ИЗВЕСТИЯ РАН. ТЕОРИЯ И СИСТЕМЫ УПРАВЛЕНИЯ, 2011, № 6, с. 88-98
СИСТЕМЫ УПРАВЛЕНИЯ ТЕХНОЛОГИЧЕСКИМИ ПРОЦЕССАМИ
УДК 62.40
A MILP BI-OBJECTIVE MODEL FOR STATIC PORTFOLIO SELECTION OF R&D PROJECTS WITH SYNERGIES
© 2011 г. I. Litvinchev, F. López, H. J. Escalante, M. Mata
Russia, Moscow Computing Center Russian Academy of Sciences Faculty of Mechanical and Electrical Engineering, UANL Received November 05, 2010
This paper presents a multi-objective MILP model for portfolio selection of research and development (R&D) projects with synergies. The proposed model incorporates information about the funds assigned to different activities as well as about synergies between projects at the activity and project level. The latter aspects are predominant in the context of portfolio selection of R&D projects in public organizations. Previous works on portfolio selection of R&D projects considered interdependencies mainly at the project level. In a few works considering activity level information the models and solution techniques were restricted to problems with a few projects. We study a generalization of our previous model and show that incorporating interdependencies and activity funding information is useful for obtaining portfolios with better quality. Numerical results are presented to demonstrate the efficiency of the proposed approach for large models.
INTRODUCTION. The evaluation of a set of project's proposals having social impact and competing for funding is a very important task in government and social (nonprofit) organizations. Usually, available funds are not sufficient to support all of the funding applications. Thus it is necessary to select a subset of proposals for funding, that is, a portfolio of project's proposals. The selected portfolio has to fulfill certain constrains determined by public regulation and also has to maximize a certain portfolio impact measure (e.g., social, politic, economic, etc.) [1]. Therefore, portfolio selection it is a very challenging task for decision makers.
In 2007 the World Bank Group appointed more than 8 billion dollars for funding public and private projects; in 2006 the United Nations Organization (UNO) and the European Union launched a humanitarian project for the Democratic Republic of Congo, the goal of this effort was to fund about 300 projects with an amount of 681 millions of dollars approximately; in 2008, eight field projects were carried out with support of the Spain-FAO Group with an inversion of about 20 millions dollars (see [2] and the references therein). These facts demonstrate that the portfolio selection problem is very important for the community and that poor solutions to this problem may result in negative social impacts.
The problem of portfolio selection in the context of research and development (R&D) projects arises in the following situation. A call for R&D project's proposals is launched by international (e.g., UNO) or nationwide organizations (e.g. National Science Foundation, NSF). Applicants submit project's proposals that require funding from the organization. The organization launching the call has a limited budget that must be distributed among a subset of the submitted proposals. Proposals can be considered in one of several areas and funding for each accepted proposal is limited by certain upper and lower bounds. The problem consists of deciding what projects to fund and how many projects can be supported [2]. There are two sub-problems related to the portfolio selection: projects' evaluation: usually made by peers reviewers,
projects' selection: made by stakeholders, which base their decisions on peers' evaluations and submitted documents.
In this paper we face the second subproblem in the context of R&D projects, assuming that all of the projects have been previously evaluated by a peer committee. A complete procedure for projects' evaluation can be found in [3].
The problem of portfolio selection of social projects is characterized as follows:
there resources are not sufficient to support all the proposals.
there may be interactions between projects affecting resource assignment.
it is desirable to select a portfolio of projects that maximizes some social goals.
The portfolio optimization of R&D projects has the additional features:
projects funds are distributed among a set of general activities that are common to all projects (e.g., equipment inversion, scholarships, etc.).
each project is associated to a certain area from the list of admissible areas.
all projects start at the same date and are expected to be finished at the same date as well.
it is desirable to select a portfolio that maximizes some impact measures.
Most published works on R&D project's portfolio optimization in public organizations consider money as the unique resource to be distributed among projects and this is treated as indivisible element (i.e., a sort of black box assignment). However, in calls for proposals launched by important R&D organizations (e.g., NSF (USA), RFBR (Russia) or CONACYT (Mexico)) a project leader has to provide a detailed report on the activities submitted for funding, with a specification of the amount of funds requested for each activity. Then during the revision process peers can modify requested funds according to their evaluation of the reviewed project, if they think the funding request does not correspond to the possible impact of the project.
The following are the main difficulties associated to the problem of portfolio selection of R&D projects in public organizations:
1) intangible assets should be considered when implementing an impact measure,
2) for a large set of proposals it is difficult to evaluate if a portfolio will fulfill organization's goals,
3) interdependences make the models harder to solve and introduce nonlinear relations,
4) when a peer suggests reducing the requested funds it is difficult to estimate the impact of this reduction in the fulfillment of project's objectives.
In [4, 5] there has been proposed a complete decision framework for R&D projects portfolio optimization in public organizations based on decision theory, fuzzy sets, rough sets, and decision support systems. Meanwhile these approaches are only applicable for middle size instances (about 400 projects).
The approach presented in [2] permits to solve instances with up to 25000 projects by using mixed integer linear bi-objective optimization models. The objectives to maximize are portfolio quality measure and the quantity of funded projects, thus, it can be said that [2] successfully addressed difficulties 1—2.
In all the above mentioned works interdependences among projects have not been considered, the assignation of funds was modeled at the project level only. However, the interdependences are actually taken into account for activity funding and to measure the project impact. Therefore, it is crucial to include that information into the model. To the best of our knowledge this problem has not been addressed so far in a general framework. In earlier works [6, 7], and more recently in [8—11] the authors present approaches applicable for a few projects. In [10, 11] the interdependency effects among the projects were considered. Nevertheless, in these works funding at the project's activities level has not been modeled. Moreover, the impact of the interdependences on the portfolio optimization has been studied. So we may conclude that the difficulties 3 and 4 have not been successfully addressed.
In this paper we present a MILP bi-objective model for static portfolio selection of R&D projects with synergies. The project's activities to be funded (inversion in equipment, buying books, participation in academic meetings, scholarships, etc.) are considered in the model. The interdependences at the activity level are introduced and an efficient MILP approach to resolve the portfolio problem in large public organizations is developed. The model presented in this paper addresses difficulties 1—4.
The rest of this paper is organized as follows. Section 1 presents some background information. The model is considered in Section 2, while Section 3 reports computational results. The last section presents conclusion remarks and outlines future work directions.
1. BACKGROUND. In the normative approach presented in [3] it was combined a nonlinear preference model derived from a fuzzy generalization of the classical 0—1 programming and the multiattribute decision theory. For medium size instances (up to hundreds projects) the corresponding nonlinear optimization problem was solved using genetic algorithms, neural networks [4] and differential evolution [5].
The main parameters of the model considered in [3] are as follows:
N (N > 1): the number of proposals participating in the call, which after a pre-screening process are certified to adhere to certain minimal acceptance criteria;
K (K > 1): the number of areas of interest. These areas may reflect the organizational structure of the institution or present the interest of the institution to balance the portfolio. It is assumed that each proposal must belong to a single area;
Mj — the amount of monetary resource required to satisfy completely the financial requirement of project j;
mj — the minimum amount of monetary resource still sufficient to execute the project. That is, if funding is less than mj there will be serious reasons to think that project j is not adequately funded;
PG — the total amount of money available for funding projects registered in the call;
Pj+ — the maximum amount of money assigned to projects of area i;
Pi — the minimum amount of money assigned to projects of area i; Decision variables dj represent the amount of money assigned to project j;
The multiobjective optimization model presented in [5] is sated as follows. The feasible region is defined by:
N
X Sj ^ (1.1)
J = i
N
X^(dj) ^ (L2)
j = i N
Xdj - Pg < 0, (1.3)
j = i
X dj - Pi+ < 0, (1
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