BUS606: Operations and Supply Chain Management

The first group of abstract micro-level models represent designing in terms of formal or logical operations. These models are developed mainly from theoretical considerations regarding the properties of design problems and the design process. Motivations for such work include that if the logic of designing could be understood and specified formally, insights might be systematically derived and aspects of the process might be supported or automated with suitable reasoning algorithms.

In one seminal paper of this type, March developed the Production–Deduction–Induction (PDI) model which clarifies how creative, evaluative, and learning processes operate and interact when designing. The model comprises three phases that repeat in an iterative cycle. In the first phase, the designer considers a desired situation in view of their existing knowledge to speculate a possible design solution. This is seen as productive or abductive reasoning. In the second phase, the candidate solution's behaviour is predicted considering its form and relevant physical principles. This is deductive reasoning. In the third phase, new knowledge concerning probable general relations between solutions and their behaviours is induced from the specific case just analysed. The cycle then repeats with the benefit of this new knowledge. While deductive reasoning is analytic, abductive reasoning and inductive reasoning are synthetic. That is, their results are influenced by the context, including the knowledge and experience of the designer.

General design theory or GDT aims to define a formal logic of design. Here, in keeping with the scope of the present article, we do not discuss the formalism but focus on the process models associated with GDT. First, the evolutionary design process model (EDPM) focuses on how designers work with multiple representations of an emerging design. According to the EDPM, design proceeds by progressively extending a metamodel from which the different product models can be derived. On each of a series of cycles, a problem is identified, specific model(s) are derived from the metamodel to analyse the design, allowing the problem to be resolved and leading to information being added to the metamodel. This is said to continue until a fully detailed design is reached. Tomiyama et al. argue that this is a mainly deductive process, complemented with additional logic operations to handle the multiple parallel paths considered during design and the need for backtracking when a problem is reached that cannot be solved by deduction. Second, Takeda et al. extend this work, placing greater emphasis on how the design process is directed from one step to the next and on the forms of logic involved. Their extended EDPM involves two levels. On the object level, the designer first develops a solution suggestion from awareness of a design (sub)problem, and then develops, details, and evaluates their proposed solution. On the action level, they decide on next steps if evaluation reveals contradictions in the proposal. Takeda et al. argue that suggesting a solution from awareness of a problem is achieved by abduction; developing details of the solution and evaluating it are both deduction; and causes of identified contradictions are found through a form of logic called circumscription. In their model, the causes of contradiction constitute new variables and a new problem to be addressed in a future design cycle. Third, Tomiyama devise a further improvement, called the refinement model, in which design is seen as a process to complete the specifications as well as to define design attributes. A detailed analysis and critique of GDT is provided by Reich. Focusing mainly on the formal axioms and theorems rather than the process models, Reich concludes that the approach "cannot be an adequate description of real design", although, he argues, it might still provide useful "guidelines" for CAD system development.

Zeng and Cheng also take a formal approach. They focus on how reasoning at each step is situated in the outcome of previous design cycles, developing a recursive logic scheme to represent this process. Zeng integrates these ideas into his axiomatic theory of design modelling. This formally presents designing as a cycle of synthesis and evaluation which operates on a hierarchical structure defining the evolving design and its environment. On each cycle, the synthesis of partial solutions contributes to the evaluation criteria for future cycles.

Braha and Reich build on the formal design theory (FDT) of to develop the coupled design process (CDP) model. CDP provides a mathematical formalism which emphasises the role of exploration in progressing a design. In overview, designing is modelled as a repeating cycle of a closure operation followed by a selection operation. The closure operation, representing exploration, involves creating a set of design descriptions which do "not differ substantially" from the output of a previous design cycle. This is referred to as a closure set. The selection operation then focuses attention on one or more design descriptions from the closure set, which form seeds for the next cycle. In CDP, each design description comprises both specifications and solutions, which are elaborated together until the design is complete. Braha and Reich argue that their model allows concepts from the mathematics of closures to be interpreted to provide insights into design, and furthermore argue that GDT is a special case of CDP. On the other hand, unlike GDT, Braha and Reich do not discuss how their formalism might be implemented computationally.

The final model to be mentioned in this subsection is the C-K theory introduced by Hatchuel and Weil. These authors argue that the two issues of creativity and the expansion of knowledge are fundamental to understanding designing, but are not comprehensively integrated within earlier models. C-K theory aims to address this by presenting designing as a process of traversing back and forth between two structured and expanding spaces. Knowledge space K comprises statements representing the designer's knowledge. Concept space C comprises propositions relating to the emerging design concept(s). These are undecided in that they are not yet known to be true or false. Designing is conceptualised as a set of operations that are applied to expand the knowledge structures in conjunction with the concept space. It concludes when the propositions necessary for a design have been developed and found to be true. Several formalisms have been developed considering the ideas of C-K theory. Some support tools and industrial applications using the theory are discussed by Hatchuel et al. A 2014 review concluded that C-K theory has been developed, applied, and adopted in more than 100 publications, and that it provides a framework which may be able to integrate earlier theories of design.