Evaluating fuzzy earned value indices and estimates by applying alpha cuts Leila Moslemi Naeni a , Amir Salehipour b,⇑ a School of Industrial Engineering, Sharif University of Technology, Tehran, Iran b School of Industrial Engineering, Islamic Azad University-South Tehran Branch, Tehran, Iran article info Keywords: Fuzzy earned value Alpha cut Uncertainty Project progress abstract The earned value technique is an essential technique in analyzing and controlling the performance of a project by providing a more accurate measurement of both project performance and project progress. This paper presents an approach to deal with fuzzy earned value indices. This includes developing new indices under fuzzy circumstances and evaluating them using alpha cut method. The model improves the applicability of the earned value techniques under real-life and uncertain conditions. A small example illustrates how the new model can be implemented in reality. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Earned Value Management (EVM/EV) is a project management technique developed to measure project progress in an objective manner. According to Project Management Institute (PMI), 1 when properly applied, EVM provides an early warning of performance problems. The EV measures project performance and progress by efficiently integrating management of three most important ele- ments of a project, i.e. cost, schedule and scope. In fact, it calculates cost and time performance indices of a project, estimates completion cost and completion time of a project, and measures project perfor- mance and project progress. Although being introduced in 2000 in PMBOK Ò guide (PMI, 2000), the first complete guide on the EV has been published in 2005 (PMI, 2005). Despite widely believed that implementing the EV techniques has many advantages and would enhance cost and schedule performances of a project; the research on the EV is very limited. Lipke (1999) developed cost and schedule ratio to manage cost and schedule reserves in projects. Later he introduced the earned schedule (ES) concept to outperform limitations of the his- torical EV schedule variance (SV) and schedule performance index (SPI) (Lipke, 2003). His studies were followed by Henderson (2003, 2004) and Vandevoorde and Vanhoucke (2005), where applicabil- ity and reliability of the ES were discussed. Anbari (2003) improved the effectiveness of EV implementation. Kim, Wells, and Duffey (2003) studied the implementation of the EV in different types of organizations and projects. Cioffi (2006) studied the EV mathemat- ics to make it more applicable and flexible. Lipke et al. (2009) pro- vided a reliable forecasting method of completion cost and duration to improve the capability of project managers for making informed decisions. Recently Moslemi Naeni et al., (2010) have worked on fuzzy earned value and applied degree of possibility method to evaluate estimates. The motivation behind this paper is derived from the fact that despite the uncertain nature of the activities’ progress involved in a project, they are considered deterministic in all available EV techniques. In reality the activities’ data come from people’s judg- ments; hence they carry some degree of uncertainty. Bringing this uncertainty into interpretations, not only helps in measuring bet- ter performance and progress of a project, but also in extending the applicability of the EV techniques under the real-life and uncertain conditions. The major contribution of this paper is to de- velop an approach to deal with fuzzy earned value indices and esti- mates when measuring project performance and project progress. Through the paper, our terminology is based on the PMBOK guide- line (PMI, 2004). For the simplicity, by ‘‘activity’’, we mean both activities and work packages. The remaining of this paper is orga- nized as follows: Section 2 brings an introduction into the earned value and fuzzy theory. The section forms the basis of the proposed approach of Section 3. Evaluation and interpretation of fuzzy earned value indices and estimates are covered in Section 3. For clarification purposes, a simple example is studied in details in Sec- tion 4. The paper ends with the conclusion. 2. The fuzzy earned value measurement technique The earned value (EV) is a set of techniques to assist project managers in measuring and evaluating project progress and pro- ject performance by estimating completion cost and completion time of a project (based on its actual cost and actual time up to any given point in the project). The EV of an activity represents 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.12.165 ⇑ Corresponding author. E-mail addresses: leila.moslemi@gmail.com (L. Moslemi Naeni), asalehipour@ ymail.com (A. Salehipour). 1 In a more accurate definition by PMI (2005), the EVM combines measurements of technical performance (i.e. accomplishment of planned work), schedule performance (i.e. behind/ahead of schedule), and cost performance (i.e. under/over budget) within a single integrated methodology. Expert Systems with Applications 38 (2011) 8193–8198 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa