A mixed integer program for cyclic scheduling of flexible flow lines

A new mixed integer programming formulation is presented for cyclic scheduling in flow lines with parallel machines and finite in-process buffers, where a Minimal Part Set (MPS) in the same proportion as the overall production target is repetitively scheduled. The cycle of parts in an MPS is not determined a priori, but is obtained along with the optimal schedule for all parts. In addition to the cyclic scheduling, a cyclic-batch scheduling mode is introduced, where within the MPS the parts of one type are processed consecutively. Numerical examples are included and some results of computational experiments are reported.

A Method for the Prediction of Design Space for a Bend Stiffener Cone

Bend stiffeners are commonly used to protect flexible flow-lines and dynamic risers from over-bending, especially in the areas where they interface with fixed or floating structures. Sizing of bend stiffeners and confirmation of their feasibility is an important step in the design of the complete riser system. The objective of this paper is to develop a method for the prediction of the design space for the bend stiffener cone, which is defined in terms of its length and diameter at the base. The analysis method is based on the analytical formulation for an elastic cone consisting of the main pipe and the hollow bend stiffener. A “marching” technique is developed which is based on combining linear solutions for several conical segments. The analysis method requires a small number of segments, and is efficient in dealing with large deflections. It is shown that even a linear solution alone for the bend stiffener cone provides good accuracy for moderate deviation angles. Criteria for setting the design space boundaries for the bend stiffener cone are discussed. The selection of load cases from the tension-angle curve is discussed and its effect on the shape of the design space is demonstrated. The method is illustrated by developing a design space for the bend stiffener of a typical flexible riser connected to the turret of an FPSO.