Groupe d’études et de recherche en analyse des décisions

G-91-29

Criteria for the Ergodicity of Hedging Point Control Policies in Single Part Manufacturing Systems

The Markov renewal viewpoint of single part manufacturing systems under hedging point control policies, subjected to a constant demand for parts rate, is used to derive sufficient criteria to guarantee ergodicity of the resulting inventory process. The criteria are simple and directly verifiable from an analysis of the continuous time Markov chain characterizing the dynamics of the discrete manufacturing system production state. One of the criteria, demand feasibility in the long run, is very intuitive and was conjectured earlier by other authors. Finally, in the process of proving our main results, we derive a recursive linear vector differential equation which can be generalized to compute any order moments of sojourn times in the regions comprised between successive hedging points in the inventory space.

, 21 pages