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Networks have been used to model fixed-site security systems and to determine optimal travel routes of thieves or saboteurs. Considered here is the problem of upgrading the security by optimally investing in means to increase the travel time and/or detection probabilities over the arcs of the network. It is shown how to formulate a single linear programming problem to answer the following question. If the cost of increasing travel time is linear for each arc, what is the minimum amount of money one must invest to guarantee that there does not exist a path for thief or saboteur of length less than a fixed time T.

Optimal improvement of networks to nuclear safeguards problems: an alternate view