Predicting the Performance of a Design Team Using a Markov Chain Model

When faced with a complex design problem, a design team may separate it into subproblems. We would like to know when this approach is superior and how subproblems should be assigned to team members. We created mathematical models of searches that represent bounded rational decision-makers ("agents") solving a design problem. These discrete-time Markov chains were used to calculate the probability distribution of the value of the solution found and the expected number of steps required. We evaluated the performance of two- and three-agent teams who used two approaches to solve design problems. In the "all-at-once" approach, they search the entire set of solutions. In the "separation" approach, they separate the problem into two subproblems. Three stopping rules and two different types of collaboration were modeled. Using a separation increases the likelihood of finding a high-value solution when high-value solutions are less likely. The optimal assignment of team members to subproblems depended upon the distribution of values in the solution space. These results suggest that more effort should be spent developing better concepts when high-quality concepts are rare. When concepts have similar performance, more effort should be spent searching for better designs that implement the selected concept.