Numerical DSM

In binary DSM notation (where the matrix is populated with "ones" & "zeros" or "X" marks & empty cells) a single attribute was used to convey relationships between different system elements; namely, the "existence" attribute which signifies the existence or absence of a dependency between the different elements.

Compared to binary DSMs, Numerical DSMs (NDSM) could contain a multitude of attributes that provide more detailed information on the relationships between the different system elements. An improved description/capture of these relationships provide a better understanding of the system and allows for for the development of more complex and practical partitioning and tearing algorithms.

As an example, consider the case where task B depends on information from task A. However, if this information is predictable or have little impact on task B, then the information dependency could be eliminated. Binary DSMs lack the richness of such an argument.

What attributes/measures can be used?

• Levels Numbers: Steward (1981) suggested the use of level numbers instead of a simple "X" mark, for certain marks in the binary matrix. Level numbers reflect the order in which the feedback marks should be torn. The mark with the highest level number will be torn first and the matrix is reordered (i.e partitioned) again. This process is repeated until all feedback marks disappear. Level numbers range from 1 to 9 depending on the engineers judgement of where a good estimate, for a missing information piece, can be made.
• Importance Ratings: A simple verbal scale can be constructed to differentiate between different important levels of the "X" marks. As an example, we can define a 3-level scale as follows:

In the above scenario, we can proceed with tearing the low dependency marks first and then the medium and high in a process similar to the level numbers method, above.

Some other attributes depend on the type of DSM used in the representation and analysis of the problem.

For example,in an Activity-based DSM, the following measures can be used:

• Dependency Strength: This can be a measure between 0 and 1, where 1 represents an extremely strong dependency. The matrix can, now, be partitioned by minimizing the sum of the dependency strengths above the diagonal. 
• Volume of Information Transferred: An actual measure of the volume of the information exchanged (measured in bits) may be utilized in the DSM. Partitioning of such a DSM would require a minimization of the cumulative volume of the feedback information.
• Variability of Information Exchanged: A variability measure can be devised to reflect the uncertainty in the information exchanged between tasks. This measure can be the statistical variance of outputs for that task accumulated from previous executions of the task (or a similar one). However, if we lack such historical data, a subjective measure can be devised to reflect this variability in task outputs (Yassine et al., 1999).
• Probability of Repetition: This number reflects the probability of one activity causing rework in another. Upper-diagonal elements represent the probability of having to loop back (i.e. iteration) to earlier (upstream) activities after a downstream activity was performed (Smith et al., 1997a). While lower-diagonal elements can represent the probability of a second-order rework following an iteration (Browning, 1998). Partitioning algorithms can be devised to order the tasks in this DSM such that the probability of iteration or the project duration is minimized. Browning (1998) devised a simulation algorithm to perform such a task. An excel macro that performs Monte Carlo simulation of the DSM is available to download from this web site. A brief description of the DSM similation technique and how it works is in another section of this tutorial. Click here if you want to jump to the DSM simulation section.
• Impact strength: This can be visualized as the fraction of the original work that has to be repeated should an iteration occur (Browning, 1998) and (Carrascosa et al., 1998). This measure is usually utilized in conjunction with the probability of repetition measure, above, to simulate the effect of iterations on project duration.

For other DSM types, measures can be devised similar to the examples shown on the following pages:

• Component-based
• Team-based
• Parameter-based

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