=(x11,…,x1T,x21,…,x2T,…,xI1,…,xIT,) is a vector with T·I binary variables which represent one

Scatter Search for Project Portfolio Selection (SS-PPS)

Multiobjective optimization is one of the research areas in which the use of metaheuristic algorithms is becoming more popular. The majority of exact techniques are designed for continuous and discrete linear problems, but when the problem involves a considerable degree of difficulty (such as nonlinear functions or constraints) the resolution can be very expensive or even unfeasible. However, these types of difficulties are very common when faced with the real-life problems of Multiobjective

Computational experiments

This section presents a set of computational experiments designed to test the performance of SS-PPS.

To this end, a large battery of 52,272 instances was generated, of which 760 were solved. These attempted to address all the possible scenarios that arise in real life when selecting and scheduling project portfolios. Of these, 523 included maximizing objective functions only, and the remaining 237 included both maximization and minimization objective functions. To make the resolution times

Conclusions

This work proposes a model for the project portfolio selection problem where we simultaneously tackle two different problems: how to select and schedule (choosing the starting point in time) efficient project portfolios. These two processes have to be considered interdependent if we want to distribute the resources better over the planning horizon. Our model includes some key elements required to make a suitable selection: multiple objectives which are often in conflict with each other; uneven

Acknowledgments

The authors wish to express their gratitude to the referees for their valuable and helpful comments, which have contributed to improve the quality of the paper. This research has been partially founded by the research projects of Andalusian Regional Government and Spanish Ministry of Educacion y Ciencia.

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