Controllability of Supply Chains, Controlled in Laplace - Transformed Space

摘要

In MRP - DRP logistics an important question is the following: which states of inventories distributed in a global supply chain are feasible? This relates to the concept of controllability where we are concerned: whether or not a control (for instance production level or distribution flow intensity) exists that can cause the state or output of a system to follow some desired paths. The paper gives a positive answer to the question above when certain conditions are satisfied in L_2 space, in general presented in Bogataj (1989). The moment of reflection inspires us to find out that the proper characterisation of state space of MRPJDRP logistic model is the Lebesgue measurable space L_2 ([0,∞),R~m) of square integrablernfunctions). The introduction of such a space is necessary to get a proper mathematical foundation of the MRP-DRP model of logistic chain, because by such an approach the one-to-one correspondence of functions in Laplace transforms is assured.