A representation model for the solving-time distribution of a set of design tasks in new product development (NPD)

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Abstract

Given the potential risks of new product development projects (NPD), the characteristics of the design tasks solving-time distributions are critical for their effective management. In OR we need to find what operational characteristics of design tasks may delay projects. Other researchers already identified the technological novelty, the magnitude of the design tasks, the interactions between design tasks in an NPD project, and the balancing between projects among the most important causes of the unpredictability of the design tasks lead times in NPD projects.

We develop a simple queuing model incorporating all these four factors, to estimate the solving-time distribution of a finite set of design tasks assigned to a team of engineers during an NPD project. Using the Kolmogorov–Smirnov goodness-of-fit test, we show the model to be statistically equivalent to several sets of experimental data from a micro-lithography firm.

This model assumes an ordering of the design tasks allocated to the team of engineers according to some optimality criteria of the upper management levels. In the more general framework of mathematical control of NPD, our model can be integrated in hierarchical planning and control solutions.

Introduction

In the field of new product development (NPD), project management and control is currently a topic of much interest in both research and industrial communities. We consider the notion of NPD project as being the new product design project translating customer/market requirements/specifications into a product definition and a manufacturing process definition.

One of new product development main characteristics is the presence of various kinds of uncertainties, making its operational control quite a challenge. These uncertainties make it difficult to foresee the time at which the design tasks composing the NPD project will be completed; thus appropriate control methods are very much needed. Several recent empirical and modelling studies have tried to better identify and classify possible causes of delays, and among them, Tatikonda and Rosenthal (2000), enumerate the technological novelty, the magnitude of the design tasks, the interactions between the design tasks in the NPD project, and the balancing between projects as being the most important causes.

Various work-specific and work-environment-related uncertainties may diminish achievement of work effectiveness. Factors associated with the operational success are the organizational process factors of process concurrency (Sobek et al., 1999), flexibility as well as the existence of an overall organizational process and structure for the project (Tatikonda and Montoya-Weiss, 2001).

We present here a new mathematical model, based on queuing theory concepts, and incorporating all four causes of delay enumerated above. The main purpose of this model is to allow the computationally feasible estimation of the solving-time distribution of design tasks in NPD projects.

Thus, this model is a step towards mathematical control of NPD, and it can, for instance, be integrated into a hierarchical control framework with multiple levels as in Dragut (2003) as an intermediate stage to set the performance characteristics of the new product at the upper hierarchical level.

For the sake of a more general picture, as well as with the purpose of clearly stating the limits of our model setting, we briefly describe a general hierarchical NPD project control framework using this model. It consists of a series of decision/scheduling/execution cycles starting at equidistant review points in time, before the project deadline. At the beginning of each review period the upper level decision maker decides whether to continue or not the NPD project. The abandonment is the result of either an expected exceeded NPD budget, or of a low product performance, which does not enable the achievement of a fully functional product before the deadline. In case of continuation, the controller modifies the targeted performance of the product, aiming at a maximal market payoff at the deadline. As mentioned earlier, a general network reflects the precedence relations among design tasks at the beginning of each review period. A hierarchical performance structure relates the product performance to the one of the needed design tasks. During each review period, we estimate the outcomes of the scheduling/execution levels using a combination of heuristic scheduling methods and the design tasks estimation model presented in this paper. This lower levels estimation allows the computation of the transition probabilities of a Markov decision process for the control of NPD projects, as well the investigation of different optimal policies.

The contributions of this paper are the following:

  • for the first time (to the best of our bibliographical knowledge) a mathematical model is derived for the solving-time distribution of design tasks for NPD accounting for both structural design tasks technological uncertainties and human factor characteristics;

  • the model is tested on real-life data for the case of one engineer, gradually showing the need of incorporating the various model elements;

  • the mathematical model has implications for project management and for scheduling in NPD projects, by providing more accurate estimates for the solving-time of the design tasks.

The remaining of the paper is organized as follows: in Section 2, we discuss the uncertainties inherent to NPD projects, leading to delays. In Section 3, we present the general setting of the model and the main parameters we wish to have in it. In Section 4, we formally describe the model and we show that its properties can be derived analytically from its parameters. In Section 5, we use eight sets of empirical data to validate the model through statistical analysis. We identify a constant difference between the model and the data sets, that can be attributed to the impact of the due date nearness on the amount of capacity allocated to a design task. Incorporating this factor in the model leads to a statistical good fit between the model and data. The conclusions are given in Section 6.

Section snippets

Design tasks lead- and solving-time characteristics

In literature, NPD projects are generally described as consisting of a set of design tasks with precedence constraints. Uncertainty exists at the design task level with respect to the amount of capacity needed to execute a design task, as well as with respect to the interactions between design tasks. Uncertainty exists also at the level of an NPD project as a whole and regards its structure; the set of design tasks that are needed to realize the design requirements. This article mainly focuses

The setting

We denote by M the number of engineers available to perform the work for the NPD project. We assume that the new product can be obtained by performing a set of partitionable design tasks derived from the product specifications. Thus, the work is presented to the engineers in units via a work breakdown structure (WBS) of a project, and we call design tasks the lowest elements of the WBS. This WBS is developed once the NPD initial system specifications are set, and, as in Aslaksen and Belcher

Model

Based on the considerations of Section 2 regarding the causes of delays for design tasks in NPD projects, we further assume that for each design task on hand, unplanned activities arrive according to an incremental stochastic processes. To avoid unnecessary computational burden, we consider this type of process to be a Poisson one. The Poisson assumption is frequently made in models of quality (Rosenblatt and Lee, 1986) and reliability (Ramamoorthy and Bastani, 1982), when modifications arise

Validation

For the case of a team with more than one engineer, the shape of the distribution function given by this model is confirmed by the data collected in the experimental research of Innam (1999) which suggest a long-tailed, skewed distribution function (see Fig. 2, Fig. 3, Fig. 4). The collected data does not refer to NPD design tasks, but to uncertain repair tasks, which can however be considered very similar from a “discovery” point of view.

For the case of one engineer, we have used the

Conclusions

Successful product development requires the understanding of the nature of its constituting design tasks variability. The main contribution of this paper is the derivation of a simple mathematical model which allows the estimation of solving-time distribution function for an NPD project design tasks. The model is based on operational characteristics of NPD projects that evolved from theoretical and empirical research on these projects. The structure of the model involves a queuing system for

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