Feeding parts with random production speed to an assembly line

The problem of production control with disturbances for processing assembly line parts is introduced. Certain identical parts can be processed with various possible speeds given as stochastic processes or random variables. Given the assembly line with deterministic rate of demand for the parts, the planning horizon and the confidence probability not to be in shortage, we have to determine the next control point and introduce proper production speeds while controlling the parts' processing. The objective function is to minimize the average actual amount of parts processed and the number of control points. A stochastic optimization formulation is presented, followed by a heuristic solution, and a numerical example is given.