Capacity dimensioning in production systems is an important task within strategic and tactical production planning which impacts system cost and performance. Traditionally capacity demand at each worksystem is determined from standard operating processes and estimated production flow rates, accounting for a desired level of utilization or required throughput times. However, for distributed production control systems, the flows across multiple possible production paths are not known a priori. In this contribution, we use methods from algorithmic game-theory and traffic-modeling to predict the flows, and hence capacity demand across worksystems, based on the available production paths and desired output rates, assuming non-cooperative agents with global information. We propose an iterative algorithm that converges simultaneously to a feasible capacity distribution and a flow distribution over multiple paths that satisfies Wardrop's first principle. We demonstrate our method on models of real-world production networks.

We asked how team dynamics can be captured in relation to function by considering games in the first round of the NBA 2010 play-offs as networks. Defining players as nodes and ball movements as links, we analyzed the network properties of degree centrality, clustering, entropy and flow centrality across teams and positions, to characterize the game from a network perspective and to determine whether we can assess differences in team offensive strategy by their network properties. The compiled network structure across teams reflected a fundamental attribute of basketball strategy. They primarily showed a centralized ball distribution pattern with the point guard in a leadership role.

However, individual play-off teams showed variation in their relative involvement of other players/positions in ball distribution, reflected quantitatively by differences in clustering and degree centrality. We also characterized two potential alternate offensive strategies by associated variation in network structure: (1) whether teams consistently moved the ball towards their shooting specialists, measured as “uphill/downhill” flux, and (2) whether they distributed the ball in a way that reduced predictability, measured as team entropy.

These network metrics quantified different aspects of team strategy, with no single metric wholly predictive of success. However, in the context of the 2010 play-offs, the values of clustering (connectedness across players) and network entropy (unpredictability of ball movement) had the most consistent association with team advancement. Our analyses demonstrate the utility of network approaches in quantifying team strategy and show that testable hypotheses can be evaluated using this approach. These analyses also highlight the richness of basketball networks as a dataset for exploring the relationships between network structure and dynamics with team organization and effectiveness.