Optimal production cycles, procurement schedules, and joint investment in an imperfect production system

In this paper, we consider the simultaneous determination of production cycles for the end product, procurement schedules for its input materials, and joint investment in setup reduction and process quality improvement for a production system with imperfect production processes. In the analysis, we assume that setup reduction and process quality are functions of capital expenditure and that the input materials, which are purchased from outside suppliers, are gradually converted into the product during manufacture. We derive a solution procedure to find the optimal production cycle time, procurement schedules, joint investment, and the corresponding total relevant cost. We present numerial examples to illustrate the procedure and to delineate the relationships among production cycle times for the end product, the procurement schedules for its input materials, and setup reduction and quality improvement.