Revision as of 14:06, 9 June 2017

In planning management with regards to time scheduling there are several ways to get an overview of the number of activities in a timeline like the Gantt plot or using the Critical Path Method (CPM) to estimate the time used and needed for activities dependent on each other. But CPM is limited in the way that it only looks at sequential activities though it is possible for a design case to have both dependent activities as well as interdependent activities. This means that the information flow is not necessarily linear but can be cyclic giving rise to situations where some activity is initiated but still needs information from a later activity. The structure of these activities through time can be sorted in a Dependency Structure Matrix (DSM) which marks all the interdependencies in a square matrix. The matrix can both be used for visualization and optimization of information flows. This article will discuss the application of DSM for use in a time scheduling situation of project management. Here some of the common ways to rearrange or change the matrix to reduce loops of information flow or to let non-dependent activities run in parallel will be discussed.

Background

For planning in construction of buildings a simple Gantt chart may be of use to schedule the work flow of different tasks. Otherwise a CPM analysis (Critical Path Method) or PERT model () can be used to sequence the different tasks such that the total cost and work time is optimized. But these models are limited to progressive flows of work meaning that the completion of one task leads to the possible start of another activity. But when designing the building a lot of iterative procedures are performed which cannot be modelled by CPM for instance. These iterative procedures imply that some tasks are not just dependent on each other but also interdependent. These cycles of iteration can lead to over-designing of the project which entails waste of time and extra costs. Donald V. Steward proposed a method in 1981 using a Design Structure Matrix to optimize the information flow for the design scenario. It was later called Dependency Structure Matrix as it went from being useful mostly for the information flow during the design phase to also being applicable for other cases, not only scheduling. Several types of DSM can be used for different purposes. There are ………… but this article will focus on the use of activity based DSM.

How to Read the Matrix

The matrix consists of all the project tasks listed as both rows and columns. This means that the matrix is an nxn square matrix where n is the number of activities. The diagonal of the matrix lists the elements themselves and the off-diagonal elements lists the dependencies by either and ‘X’ mark or a ‘0’/left out. It is crucial for the use of the activity based matrix that all the tasks are listed in progressing order from the first in the upper left to the last in the bottom right. There are two ways of reading the matrix, the IR/FAD and IC/FBD convention. The first one is the one typically used for scheduling activities in construction. This states that the rows list all the requirements or inputs that a certain task needs to have to begin. The columns on the other hand list all the outputs from the activity. This means that all the interdependencies can be stated for the whole project in a single matrix. In the other convention, the way of looking at the rows and column is reversed effectively meaning that the matrix is transposed. Thus, all the observations in the following are based on the IR/FAD convention but can easily be converted to the IC/FBD convention by reversing the rows and columns. Especially the elements in the upper triangle of the matrix are important. In the IC/FBD convention these elements are therefore in the bottom triangle.

Using the Matrix/Matrix Operations

The position of the ‘X’ marks in the matrix tells about the type of processes in the project. No mark results in no correlation meaning that the processes are independent or parallel. A single mark results in a correlation giving the typical dependent or sequential process. There is lastly the type of interdependent or coupled tasks which can also be seen in loops. These can be seen by cross-diagonal markings which is the coupled tasks and markings that fit within an imaginary box with center at the diagonal are the circular tasks or loops. It is especially the interdependent or circular processes that are of interest as these define the large amount of rework or iteration needed for the full completion of the project. In the standard notation all the marks below the triangle define the linear dependencies meaning that if the matrix was a lower triangle matrix all the tasks could run in the defined order without iterations. But any marks in the upper triangle part of the matrix show the feedback from a later process to a previous one thus giving rise to iterations of work. The whole point of using DSM is to reduce the amount of rework or eliminating it by making good approximations which effectively cancels the need for the feedback information. The way all the processes are ordered is not necessarily the best solution for the sequence. By making different operations on the matrix this can be optimized. The methods for optimization are called sequencing or partitioning and tearing.

Shearing

Sequencing alters the order in which the tasks are completed. This can be done by several methods like Path searching, Powers of the adjacency matrix method, the reachability matrix method among others. An overview of how the more simple Path searching method works is illustrated in the following.

After applied sequencing the matrix is optimized with respect to the order of the independent tasks and the interdependent tasks are clustered so that less time is used before an iteration is completed. Obviously this is the best sequence of the tasks if they should run with iterations but this is a costly affair. Thus the links in the circular tasks are attempted to be severed. The process of tearing is discussed in the following.

Tearing

The circular path of some activities is severed by using assumptions for the feedback information. This means that a mark in the upper triangle can be discarded and the process of sequencing can be reused to optimize the blocks of interdependent tasks. Though several feedback marks can be present in the same block. It is not wanted to tear all the markings in upper triangle. If the optimal solution is sought maybe only one tear is needed and resequencing can solve the interdependencies for the block. The way of choosing the most critical tasks, where assumptions can be made, is a very important step and no general solution is given. It all depends on the type of project and the given activities. Here the use of a numerical DSM can come in handy.

Establishing the Matrix

Performing operations on the matrix is per se the easiest or most reliable part of the process. To even get to having a DSM one needs to extract information about the project tasks and information flows from the people actually working with the different activities of the project. This is not so easily accomplished.

Advantages of the Method

Disadvantages of the Method

^[1]

Annotated Bibliography

Articlename^[1]

• text

References

1. ↑ ^{1.0 1.1} name