We discuss computational issues surrounding current research that investigates the relevance of graph centrality metrics to the management of ecological food webs. Ecological food webs can be viewed as directed acyclic graphs. The work uses Markov decision processes to build upon previous research, which utilises Bayesian networks, to model the management of food webs, by including a temporal aspect to the dynamics of the food web. Using dynamic programming we optimally solve the management of an Alaskan food web through time so as to maximise the expected number of species surviving. To generalise our results we investigate policies on generated food webs of varying size. For large food webs the state space is too large for dynamic programming to be computationally feasible and we use heuristic methods to approximate the optimal policy.