Further theoretical considerations on the relationship between MRP, input-output analysis and multi-echelon inventory systems

In recent papers relationships between input-output analysis and material requirements planning have been studied. A generalized input-matrix has been designed to incorporate requirements as well as production lead times by means of z-transform methodology in a discrete time model. In this paper, previous findings are generalized in different directions. On the one hand, the theory is extended to continuous time using the Laplace transform, which enables it to incorporate the possibility of batch production at finite production rates. Also conditions for the detailed coordination problem are investigated in relation to the multi-echelon lot-sizing problem.