A zero-one model for project portfolio selection and scheduling

Abstract

A zero-one integer linear programming model is proposed for selecting and scheduling an optimal project portfolio, based on the organization's objectives, and constraints such as resource limitations and interdependence among projects. The major contribution of the paper is that the proposed model not only suggests projects that should be incorporated in the optimal portfolio, but it also determines the starting period for each project. Scheduling considerations can have a major impact on the combination of projects that can be incorporated in the portfolio, and may all ow the addition of certain projects to the portfolio that could not have been selected otherwise. Moreover, the model handles situations that frequently happen in real world applications, in which the amount of available and consumed resources varies in different periods. An example problem is described and solved with the proposed model to ill ustrate the approach, and some areas for future research are discussed .

Contingent Portfolio Programming for the Management of Risky Projects

“…Although several approaches based on utility functions (see, e.g., Mehrez and Sinuany-Stern 1983), fuzzy set theory (see, e.g., Decision trees X X X Real options X X Key: CO = correlation or other probabilistic interaction between project outcomes, FP = follow-up projects, PV = project versions, RC = resource constraints, RD = resource dynamics, RN = reaction to new information, SY = synergies (cross terms for project outcomes), VA = variability aversion, X= feature present in basic model, C = chanceconstrained model 26/11/2003 16:06 4 Booker and Bryson 1985, Weber et al 1990, and chance-constraints (see Gear et al 1971, Jackson 1983, Czajkowski and Jones 1986 have been proposed, the resulting models are problematic as they rely on restrictive assumptions about the nature of uncertainty or the DM's risk preferences. For example, the models of Gear and Lockett (1973) and Heidenberger (1996) do not account for the variability of portfolio returns, even though the DM may react to new information.A further limitation of some optimization models (e.g., Gear and Lockett 1973, Czajkowski and Jones 1986, and Ghasemzadeh et al 1999) is that project inputs are separated from outputs, wherefore projects cannot produce inputs for other projects, for instance. These models typically assume that there exists a predefined, static supply of resources in each time period (see, e.g., Ghasemzadeh et al 1999 andGear and which makes it impossible to invest profits for later or immediate use.…”

“…These projects involve many characteristics -such as uncertainties and interdependent resource constraints -that are potentially amenable to analysis by OR techniques. Indeed, there exists a variety of related methods, ranging from scoring methods such as value trees (e.g., Keeney and Raiffa, 1976) and the Analytic Hierarchy Process (AHP; Saaty 1980) to optimization models (see, e.g., Luenberger 1998, p. 106, Gear et al 1971, Baker 1974, Baker and Freeland 1975, Jackson 1983, Fox et al 1984, Schmidt and Freeland 1992, Ghasemzadeh et al 1999 and dynamic programming methods such as decision trees and real options (Hespos and Strassmann 1965, Dixit and Pindyck 1994, Trigeorgis 1996. Yet, despite this plethora of methodological approaches, the industrial uptake of these methods has remained limited (see, e.g., Liberatore and Titus 1983), possibly due to the difficulties of capturing the full range of phenomena that are relevant to the problem of selecting and managing R&D projects.…”

“…A further limitation of some optimization models (e.g., Gear and Lockett 1973, Czajkowski and Jones 1986, and Ghasemzadeh et al 1999) is that project inputs are separated from outputs, wherefore projects cannot produce inputs for other projects, for instance. These models typically assume that there exists a predefined, static supply of resources in each time period (see, e.g., Ghasemzadeh et al 1999 andGear and which makes it impossible to invest profits for later or immediate use.…”

“…These models typically assume that there exists a predefined, static supply of resources in each time period (see, e.g., Ghasemzadeh et al 1999 andGear and which makes it impossible to invest profits for later or immediate use. There is consequently a need for dynamic modeling of resources; early attempts into this direction have been presented by Brandenburg and Stedry (see Gear et al 1971).…”

Many-Objective Portfolio Optimization of Interdependent Projects with ‘a priori’ Incorporation of Decision-Maker Preferences

“…In [21], Ghasemzadeh et al model preferences using a weighted-sum function. They approximate the Pareto frontier by changing the weights and solving the resultant model by 0-1 programming.…”