BUS606: Operations and Supply Chain Management

To recap, task dependency models represent the information dependencies between tasks as well as, or instead of, a procedure for attempting them. Such models emphasise that the tasks could be organised in several ways. For example, they could be attempted in different sequences or in parallel. Approaches which incorporate dependency models are based on the premise that a process can be improved by studying the underlying structure of the situation.

The most well-known model in this category is probably the design structure matrix (DSM) introduced by Steward. A DSM is a square matrix in which a mark in a cell indicates that the element in the row depends upon that in the column (see the example in Fig. 9). Where the elements represent tasks and the connections represent information dependencies, the matrix is called a Task DSM. If all the marks lie below the leading diagonal in one or more of the possible orderings of the rows and columns, the process may be completed by attempting tasks sequentially or in parallel. Conversely, if it is not possible to find such an ordering, some of the tasks are interdependent and iteration may be required to resolve them. Algorithms have been developed to analyse a DSM to examine or exploit such structural characteristics. The algorithms include: sequencing, which is attempting to find a lower diagonal reordering, i.e., a sequence of tasks to minimise information feedback and, therefore, reduce the possibility of iteration; banding, identifying independent elements in a sequenced DSM, i.e., tasks which may be attempted in parallel; and clustering, attempting to group elements into strongly connected sets with low inter-cluster connectivity, i.e., groups of tasks that may be appropriate to perform essentially in isolation.

The Task DSM has been extensively adopted in research literature as the basis of models to analyse DDP characteristics, especially those related to decomposition and integration. The key consideration here is that when a high-level task such as designing a system is decomposed into subtasks that will be undertaken by different people or teams, interdependencies are invariably created between those subtasks. It is, therefore, important to carefully organise the subtasks and manage the information flows between them to minimise the rework that might be generated when tasks' outputs are reintegrated - especially if some of the work will be done concurrently. One seminal meso-level model considering these issues is the work transformation matrix (WTM) developed by Smith and Eppinger. The WTM focuses on situations in which interdependent tasks are executed in parallel with frequent information transfer to manage their interdependencies. It assumes that each task in such a group continuously creates iteration work for the others that depend on it, at a constant rate. The dependencies and their corresponding rates are represented in a Task DSM. Smith and Eppinger show how eigenstructure analysis can be used to identify the drivers of iteration within a coupled task group if the WTM assumptions hold. Assuming instead that tasks are executed in sequence, such that each task might create rework for others already completed if a dependency exists between them, Browning and Eppinger build on the earlier work of Smith and Eppinger to develop a Monte Carlo simulation model which they use to evaluate the cost and schedule risk associated with different task sequences and thereby identify the best sequence for a given task decomposition. These two models, respectively, described as parallel and sequential rework models, have influenced many other research articles.

The Task DSM provides a compact notation which can be especially useful for processes involving dense structures of information dependency. It is also useful to concisely visualise the properties of different dependencies, if meaningful symbols and/or numbers are placed in each cell. Achieving a comprehensible visual layout is likely to be easier than when graphical networks are used. Another advantage is that the approach can be applied without specialised software. Many computations can be expressed and programmed as operations over the matrix cells. On the other hand, some weaknesses are also apparent. DSMs are not well suited to convey detail, and thus, it can be easy to misplace marks when constructing or reading large matrices. It is not clear how to deal visually with opening and closing hierarchical structures in a DSM model. Sequential and parallel flow structures are difficult to visualise, because, although clusters of tasks can be easily indicated as shown in Fig. 9, there is no equivalent of swimlanes. More information on the Task DSM and the many related models can be found in Eppinger and Browning and the review article by Browning.

Another established dependency modelling approach is IDEF0, which uses a hierarchically structured set of diagrams to represent a system in terms of functions and the interactions between them. Applied to the DDP, functions are in essence similar to tasks. Each IDEF0 diagram comprises between three and six functions, which are represented as boxes and interconnected by labelled arrows. Arrows indicating a function's inputs enter at the left of the box, and are transformed to produce outputs which leave from the right of the box. Control arrows enter the top of a box and indicate constraints on the function's operation. Mechanism arrows enter the bottom of a box and indicate provision of a means for executing the function. Any function box can be decomposed into a more detailed diagram showing its subfunctions. Functions can be linked across and between levels in the hierarchy, and the model may include a glossary of terms. In comparison to DSM, the IDEF0 approach is more expressive, but less concise. A large set of diagrams is often needed, which can be time-consuming to produce.

Although not as prominent as DSMs in the research literature, IDEF0 has been quite widely applied for DDP modelling. For example, Kusiak et al. discuss its use to support reengineering of design and manufacturing processes, arguing that the notation can help with perceiving a process at different levels of detail and with exploring how the constraints on a task's execution can be relaxed. ADePT PlanWeaver is a planning support tool for the construction industry which is based on an IDEF0-style representation, enhanced to indicate the discipline associated with each flow into a task, as well as the strength of the dependency. In the approach, a library of generic construction processes is used to construct a customised process model for a specific project, which can be viewed as a Task DSM and then sequenced to minimise the scope of cycles that may cause iteration. Identifying dependency loops that remain and finding ways to eliminate them, for instance by splitting some tasks into several parts, allows the project to be sequenced and a schedule to be produced. More recently, Romero et al. introduce an enhanced IDEF0+ approach. This includes additional symbols to distinguish the main flow of information from other interactions, such as coordination and cooperation, that are needed in a collaborative design process.

To summarise, the main advantage of task dependency models is their emphasis on information flow constraints rather than procedures - because understanding constraints is helpful when constructing a plan or seeking opportunities for process improvement. On the other hand, Austin et al. identify one disadvantage in that untrained readers tend to incorrectly assume a task sequence.