The objective of this thesis to Provide a better insight into the effect of the amount of in-process storage has on the efficiency of production line with variable operation times. It is assumed that the material enters the line at the first work station and is then processed progressively through the line until it exits at the last work station, a finite amount of in-process storage is provided before all but the first work station of the line and the operation time of the work stations are statistically independent and follow exponential distribution. Under the above assumption, optimum allocation model is developed and following two approaches are used : 1) Given the available storage capacity, optimum allocation which minimizes the number of items in the line. 2) Given the available storage capacity, optimum allocation which. maximizes the utilization factor of the line. In a balanced three stage line, the production line efficiency is maximized under both categories when the second in-process storage is larger than the first.