توسعه تجزیه و تحلیل زمان - هزینه پروژه با حذف روابط تقدم و جریان کار

Faster completion of projects continues to be an important problem in project management. The traditional approach to reduce completion time has been to shorten the time required for performing a particular activity, often called crashing. In this paper, we propose the addition of two related approaches to expedite a project: increasing the parallel processing of tasks by completely removing precedence relationships, or streaming tasks by fractionally removing precedence relationships. We present a quadratic mixed integer programming approach for reducing project completion time that considers crashing as well as the removal and modification of precedence relationships. Our model extends the linear formulation of the deadline time–cost problem. Two examples are presented to illustrate the suggested approach. Project managers who wish to expedite their projects are advised to consider the benefits and costs of doing more tasks concurrently, or overlapping them, in addition to compressing task times.

Faster completion of projects has always been an important problem in virtually all project environments. Completing a project earlier may generate additional revenue, although added costs may also be incurred to speed completion of certain tasks. For example, in construction often there are financial incentives for expediting the completion of a project. In pharmaceutical product development, shorter development time can lead to extended patent-protected product sales. In addition, earlier project completion can create time savings in which firms can generate sales, enter markets early, grow those markets quickly, and invest in future R&D initiatives. A recent study estimated that direct out-of-pocket expenditures for Phase I through the final phase of new drug applications are approximately $30,000 per day [11]. A number of approaches have been proposed to expedite project completion. Consider the following example concerning a typical construction project. The erection of formwork always precedes the placing of concrete. This precedence relationship cannot be removed, at any expense. On the other hand, we might initially assume that landscaping work could not begin until after the installation of the gutters and downspouts was completed. It is certainly conceivable to allow the landscaping and the work on the downspouts and gutters to happen concurrently (or even to start the landscaping first). It is quite possible that doing the tasks in parallel in this way could lengthen the time needed for the landscaping a bit (for instance, some extra raking and cleanup near the downspouts). Yet removing the precedence relationship could reduce the total project completion time if both of these tasks were on the original critical path, even though it involves lengthening the duration of one of the tasks. Alternatively, we might decide to overlap both activities, initiating landscaping work once a portion of the gutter and downspout work has been completed. Again, this may lengthen the landscaping work but perhaps not to the same extent as in the previous example and perhaps not with the same time savings. The purpose of this paper is to present an integrated modeling approach that considers all three methods for finding the most cost-effective plan for expediting the completion of a project.

Task time compression and concurrent processing in project design are approaches often proposed for speeding up the completion of projects. However, in addition to crashing task durations, allowing complete removal of specific precedence arcs and task streaming with fractional removal of precedence arcs has not been studied in the project scheduling literature. In this paper we present a general quadratic mixed integer programming approach for reducing project completion time that considers both the reduction of activity times and the complete and fractional removal of precedence relationships. Our formulation extends the linear formulation of the deadline time–cost problem. Two examples are presented to illustrate the suggested approach. The first example is a special case that considers complete removal of precedence arcs only and is a mixed integer linear program. The concepts we present here could also be applied to more general situations, including precedence relationships other than lagged start–start, and nonlinear or discrete versions of the budget problem. Project managers who wish to expedite their projects may wish to consider the benefits and costs of doing more tasks concurrently (wholly removing precedence relations) and/or overlapping tasks (fractionally removing precedence relations), in addition to compressing task times. In most real problems, the number of precedence relations which can be wholly or fractionally removed is likely to be a small fraction of the network, and so the data collection effort and the computational time needed to solve even the general mixed integer quadratic program we present here should be reasonable. We leave detailed exploration of this question for further research. By adding new possibilities, our approach can result in more cost-effective solutions than standard time/cost analysis.