This paper presents a fast branch and bound algorithm for solving flow shop scheduling problem when operation processing times are themselves decision variables. Models of operations are assumed to be duration versus resource convex functions. The problem under consideration is a generalization of the classical flow shop problem. Due to the presented elimination properties, the search tree of the branch and bound procedure is strongly restricted. To obtain quickly a good upper bound some special expressions evaluating all the descendants, which can be received from a current solution, are employed. Computational results are also included.