The product cycling problem under increasing yield rates

We investigate the product cycling problem (also known as the common cycle scheduling problem) when there are economies of scale due to increasing yield rates. Increasing yield rates are characteristic of production processes in which the percentage of acceptable parts increases with the duration of the production run, usually owing to adjustments made during the initial portion of the production run. We develop a solution procedure that is optimal for a wide range of production cost functions under very mild conditions. We then compare optimal solutions with those obtained from the commonly used 'fixed-plus-linear' approximation of costs. Computational results suggest that the 'fixed-plus-linear' approximation generally performs well, but may result in substantial errors under certain extreme conditions.