A net present value approach to safety stocks in a multi-level MRP system

The Laplace transform and input–output analysis have been used for formulating a basic theory for material requirements planning (MRP) in a sequence of recent papers. The transform has been used for describing time developments and lags of the relevant production, demand and inventory variables in a compact way including effects of order flows and lead times. Secondly, the transform has functioned as a generating function, and thirdly, the transform has been applied for assessing cash flows adopting the net present value (NPV) principle (or the annuity stream, which is a variation of NPV). Input–output analysis, in particular, the input matrix, has been applied for describing multi-level product structures. This has made the analysis compact and distinct. In the current paper the analysis of determining optimal safety stock levels in MRP systems is extended from a single-level model recently investigated to a multi-level system assuming production to take place according to a lot-for-lot (L4L) policy when applying the NPV as the objective criterion and disregarding the opportunities for joint set-ups. Relaxing the L4L assumption is also discussed.