On the Structure of Bottlenecks in Processes

Process capacity and the associated notions of bottleneck activities and bottleneck resources-which are responsible for limiting process capacity to its present value-are fundamental concepts in the operations management literature. However, for processes that involve collaboration and multitasking, there is little clarity in the literature on what bottlenecks are, what they look like, and how they can be identified. In this paper, we formulate and analyze graph-theoretic optimization problems that determine bottleneck structures of activities and the associated bottleneck sets of resources in deterministic, singleproductprocesseswithpossiblymultiplecopiesofoneormoreresourcesandpossiblymultiple sets of resources that can perform each activity. In the presence of both collaboration and multitasking, sets of activities that are interconnectedin a specificmanner via sharedresources formbottleneck structures that are responsible for limiting capacity.We use the collaboration graph of the process to either characterize bottleneck structures completely or identify graphical structures that must necessarily be part of any bottleneck structure. Our analysis reveals a natural hierarchyin the algorithmicapproach for identifyingbottleneck structures as processes become increasingly sophisticated, ranging from the "easy"case where the simple bottleneck formula correctly identifies bottlenecks to more complex cases where one needs to solve progressively complicated mathematical programs. In turn, this understanding helps us obtain prescriptive answers to several questions of interest to managers, for example, the budget-constrained procurement of resources to maximize capacity improvement and the design of processes to increase capacity without procuring additional resources.