We present a deterministic model that specifies lane direction in a multi-laned bridge that has a movable barrier that divides the two directions of traffic flow, in order to reduce congestion. A probabilistic dynamic programming formulation for a stochastic extension of the model is also presented. Analysis of the special structure of the dynamic programming formulation provides new insights into important aspects of certain traffic planning problems and represents a useful addition to the traffic network planner's toolkit. A case study involving the lane direction management of an actual bridge is also provided.