توسعه مدل سازی شبکه توسعه محصول برای روش حذف چرخه Product development network modelling extensions to the cycle elimination method

1. Introduction Product development (PD) projects are notorious for their iterative nature, where ignoring rework potential results in inaccurate estimates of project duration (and cost) and can lead to misleading analysis and managerial decisions (Browning & Yassine, 2016; Meier, Browning, Yassine, & Walter, 2015). Iterative rework is denoted by a feedback loop in an Activity on Node (AON) representation of the PD project network, where the completion of a downstream activity may cause one or more upstream activity to be reworked (Yassine & Braha, 2003). The stochastic nature of the activity duration along with the probabilistic occurrence of feedback loops, significantly increases the complexity of estimating the duration of the PD project (Browning & Ramasesh, 2007; Unger & Eppinger, 2009). Feedbacks are a typical characteristic of any complex design and development project and a potential source of design iterations, which can account for one-third to two-thirds of the project duration and cost (Meier, Yassine, & Browning, 2007). This fact makes the study of project management in the presence of iteration, as suggested in this paper, a central issue for the PD community. In the absence of stochastic feedback, the PD network reduces to a classical project network where traditional and well-established techniques can be utilized such as the critical path method (CPM) and program evaluation and review technique (PERT) (Mantel, Meredith, Shafer, & Sutton, 2007; Pinto, 2012). When considering project networks which exhibit feedback, the majority of the literature utilizes simulation techniques (e.g., Abdelsalam & Bao, 2006; Browning & Eppinger, 2002; Cho & Eppinger, 2005) or heuristic algorithms (e.g., Browning & Yassine, 2016; Jun, Park, & Suh, 2006) to estimate the duration of the project. Analytical approaches to approximate the expected duration of PD projects exist but not without limitations; for example, the Reward Markov Chain (RMC) approach (Smith & Eppinger, 1997) and the Signal Flow Graph (SFG) approach (Eppinger, Nukala, & Whitney, 1997) are both used for sequential PD networks. More recently, the Cycle Elimination (CE) approach (Nasr, Yassine, and Abou Kasm (2016)) investigated the duration of a PD network for sequential and parallel networks. The CE method uses the RMC approach as a starting point and is extended to include finding the expected duration and variance of sequential, parallel, and mixed (i.e., combination of sequential and parallel activities) activity networks. The CE method mainly works by transforming the PD network into a traditional network (i.e. eliminating feedback) and then traditional project management techniques such as CPM and PERT can be used to calculate the expected duration and variance of the network. Pinkett (1998) also implemented modifications to previous analytical methods, namely the signal flow graph (SFG) and the RMC. The modifications include rework proportions (i.e. repeating a fraction of the original activity duration when feedback is triggered). Another modification is accounting for “terminal probabilities”. The terminal probability as explained by Pinkett (1998) is the probability that a certain activity will have to be reworked after the downstream activity, responsible for triggering the rework, is worked a second time (or more). Also, a modification to account for forward probabilities (pf), the probability to skip an activity in the first iteration, is discussed. The terminal probability (identified as dynamic probability in our work) and the forward probability modifications in the case study presented by Pinkett (1998) inspired us to investigate further real case scenarios through a real world case study of our own accompanied by discussions with managers of a product development company. Pinkett’s modifications along with different real case complications that were discovered are presented and discussed in this paper.