Production control in semi-automated systems: Comparison between constant and stochastic speeds

This paper deals with a production system which includes a deterministic assembly line and a supplementary production unit processing, with random disturbances, parts for the line. The decision-maker must determine both the speed to be introduced at each control point and the timing of the next control point, given the actual accumulated production observed at the control point, the deterministic rate of demand of the assembly line and a specified probability that there will be no on-line shortage of parts. This problem does not yet have an optimal solution; however, a subproblem can be formulated in which the speed is given and only the next control point has to be determined. Analytical optimal solutions were found for this subproblem under two extreme assumptions: (1) speed is a random variable that changes at the routine control point and remains constant until the next control point; (2) speed behaves like a Brownian motion, i.e. it changes continuously between two adjacent control points. This paper focuses on the comparison between the solution of the constant and the stochastic assumption for the normal distribution. Practical applications arising from this comparison are also given.