Production lot sizing with variable production rate and explicit idle capacity cost

This paper develops a model for simultaneously determining the optimal run length and the rate of production for a single item. As opposed to traditional approaches, the item's output rate is treated as a decision variable. It is assumed that the production cost per unit is a quadratic function of the production rate, in an effort to capture the effect of increased unit cost as a result of deviating from the ‚nominal’ rate of output, for which the system was designed. In addition a linear function is incorporated in the proposed model to represent the desirability or undesirability, as the case may be, of unused capacity. The iterative solution procedure developed is illustrated through a numerical example and extensive sensitivity analysis is performed for examining the major tradeoffs involved.