Estimating the reduction in labor hours due to a new technology under uncertain demand

When investing in a new machine one must estimate the reduced labor costs. In the past, this was usually done in a deterministic way, assuming that we have accurate (point) estimation of demand rates and the reduction in labor costs is proportional to the reduction in labor hours. However, if demand rates of products are known probabilistically the expected reduction in labor hours follows a probability distribution. This distribution (not just the mean value) is important because (1) it shows the effect of the uncertainty in demand on estimating the reduction in labor hours, and (2) it allows better estimation of labor cost savings when labor costs are not proportional to labor hours. Using the distribution of product demand rates this paper presents a procedure for estimating the distribution of reduction in labor hours obtained from a new machine.