بهبود صحت پیش بینی پروژه با تلفیق مدیریت ارزش کسب شده با برآورد (هموار سازی) نمایی و پیشگویی کلاس مرجع Improving project forecast accuracy by integrating earned value management with exponential smoothing and reference class forecasting

۱٫ Introduction Forecasting an ongoing project’s actual duration and cost is an essential aspect of project management. One of the most widely used and best performing approaches for obtaining such forecasts is that based on the earned value management (EVM) methodology. To ensure the standalone comprehensibility of this paper, a concise summary of EVM’s key definitions and formulas is included in Table 1. The metrics below the middle line in Table 1 can be used to indicate a project’s schedule and cost performance at a certain point during project execution (i.e. at a certain tracking period). More specifically, a schedule variance SV or SV(t) b0 (N0) and a schedule performance index SPI or SPI(t) b1 (N1) express that the project is behind (ahead of) schedule. Similarly, regarding project cost, a cost variance CV b0 (N0) and a cost performance index CPI b1 (N1) reflect a project that is over (under) budget. When the schedule or cost variances are equal to zero, the project is right on schedule or on budget, respectively. This corresponds with schedule or cost performance indices that are equal to unity. The utility and reliability of EVM as a method for evaluating a project’s current cost performance and forecasting its actual cost has been endorsed ever since the introduction of the technique in the 1960s. The performance of EVM for the time dimension, however, only got the necessary boost from the introduction of the extending concept of earned schedule (ES) by Lipke (2003). A recent study (Batselier and Vanhoucke, 2015b) explicitly showed that, when implementing ES, EVM time forecasting is at virtually the same accuracy level as EVM cost forecasting. Therefore, the EVM technique can indeed be deemed a viable and valuable basis for the forecasting of both project duration and cost. Furthermore, multiple extensions of the traditional EVM forecasting approaches have been proposed in literature the past several years (Kim and Reinschmidt, 2010; Lipke, 2011; Elshaer, 2013; Khamooshi and Golafshani, 2014; Mortaji et al., 2014; Baqerin et al., 2015; Chen et al., 2016). This list is obviously not exhaustive, as to provide a complete overview and description of the existing EVM extensions is beyond the scope of this study, and so is the quantitative comparison of all those techniques (including the one developed in this paper). The latter defines an evident subject for future research, similar to the study performed by Batselier and Vanhoucke (2015c), in which three EVM forecasting extensions (Lipke, 2011; Elshaer, 2013; Khamooshi and Golafshani, 2014) are compared and combined. Another widely used and well-performing technique for making forecasts based on time series data is exponential smoothing. This technique arose in the late 1950s and early 1960s (Brown, 1956, 1959, 1963; Holt, 1957; Holt et al., 1960; Muth, 1960; Winters, 1960) 1 and has formed the basis for some of the most successful forecasting methods ever since. The main feature of an exponential smoothing method is that the produced forecasts are based on weighted averages of past observations, moreover, with the weights decaying exponentially as the observations age. Furthermore, the technique enables forecasting for time series data that display a trend and/or seasonality. For more background information regarding the origins, formulations, variations, applications, and state-of-the-art of exponential smoothing, the reader is referred to Gardner (2006). Nevertheless, the formulations relevant to the study in this paper will also be presented in later sections. Although the technique of exponential smoothing is mainly used in financial and economic settings, it can in fact be applied to any discrete set of repeated measurements (i.e. to any time series). Since the tracking data gathered during project progress constitute a time series, exponential smoothing can also be applied to forecast project duration and project cost. Intuitively, this shows potential. Indeed, traditional EVM forecasting assigns equal importance (or weight) to all past observations, whereas the exponential smoothing approach makes it possible to gradually decrease the weights of older observations. The latter could be a very useful feature in a project management context, as it allows to account for the effect of both natural performance improvement and corrective management actions that might occur during the course of a project (see Section 2.1 for a more elaborate discussion). Therefore, a novel forecasting approach for both project duration and project cost based on the integration of well-known EVM metrics in the exponential smoothing forecasting technique is developed in this paper. From now on, this novel approach will be referred to as the XSM, which is an acronym for eXponential Smoothing-based Method. Moreover, note that the general notation of XSM refers to both the time and cost forecasting dimension of the novel technique. As an overview, all notations for the different components of the XSM that will be introduced and discussed later in this paper are presented in Appendix A. The outline of this paper can be summarized along the following lines. The derivation of the XSM formulations and explanation of their application (static/dynamic) will be the subject of Section 2, preceded by a qualitative discussion on the motivation for adapting the current EVM forecasting methods and why the exponential smoothing technique is appropriate for this. Furthermore, in the same section, we will make the link between the XSM and the established EVM forecasting methods. Section 3 then proposes an evaluation approach for the XSM, based on accuracy comparison with the known EVM top forecasting techniques. Furthermore, the proposition to incorporate the reference class forecasting (RCF) technique – in which a relevant reference class of similar historical projects is used as a basis for making forecasts for the considered project – into the XSM methodology is made in Section 3.2. In Section 4, the results of the evaluation are presented and discussed, for time forecasting as well as for cost forecasting. Moreover, both a static and a dynamic approach to the XSM will be assessed. Finally, Section 5 draws more general conclusions and suggests several future research actions.