The Acquisition of Automation Subject to Diminishing Returns

In this paper, it is assumed that the purchase of automation has the effect of reducing the per unit production and in-process inventory costs. The optimal dynamic mix of automation and manual output is derived to minimize the cost incurred over the planning horizon due to (1) deviating from the future goal levels of output, (2) production, (3) inventory, (4) changing the level of manual output, and (5) acquiring automation. The cost of purchasing automation and the effectiveness of automation on reducing the per unit. production and in-process inventory costs are expressed as functions of time to include the impact of learning or anticipated technological advancement. Furthermore, the effectiveness of automation on reducing the per unit production and in-process inventory costs is assumed to decrease as the level of automation held by the organization increases due to diminishing returns. We show that it is rarely optimal to increase automation without simultaneously modifying the level of manual output. In addition, a numerical solution algorithm is presented to compute the optimal times and levels of changes in automation and manual output.