A net present value approach to safety stocks in planned production

In a number of recent papers, the Laplace transform together with input-output analysis has been applied for the sake of formulating a basic theoretical description of material requirements planning (MRP). The transform approach has had a threefold use; on the one hand, it has been useful for describing time developments of the relevant production, demand and inventory properties in a compact way including effects of order flows and lead times. Second, the transform also captures stochastic properties by functioning as a generating function, and, third, the transform is easily applied for assessing the resulting cash flows when adopting the net present value (NPV) principle (or the annuity stream principle which is a variation of NPV). Input–output analysis, in particular the input matrix, is applied for describing multi-level product structures, which has made the analysis concise and distinct. In this paper we extend the analysis of determining optimal safety stock levels for a sequence of planned production decisions (a one-level MRP system) by applying the annuity stream as a criterion to a simple model instead of the average cost approach previously used.